charge exchange collisions and spectroscopy of metastable

Charge Exchange Collisions andSpectroscopy of Metastable

Helium-like Ions

Naoki Numadate

Atomic and Molecular Physics LaboratoryDepartment of Physics

Tokyo Metropolitan University

February 27, 2019

首都大学東京博士（理学）学位論文（課程博士）

論文名

準安定ヘリウム様イオンの電荷交換衝突と分光実験

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TITLE：

Charge Exchange Collisions and Spectroscopy

of Metastable Helium-like Ions

AUTHOR：

Naoki Numadate

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Abstract

It is well known that part of soft X-ray background emission stems fromcharge exchange collisions between solar wind ions and neutrals in the helio-sphere, and this phenomenon is called Solar Wind Charge eXchange (SWCX).The SWCX emission has attracted much attention, because it appears in softX-ray spectra obtained by observatory satellites as foreground emission whenastronomical objects are observed, and can act as a new probe of low den-sity neutrals in the solar system. According to observations by the Suzakusatellite, the forbidden 1s2 1S0–1s2s 3S1 transition in metastable He-like O6+

ions produced by charge exchange is one of main features in the SWCX. Inorder to analyze the observed spectra and to construct a model of the softX-ray emission, absolute values of emission cross sections are required byastrophysicists, but the forbidden transition following the SWCX had notbeen observed in ground based experiments.

Moreover, K-shell emissions from inner-shell excited Li-like ions have agreat potential for astrophysical applications such as precise diagnostics ofastrophysical plasma and dense planetary atmosphere. Whereas numerouspapers about the Auger electron spectroscopy of the inner-shell excited ionshave been published, papers about the X-ray emission spectroscopy of suchions are very few, because radiative rates are much smaller than Auger ratesfor inner-shell excited light elements.

In these contexts, we aimed to investigate charge exchange collisions andspectroscopy of metastable He-like ions. In particularly, we developed an iontrap system for externally injected metastable ions, conducted a laboratoryobservation of the forbidden transition following the SWCX by using theion trap. We also observed soft X-ray emissions from the inner-shell excitedLi-like ions produced by charge exchange collisions of metastable He-like ions.

1

2

Development of a Kingdon ions trap

We have developed a Kingdon ion trap in order to observe the X-ray forbid-den transitions following charge exchange in ion beam experiments. Exter-nally injected Arq+(q = 5–7) with kinetic energies of 6q keV were successfullytrapped in the ion trap. The energy distribution of trapped ions was deter-mined by numerical simulations. As a performance test of the instrument,we measured trapping lifetimes of Arq+(q = 5–7) under a constant numberdensity of H2. Moreover, we determined the charge transfer cross sections ofArq+(q = 5, 6)–H2 collision systems at binary collision energies of a few eV.It was confirmed that the present data is consistent with previous data andthe values estimated by some scaling formula.

Laboratory observation of forbidden transition following the SWCX

The dominant electron capture level in collisions of O7+ ions with He isa principal quantum number n = 4 according to the classical over barriermodel and the two-center atomic orbital close coupling method. After thecharge exchange, populations of the metastable 1s2s 3S states of He-like O6+

ions become large due to cascade transitions from the higher excited states.Therefore, the long-lived forbidden transition to the 1s2 1S0 ground state isone of main features observed in the charge exchange spectra.

By using a spectroscopic beamline at Tokyo Metropolitan University, wehave reproduced the SWCX between H-like O7+ ions with He gas at colli-sion energies of 42 keV and also observed soft X-ray emission form trappedmetastable He-like O6+ ions produced by single electron capture. The mea-sured soft X-ray spectrum had a peak at 560 eV which corresponds to theenergy of the forbidden 1s2 1S0–1s2s 3S1 transition in the O6+ ion Moreover, areasonable energy difference of 10 eV between peak positions of the observedforbidden and resonance lines was found, which ensured that we succeededin observing the forbidden transition of the metastable O6+ ions.

Spectroscopy of inner-shell excited Li-like ions

We conducted collision experiments of metastable He-like C, N, and O ionswith He, Ne, Ar, Kr, Xe, N2, O2 and CO2 targets in order to investigate ra-diative transitions of inner-shell excited Li-like ions and target dependence ofemission spectra. In this experiment, we took advantage of the fact that anHe-like ions produced by an ECRIS include metastable 1s2s states at least a

3

few percent of the total beam. The inner-shell excited Li-like ions were pro-duced by electron capture and transfer-excitation between He-like ions in the1s2s 3S1 state and neutral atoms and molecules. Most of observed soft X-rayemissions are identified as the resonance and inter-combination 1s–2p, 3p,4p transitions of the 1s2s(3S)nl and 1s2p(1,3P)nl states. The present spectrawere clearly different from those measured in previous experiments, in termsof the number of the observed lines and line intensity ratios in spite of thesame collision systems and collision energies being used. Furthermore, theemission spectra depend on the choice of target, and significant differenceswere observed especially between the spectra on the Xe and O2 gas targetsregardless of their having similar ionization potentials. With rare gas tar-gets, spectra show characteristic lines and their intensities increase with theincreasing atomic number of the targets. These new lines are identified astwo-electron one-photon (TEOP) transitions from highly excited 1s2s(3S)4lstates. This is the first observation of the discrete TEOP lines followingcharge exchange collisions of C4+ and N5+ ions. In the oxygen spectra, aline with the same target dependence was observed, but it is due to theone-electron one-photon transitions.

Contents

1 Introduction 71.1 Solar Wind Charge eXchange . . . . . . . . . . . . . . . . . . 7

1.1.1 Solar Wind . . . . . . . . . . . . . . . . . . . . . . . . 81.2 Charge eXchange outside Solar System . . . . . . . . . . . . . 91.3 Inner-Shell Excited Li-like Ions . . . . . . . . . . . . . . . . . 91.4 Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4.1 Ground-Based Experiments of SWCX . . . . . . . . . . 111.4.2 Spectroscopy of Inner-Shell Excited Li-like Ions . . . . 13

1.5 Purpose of This Research . . . . . . . . . . . . . . . . . . . . 13

2 Principles 152.1 Slow Collisions of Multiply Charged Ions . . . . . . . . . . . . 15

2.1.1 Collision Processes . . . . . . . . . . . . . . . . . . . . 152.1.2 Classical Orbiting by Polarization Forces . . . . . . . . 162.1.3 Reaction Rate Coefficients . . . . . . . . . . . . . . . . 18

2.2 Charge eXchange . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1 Classical Over-Barrier Model . . . . . . . . . . . . . . 202.2.2 Scaling Formulae for CX Cross Sections . . . . . . . . 27

2.3 Optical Transitions . . . . . . . . . . . . . . . . . . . . . . . . 292.3.1 Einstein A Coefficients . . . . . . . . . . . . . . . . . . 292.3.2 Electric Dipole (E1) Transitions . . . . . . . . . . . . . 302.3.3 Magnetic Dipole (M1) Transitions . . . . . . . . . . . . 302.3.4 Selection Rule for E1 and M1 Transitions . . . . . . . . 322.3.5 Cascade Transitions . . . . . . . . . . . . . . . . . . . . 332.3.6 Yrast Transitions . . . . . . . . . . . . . . . . . . . . . 33

2.4 Theoretical Calculation . . . . . . . . . . . . . . . . . . . . . . 342.4.1 Hartree-Fock Method . . . . . . . . . . . . . . . . . . . 342.4.2 Cowan’s Suite of Atomic Structure Codes . . . . . . . 36

4

CONTENTS 5

3 Experimental apparatus 373.1 Electron Cyclotron Resonance Ion Source . . . . . . . . . . . . 373.2 Kingdon Ion Trap . . . . . . . . . . . . . . . . . . . . . . . . 423.3 Ion Trapping Experiments . . . . . . . . . . . . . . . . . . . . 46

3.3.1 ECRIS at Sophia Univ. . . . . . . . . . . . . . . . . . . 463.3.2 Production of Multiply Charged Argon and Oxygen Ions 463.3.3 Beamline at Sophia Univ. . . . . . . . . . . . . . . . . 473.3.4 Kingdon Ion Trap . . . . . . . . . . . . . . . . . . . . . 483.3.5 Time-of-Flight Mass Spectrometer . . . . . . . . . . . . 51

3.4 Forbidden Transition Measurements . . . . . . . . . . . . . . . 543.4.1 TMU-ECRIS . . . . . . . . . . . . . . . . . . . . . . . 543.4.2 Production of Multiply Charged Oxygen Ions . . . . . 553.4.3 Beamline at TMU . . . . . . . . . . . . . . . . . . . . 553.4.4 Silicon Drift Detector . . . . . . . . . . . . . . . . . . . 57

3.5 Spectroscopy of Inner-Shell Excited Li-like C, N and O Ions . 593.5.1 Production of Inner-Shell Excited Li-like Ions . . . . . 593.5.2 Spectroscopic Beamline at TMU . . . . . . . . . . . . . 593.5.3 Grazing-Incidence Spectrometer . . . . . . . . . . . . . 59

4 Ion Trapping Experiments 634.1 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . 634.2 Velocity Distribution of Trapped Ions . . . . . . . . . . . . . . 68

4.2.1 Ideal Logarithmic Potential . . . . . . . . . . . . . . . 684.2.2 Realistic Potential . . . . . . . . . . . . . . . . . . . . 68

4.3 Trapping Externally Injected Argon Ions . . . . . . . . . . . . 734.4 TOF Measurements . . . . . . . . . . . . . . . . . . . . . . . . 754.5 Trapping Lifetime of Externally Injected O6+ Ions . . . . . . . 784.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5 Forbidden Transition Measurements 815.1 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . 81

5.1.1 Energy Calibration of SDD . . . . . . . . . . . . . . . 825.2 1s2–1s2s 3S (M1) Transition Measurements . . . . . . . . . . . 835.3 1s2–1s2p 1,3P (E1) Transition Measurement . . . . . . . . . . . 845.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

CONTENTS 6

6 Spectroscopy of Inner-Shell Excited Li-like Ions 886.1 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . 88

6.1.1 Soft X-ray Emission Spectra . . . . . . . . . . . . . . . 896.1.2 Second Order Diffraction . . . . . . . . . . . . . . . . . 896.1.3 Wavelength Calibration . . . . . . . . . . . . . . . . . 90

6.2 Collision Processes . . . . . . . . . . . . . . . . . . . . . . . . 936.3 Radiative Decay Processes . . . . . . . . . . . . . . . . . . . . 936.4 Soft X-ray Spectra for Each Collision System . . . . . . . . . . 986.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7 Summary 109

Chapter 1

Introduction

1.1 Solar Wind Charge eXchange

The Roentgen satellite, ROSAT, which was launched in 1990 as an X-rayobservatory satellite, conducted the all-sky survey of soft X-ray backgroundemission. In 1994, soft X-ray emission whose intensity varied in cycles ofseveral days was observed during the all-sky survey [1]. This emission camefrom areas where there was no particular hot object, so it remained mys-terious. It had known that the galactic discs and halos could not be theorigin of the soft X-rays with such short time intensity fluctuation. There-fore it had been assumed that the solar system was attributed to the softX-ray enhancement but its origin was not identified at the time. In 1996,the ROSAT also observed the soft X-ray emission from Comet C/Hyakutake1996 B2 approaching to Earth [2]. This was also mysterious and surprising,because the comet which was composed mainly of ice and dust was too coldto emit soft X-rays. Following this initial observation, soft X-ray emissionwas subsequently observed from various comets. According to Cravens’ sug-gestion [3], it has been recognized that part of the soft X-ray backgroundemission stems from charge exchange collisions between solar wind ions andneutrals in the heliosphere, and this phenomenon is called Solar Wind ChargeeXchange (SWCX). During the all-sky survey, intensity fluctuation of solarwind proton observed by the ACE satellite corresponded to that of the softX-rays, which supports the SWCX [4, 5]. The Suzaku satellite installing ahigh resolution detector had also observed the SWCX emission, whose oper-ation was terminated in 2015. According to the observations, the forbidden

7

Chapter 1. Introduction 8

1s2 1S0–1s2s 3S1 transition from metastable O6+ ions produced by chargeexchange was one of main features in the SWCX [6, 7]. Forbidden, reso-nance and inter-combination transitions following charge exchange collisionsof H-like ions with neutrals can be written as

H-like P (1s 2S) + T → He-like P (1snl 1,3L) + T+

→ He-like P (1s2s 3S) + hν1

→ He-like P (1s2 1S) + hν2

or


→ He-like P (1snp 1,3P) + hν3

→ He-like P (1s2 1S) + hν4

where P and T mean projectile ion and neutral targets, respectively. TheSWCX emission has attracted much attention, because it appears in soft X-ray spectra obtained by observatory satellites as foreground emission whenastronomical objects are observed, and can act as a new probe of neutraldensity measurements in the solar system.

1.1.1 Solar Wind

The solar wind is a fast and thin flow of charged particles. This plasmais almost completely ionized and electrically neutral as a whole. The maincomposition of the solar wind is shown below.

Negative charge Positive chargee− H+, He2+, Cq+, Nq+, Oq+, Neq+, Mgq+, Siq+, Feq+...

Typical charge states of the positive ions correspond to those of H-like orHe-like ions. H+ accounts for 95% of the positive ions, He2+ for 4% and therest is carbon, nitrogen, oxygen, neon, magnesium, silicon, iron ions and soon [8]. Near the earth, solar wind particle density is approximately 10 cm−3

and temperature is approximately 105 K. The solar wind can be classified asfast and slow components and each has velocity of about 700–800 km/s and300–400 km/s, respectively. The solar wind ions come towards the earth atthe incident angle of about 45◦ to the Sun-Earth line due to the geomagneticfield.


1.2 Charge eXchange outside Solar System

Recently, X-ray emission was observed from some astrophysical objects out-side the solar system such as large supernova remnants (SNRs) of the Vela [9],the Puppis A [10] and the Cygnus Loop [11]. It has considered that RNSsare hot plasmas and emit X-ray by thermal bremsstrahlung and non-thermalsynchrotron radiation. These SNRs have been observed by some X-ray obser-vatory satellites and characteristic soft X-ray line structures which could notbe explain with thermal radiation and synchrotron radiation were discovered.This was due to charge exchange reactions because observed forbidden lineswere stronger than resonant lines. The enhancement of the forbidden lines isone of features of the charge exchange. X-ray emission following the chargeexchange reactions was also observed from a starburst galaxy, Messier 82 [12].The observed lines mainly consisted of inter-combination and forbidden lineswhich can not result from thermal excitation.

In order to analyze the observed spectra and to construct a model of thesoft X-ray emission, absolute values of emission cross sections are requiredby astrophysicists [13, 14].

1.3 Inner-Shell Excited Li-like Ions

An inner-shell excited state means an excited state which has inner-shellvacancy. This state has an potential above an ionization energy and henceradiative and Auger transitions are competitive decay processes of inner-shellexcited states. These two processes have attracted much attention becausephoton and electron emissions from this state are of great importance fordiagnostics of fusion and astrophysical plasmas [15], investigations of decaydynamics of molecules [16] and radiation induced damage on DNA [17]. Fur-thermore, multi-electron correlation effects such as post-collision interactionshave been studied in Auger electron spectroscopy [18, 19]. Whereas numer-ous papers about the Auger electron spectroscopy of the inner-shell excitedatomic and molecular ions have been published [20, 21, 22, 23, 24], papersabout the X-ray emission spectroscopy of such ions are very few, because ra-diative rates are much smaller than Auger rates for inner-shell excited lightelements [25]. These states of multiply charged ions are closely related toastrophysics, and we focus attention on application to diagnostics of astro-physical plasma in this thesis.


It is well known that part of K-shell emission observed by observationsatellites are caused by charge exchange reactions between solar wind H-likeions and neutrals in the heliosphere as described in Section 1.1. After thereactions, metastable He-like ions (1s2s 3S1) are mainly produced. If thesequential charge exchange occurs before they de-excite, inner-shell excitedLi-like ions can be produced as below.


→ He-like P (1s2s 3S) + hν (1.1)

He-like P (1s2s 3S) + T′ → Li-like P (1s2s 3S nl) + T′+

→ Li-like P (1s2s 3S n’p) + hν ′

→ Li-like P (1s22s 2S) + hν ′′ (1.2)

X-ray emissions following this sequence of charge exchange collisions canoccur in the regions with high particle gas density such as comets, molecularclouds and exospheres of planets. Soft X-ray derived from the SWCX wasactually observed not only in comets but also in Mars and Venus [26, 27].Furthermore, it has known that Jupiter’s X-ray aurora is strongly related tothe solar wind [28, 29]. These X-ray emissions following the SWCX can bea new tool for diagnostics of dense planetary atmosphere.

In addition to the above, the radiative decay processes of the inner-shellexcited Li-like ions are important for diagnostic of photo-ionized plasmassuch as active galactic nuclei and planetary nebulae. Soft X-ray emitted fromtheir own hot cores can produce inner-shell excited Li-like ions on the outside.Ratio of resonance, intercombination and forbidden lines of He-like ions area great tool for plasma diagnostic [30]. However, Wang et al. proposedthat satellite lines from Li-like ions contribute temperature diagnostics withthe He-like triplet lines in photo-ionized plasma [31]. Kα and Kβ emissionsfrom inner-shell excited multiply charged heavy ions were also observed inthe measurement of Tycho’s supernova remnant (SNR) [32]. The atomicinner-shell processes in SNRs make it difficult to analyze X-ray spectra, butinformation about physical states and evolutions of the observed SNRs can beextracted from them [33, 34]. K-shell emissions from the inner-shell excitedLi-like ions have a great potential for the astrophysical analysis.

As described before, absolute values of emission cross sections are neededin order to extract quantitative information from the observed spectra, but


it is significantly difficult to measure them experimentally. Therefore, the-oretical calculations such as n, l state-selective charge transfer cross sec-tions and cascade calculations including both Auger and radiative transi-tions, are required for X-ray astrophysics. Recently, some groups have con-ducted slow He-like ion-neutral collision spectroscopy and related calcula-tions [35, 36, 37, 38]. They have focused on only ground states as projectileions but metastable ion-neutral collisions are also important. Experimentaldata will be useful for verifying the validity of the theoretical calculations.

1.4 Previous Studies

1.4.1 Ground-Based Experiments of SWCX

Laboratory studies of the SWCX started around 2000, which were mainlysoft X-ray spectroscopy and cross section measurements.

Jet Propulsion Laboratory

Greenwood et al. performed collision experiments with an electron cyclotronresonance ion source (ECRIS) and gas cell. They measured charge ex-change and X-ray emission cross sections in collisions of solar wind ionswith cometary neutrals by using a Ge solid-state detector with a Be win-dow [39, 40]. However, they have not measured absolute values of emissioncross sections yet.

Kernfysisch Versneller Instituut Groningen

Bodewits et al. conducted collision experiments with an ECRIS and a su-personic neutral gas jet. They measured high resolution VUV spectra witha grazing incidence spectrometer in collisions of He, C and O ions with H2O,CO2, CO and CH4 targets [41].

Oak Ridge National Laboratory

Draganic et al. carried out collision experiments of bare and H-like C and Oions with H atom target by using a merged-beams technique [42, 43]. Thismethod enables very low velocity collision experiments by changing relativevelocity of the ion and neutral target beams. Moreover, they measured high


resolution soft X-ray spectra with a micro calorimeter in gas target experi-ments using a gas cell [44]. In the SWCX, long-lived forbidden transitionsfollowing charge exchange are more important, but only resonant transitionswith short lifetimes were subject to their studies.

Lawrence Livermore National Laboratory

Beiersdorfer et al. conducted charge exchange spectroscopy with an electronbeam ion trap (EBIT). They measured high resolution soft X-ray spectra incollisions of C, N and O ions with CO2 and CH4 targets by using a microcalorimeter [45]. The EBIT makes it possible to observe long-lived forbiddentransitions following charge exchange because it can produce and confinemultiply charged ions for a long time. However, collision energy in the EBITis much lower than that in the SWCX, and hence it is difficult to make useof the obtained data for analysis of astronomical observations.

Tokyo Metropolitan University (TMU)

In 2011, atomic and molecular physics lab. in TMU started a project of lab-oratory observations of forbidden transitions in the SWCX. At first, resonanttransitions were observed by using an ECRIS. Kanda et al. measured soft X-ray spectra in collisions of H-like N and O ions with He target with a window-less Si(Li) detector with an energy resolution of 160 eV at 5.9 keV [46]. Theobserved dominant emission lines corresponded to the 1s2–1s2p transitionsfrom He-like ions produced by single electron capture. According to the TC-AOCC (two-center atomic orbital close coupling) method, the direct capturecross section into the 2p states were much smaller than those into the n = 3and 4 states. This could be understood by considering cascade effects afterthe charge exchange. In this measurement, the target gases were ejected froma multi-capillary plate as an effusive beam, but this method had a problemthat the target gas density could not be measured directly.

In order to measure absolute values of cross sections, Ishida et al. adopteda gas cell system instead of the gas jet system and made it possible to measureabsolute pressure of the target gas by installing a capacitance manometer.A window-less silicon drift detector with an energy resolution of 135 eV at5.9 keV was also installed to obtain high resolution spectra. Shimaya et al.measured soft X-ray spectra in collisions of bare O ions with He target [47].The observed dominant emission line corresponded to the 1s–2p transitions


from H-like O ions and other emission lines corresponded to the 1s–3p, 1s–4pand 1s–5p transitions.

1.4.2 Spectroscopy of Inner-Shell Excited Li-like Ions

Still now, many papers about Auger electron spectroscopy of the inner-shellexcited Li-like light ions have been published, but very few about soft X-rayspectroscopy. In this section, some of them are briefly introduced here.

Centre d’Etudes Nuclbaires de Grenoble

Druetta et al. measured VUV spectra in collisions of metastable He-like Cand N ions with H2 and He targets [48]. They produced the metastable ionsby an ECRIS and single electron capture of H-like ions with the neutrals andobserved radiative transitions from the inner-shell excited Li-like ions witha crystal spectrometer. They also measured metastable beam fractions andthe absolute values of emission cross sections of the observed lines.

Suraud et al. observed soft X-ray following the 1s22s–1s2snl resonanttransitions from inner-shell excited Li-like C, N and O ions [49, 50, 51]. TheLi-like ions were produced by single electron capture and transfer-excitationin collisions of metastable He-like ions with H2 and He targets. The experi-ments were performed by using an ECRIS and gas cell and emission spectrawere measured with a crystal spectrometer.

Heidelberg

Steinbrugge et al. measured absolute radiative and Auger decay rates ofK-shell-vacancy states in multiply charged Fe ions by simultaneous measure-ments of photoions and X-ray fluorescence [52, 53]. The multiply chargedFe ions were produced with an EBIT and then inner-shell excited stateswere produced by K-shell photoionization with synchrotron radiation. Thephotoions were detected by using a Wien type velocity filter and positionsensitive ion detector and X-ray fluorescence was detected by Ge detectors.

1.5 Purpose of This Research

Absolute values of emission or charge transfer cross sections are required forquantitative analysis of X-ray spectra observed with observatory satellites.


The forbidden 1s2 1S0–1s2s 3S1 transitions from O6+ ions is one of the maintransitions following the SWCX, but had not been measured yet in the labo-ratory. This is because that the solar wind ions travel several hundred metersduring the forbidden transitions due to their velocities of 300–800 km/s andtransition lifetimes of milliseconds. However, this background motivated usto try the first laboratory observation of the forbidden transitions followingthe SWCX. Furthermore, the radiative transitions from the inner-shell ex-cited light ions are also important for diagnostic of the astrophysical plasmas,but very few studies have been conducted. Therefore, we also performed softX-ray spectroscopy of the inner-shell excited Li-like C, N and O ions pro-duced by electron capture and transfer-excitation in collisions of metastableHe-like ions with neutrals.

In summary, three contents below are mainly discussed in this thesis.

(i) Development of an electrostatic ion trap and its performance test withAr5,6+ and O6+ ions produced with an ECRIS

(ii) Laboratory observation of the forbidden 1s2 1S0–1s2s 3S1 transitionsfrom O6+ ions produced in the SWCX by using the ion trap

(iii) Measurements and line identifications of soft X-ray spectra of the inner-shell excited Li-like C, N and O ions produced by charge exchangecollisions of metastable He-like C, N and O ions with several rare gasand molecular targets.

Chapter 2

Principles

In this chapter, basic principles and theoretical models associated with thepresent study are given. Mechanism and models in collisions of multiplycharged ions, and optical transitions from excited ions are explained.

2.1 Slow Collisions of Multiply Charged Ions

Multiply charged ions mean ions with electric charge of two or more, and havevery high internal energy due to coulomb potential and likely to interact withmatters. The internal energy of a multiply charged ion is a sum of ionizationpotentials from a neutral to the charge state.

2.1.1 Collision Processes

The following four inelastic processes can be considered in collisions of mul-tiply charged ions with neutral targets.

Xq++Y −→

X(q−r)+ + Y r+ : Charge exchangeXq+ + Y r+ + re− : Ionization of targetX(q+r)+ + Y + re− : Ionization of projectile ionXq+ + Y ∗ : Excitation of target

Cross sections of each process above depend on relative velocity betweena projectile ion and target. The collision velocity is classified as “fast” or“slow”, which depends on whether the relative velocity is higher than electronorbital velocity in a hydrogen atom in a Bohr’s model, namely 1 a.u. ('

15

Chapter 2. Principles 16

2.19× 106 m/s) or not. In the case of collisions between projectile ions andtargets with very high velocity, charge exchange is unlikely to occur andionizations of the ion or target are dominant. It is because that the ionquickly move away from a target before an electron in the target is capturedinto an electron orbital in the ion. Contrary to this, when the ion slowlyapproaches the target, the two particles become a quasi-molecule. Hence,an electron in the target is likely to transfer to the ion and charge exchangeis dominant. In our experiments, “slow” collisions of multiply charged ionswith atoms or molecules have been performed, which is dominated by chargeexchange.

2.1.2 Classical Orbiting by Polarization Forces

Atomic and molecular targets are polarized by coulomb fields produced byprojectile ions in very “slow” collisions. An trajectory of the projectile ionis bent due to the attractive polarization forces between the ion and target(Fig. 2.1). An effective potential Veff between them is shown as below,

Veff =b2

r2Ecm −αq2

2r4 (2.1)

where b, r, Ecm and α mean impact parameter, internuclear distance betweenthe ion and target, collision energy in the center-of-mass system and polar-izability of the target, respectively. In the case that the impact parameteris much smaller than borb (b3 in Fig. 2.1), a local maximum of the effectivepotential is smaller than an energy of the projectile ion and the ion moves tothe collision center through a spiral path. When the impact parameter borb

is adjusted so as to get the effective potential maximum, Eeff = Ecm and ∂Veff/∂ R = 0 are given. From these, we obtain relation between borb and rorb

as below.

borb =√

2rorb =

(2αq2

Ecm

) 14

(2.2)

A cross section for such collision is described as below.

σL = πb2orb = πq

(2α

Ecm

) 12

(2.3)


This cross section of σL is inversely proportional to collision velocity, and itis well known as the Langevin cross section or orbiting cross section. Theorbiting radius of rorb increases as collision energy decreases. When thecollision energy is very low, the orbiting radius of rorb becomes bigger thanreaction region between the ion and target. Hence, a cross section for suchreaction is approximated as below,

σ = 2π

∫ borb

0

P (v, b) b db ≈ 2Pπ

∫ borb

0

b db = PσL (2.4)

where P is an average of reaction probabilities P which is a function of vand b. This indicates that the Langevin cross section gives an upper limit ofthe reaction cross section. The product of the cross section σ and velocity vis defined as a reaction rate constant k, which is independent of the collisionvelocity and temperature. The rate constant measured in slow collisions isapproximately constant, but in fast collisions, it practically depends on thecollision velocity and temperature. In the b > borb range, relation of impactparameter b1 and closest internuclear distance r1 is given as below.

b1 = r1

(1 +

αq2

2r41Ecm

) 12

= r1

(1 +

r4orb

r41

) 12

(2.5)

A ring region produced by two circles with radius of impact parameters of b1

and b2 in Fig. 2.1 is smaller than that produced by two circles with radius ofinternuclear distances of r1 and r2. This impact parameter ring area increasesas the collision energy decreases.

π(b21 − b2

2) = π

{r2

1

(1 +

r4orb

r41

)− r2

2

(1 +

r4orb

r42

)}= π(r2

1 − r22)

(1− r4

orb

r21r

22

)(2.6)

From this equation, it is considered that an energy dependence of the reac-tion cross section changes significantly because of a relationship between theinteraction region and orbiting radius. In fact, it is well known that chargeexchange reactions occur state-selectively at a specific internuclear distancein collisions of multiply charged ions with neutrals.


Figure 2.1: Impact parameters and orbiting trajectories.

2.1.3 Reaction Rate Coefficients

A + BC→ AB + C (2.7)

In a reaction above, a reaction rate R and reaction coefficient k are definedas below.

R = −d[A]

dt= − [BC]

dt(2.8)

R = k[A][BC] (2.9)

[A] and [BC] mean each particle density cm−3. Reaction rate means thenumber of collisions between A and BC per unit volume and time. Therefore,collision cross section σ can be described as below,

R =< σv > nAnBC (2.10)

where nA, nBC and v indicate particle densities of A and BC and relativevelocity of A with respect to BC, respectively. By comparing this to Eq. (2.9),the following can be deduced.

k =< σv > (2.11)

Denoting distribution function of the relative velocity as f(v), Eq. (2.11) is


given as below.

k =< σv >=

∫ ∞0

σ(v)vf(v)dv∫ ∞0

f(v)dv

(2.12)

The following shows normalized Maxwell-Boltzmann distribution at a tem-perature of T .

f(v)dv = 4πv2

(µ

2πkBT

) 32

exp

(− µv2

2kBT

)dv (2.13)

Therefore, reaction rate constants can be written as below.

k(T ) =

∫σ(v)vf(v)dv (2.14)


2.2 Charge eXchange

Charge exchange processes as below can occur in collisions of multiply chargedions with neutrals.

Single Electron Capture:Aq++B→A(q−1)+∗+B+→A(q−1)++B++hν

Transfer Ionization:Aq++B→A(q−2)+∗∗+B2+→A(q−1)++B2++e−

True Double Capture:Aq++B→A(q−2)+∗+B2+→A(q−2)++B2++hν

In the energy range from dozens to hundreds keV, single electron capture pro-cess is usually dominant. Its cross section is almost independent of projectileion energy and approximately 10−15 cm2. When electron capture process isdominant, relative velocity of projectile ions to targets is lower than classicalvelocity of an electron in hydrogen atom (1 a.u. ' 25 keV/amu).

Double electron capture has two categories, namely transfer ionizationand true double capture. In transfer ionization process, a captured electronde-excites without radiation and gives its energy to the other captured elec-tron. Then the electron which receive the energy is emitted from the ion.It is difficult to distinguish this process from single electron capture becauseboth processes give the same final state. True double capture results inde-excitation by radiations. Recently, experiments on multielectron capturehave been performed in various collision systems due to improvements of ex-perimental technique and triple electron capture cross sections which is verysmall have been measured. Especially Recoil Ion Momentum Spectroscopy(RIMS) made it possible to separate reaction processes precisely. All ionsafter reactions can be measured by using this technique.

2.2.1 Classical Over-Barrier Model

The over-barrier model provides estimation of dominant capture level (princi-pal quantum number n) after charge exchange reactions. This is based on anidea that an electron can transfer from a multiply charge ion to a target whenpotential barrier between collision particles gets lower than binding energyof the electron as shown in Fig. 2.2. The COBM was formulated by Ryufukuet al. for single electron system of a bare ion and hydrogen atom [54]. Then


it was extended to multielectron system by Barany et al. [55], and Niehausrefined it [56]. Niehaus’s model is called the Extended Classical Over-BarrierModel (ECOBM) or the Molecular Coulombic Barrier Model (MCBM) andwidely accepted as a standard model.

Figure 2.2: Single electron capture process based on the COBM.


Single Electron Model (Bare Ion - Hydrogen)

This is a one dimension model depending on inter-atomic distance R based ona classical theory. By putting a nucleus A with a charge of ZA on coordinateorigin and defining coordinates of an electron and a nucleus B with a chargeof ZB as x and R, respectively, Coulomb potential for the electron can bewritten as below.

V (x,R) = −ZA

x− ZB

R− x(2.15)

Maximum of the potential exists between the nuclei A and B (0 < x < R).Considering this three dimensionally, the maximum can be regarded as asaddle point. Hence, by defining its position to xsp, it meets the followingcondition.

dV (x,R)

dx

∣∣∣∣x=xsp

=ZA

x2sp

− ZB

(R− xsp)2= 0 (2.16)

This give us the following results.

xsp(R) =

(1 +

√ZB

ZA

)−1

R (2.17)

Vsp(R) = − 1

R

(√ZA +

√ZB

)2

(2.18)

In the case that the electron is around B at first, energy of the electron isequal to −Z2

B/2. Ionization energy of the atom, IB, is written as Z2B/2. As

A approaches B, energy of the electron in B, EB, gradually decreases due tocoulomb field produced by A. When the internuclear distant has a specificvalue, R, EB corresponds to the potential of the saddle point.

EB(R) = −IB −ZA

R= −Z

2B

2− ZA

R= Vsp(Rc) (2.19)

The internuclear distance and potential energy which meet the conditionabove are called the critical internuclear distance Rc and critical potential


energy Vc. By using the equation above, Ec and Vc can be written as below.

Ec =ZB + 2

√ZAZB

IB

(2.20)

Vc = −

(√ZA + ZB

)2

ZB + 2√ZAZB

IB (2.21)

In R < Rc, A and B become a quasi-molecule because the electron is sharedby them. When they are separated again, the electron is captured by A orB. If the electron is captured by A, the electron energy of EA is expressed asbelow by using the formula for H-like ions.

EA(R) = − Z2A

2n2− ZB

R(2.22)

A condition below is required to bring about the reaction.

EB(R) = −EA(R) ≥ Vsp(R) (2.23)

Therefor, the principal quantum number n and internuclear distance Rn(R)in this case are given as below.

n ≤

ZB + 2√ZAZB

2IB

(ZA + 2

√ZAZB

)

12

ZA

=

(ZB + 2

√ZAZB

ZA + 2√ZAZB

) 12ZA

ZB

(2.24)

Rn(R) =2(ZA − ZB)n2

Z2A − Z2

Bn2

=2(ZA − ZB)

Z2A/n

2 − Z2B

(2.25)

Assuming the straight line trajectory, charge exchange cross section σ isobtained as the product of reaction probability W and geometrical area of a


circle with radius of Rnp corresponding to maximum n(= np).

σ = πR2npW (2.26)

Ryufuku et al. approximated W = 12, but in multiply charged ion collisions

(ZA � ZB), we can assume W ∼ 1. As shown above discussions, this modelincludes no term of collision velocity. Charge exchange cross section hasalmost constant value at collision velocity lower than 1 a.u. It is consideredthat the cross sections estimated by the COBM correspond to this velocityregion. On the other hand, at collision velocity higher than 1 a.u., the crosssections gradually decrease as the velocity increases.

Multielectron Model

Before collisions, t-th electron from the outermost in a target is screened fromnuclear charge by inner electrons. When the screen is neglected, effectivenuclear charge is considered to be equal to +t. By using this model, theeffective nuclear charge of a multiply charged ion, +q, is kept after electroncapture to the outer shell. Models by Barany et al. and Niehaus have largediscrepancy in the way of handling the effective nuclear charge. In the firsthalf part of the collisions (‘way in’) which means A is approaching to B, theposition of the potential saddle point xin

sp(R) for the t-th electron, its heightV in

sp (R), the internuclear distance Rint and its energy Ein

t , where the potentialbarrier corresponds to the electron energy, are given as below.

xinsp(R) =

(1 +

√t

q

)−1

R = αtR (2.27)

V insp (R) = − 1

R

(√q +

√t)2

= − q

α2tR

(2.28)

Rint =

t+ 2√qt

It=

{q

(1

αt

− 1

)+

t

1− αt

}1

It(2.29)


Eint = −

(√q +

√t)2

t+ 2√qt

It = − q

α2tR

int

(2.30)

As shown in Eq. (2.29), on the ‘way in’, the particles become the quasi-molecule in ascending order of t, that is, as the internuclear distance de-creases. In the model by Barany et al., it is considered that the electronwhich once put into orbitals in the quasi-molecule must be captured into themultiply charged ion. However, in the Niehaus’s model, re-capture processon the ‘way out’ is taken into account. The ‘way out’ is the latter half ofthe collisions, which means A is coming away from B. On the ‘way out’,the internuclear distance gradually increases and the electron is re-capturedinto the atomic orbitals from the quasi-molecular orbitals. The height of thepotential barrier for the t-th electron depends on the number of electronscaptured into the multiply charged ions, where the electrons are restrictedto the range from (t + 1) to N . Hence, the effective nuclear charges of theprojectile ion and target atom are expresses to be q − rt and t+ rt, and thepotential barrier for the t-th electron can be written as follows.

xoutsp (R) =

(1 +

√t+ rtq − rt

)−1

R = βtR (2.31)

V outsp (R) = − 1

R

(√q − rt +

√t− rt

)2

= −q − rtβ2tR

(2.32)

Next, we consider whether the t-th electron is captured into the projectileor re-captured into the target at the point where the height of the potentialbarrier corresponds to Ein

t . Its internuclear distance Routt and energy Eout

t

are provided as follows.

Routt,rt =

(q − rtβt

+t+ rt1− βt

)(It +

q

Rint

)−1

(2.33)

Eoutt,rt = −It −

q

Rint

= − 1

Routt

(q − rtβt

+t+ rt1− βt

)−1

(2.34)


Since the electron captured into the quasi-molecular orbitals atRint is bounded

in either the projectile or target at Routt,rt , considering the Stark shift by the

opponent ion at that moment, the energies of A and B at R = ∞ are givenas below.

EA(t, rt) = −It −q

Rint

+t+ rtRout

t,rt

= −εA(t, rt) (2.35)

EB(t, rt) = −It −q

Rint

+t− rtRout

t,rt

= −εB(t, rt) (2.36)

These energies, EA and EB, are negative, and εA and εB are binding energiesfor A and B. The principal quantum numbers corresponding to each thebinding energies are obtained as below. At first, by considering that themultiply charged ion A is regarded as H-like ion with the charged of (q− rt),the principal quantum number of A is approximated as follows.

nA ∼q − rt√2εA(t, rt)

(2.37)

On the other hand, the correction of difference from the one electron approx-imation is required by using the quantum defect d to obtain the principalquantum number of B.

nB ∼t+ rt√2εB(t, rt)

− d(rt) (2.38)

d(rt) =t+ rt√2It+rt

− noB (2.39)

Now, It+rt and noB mean the (t + rt)-th ionization energy and the principal

quantum number of the outer orbital, respectively.


Dominant Electron Capture levels n

According to the model by Niehaus, the dominant electron capture level n1

in the case of t = 1 and rt = 0 is given as below.

n1 ∼ nA(t = 1, rt = 0) =

1 + 2√q

2I1

(q + 2

√q)

12

q (2.40)

Considering I1 = Z2B/2 for H-like ion, this result is completely consistent with

that by Ryuhuku et al. In the model by Niehaus which assumes that electronsouter than the t-th electron do not screen the charge +q of the multiplycharged ion in the case of rt = 0 and t ≥ 2, the equation of Rin

t = Routt,rt=0 is

established. The dominant electron capture level nt is given as below,

nt ∼ nA(t, rt = 0) ∼

t+ 2√qt

2It

(q + 2

√qt)

12

q (2.41)

where It is t-th ionization energy of the target. When more than two electronsare transfered (rt ≥ 0), the equation of nt is expressed as below.

nt ∼ nA(t, rt)

∼

(t+ 2

√qt){

q + t+ 2√

(q − rt)(t+ rt)}

2It

(q + t+ 2

√qt){

q − t+ 2√

(q − rt)(t+ rt)}

12

(q − rt)

(2.42)

This equation corresponds to Eq. (2.41) in the case of rt = 0. Moreover, inthe case of t = 1, it agree with Eq. (2.40).

2.2.2 Scaling Formulae for CX Cross Sections

Charge exchange cross sections of multiply charged ions are almost indepen-dent of their energies in keV range. Therefore, some scaling formulae whichare described by only a charge state q of projectile ions and ionization poten-tial I of targets have been proposed. At first, Muller and Salzborn proposed


an empirical formula [57].

σq,q−1 = 1.43× 10−12 · q1.17

(I/eV )2.76 (2.43)

This formula means single electron capture cross section of the multiply ionswith a charge of q, but also includes autoionization which is a process ofsingle electron emission after double electron capture. The cross section isproportional to q and inversely proportional to I. However, this formula hasno theoretical support.

Furthermore, Kimura et al. proposed a new formula which derived fromthe classical over barrier model extended to multielectron system [58]. Totalcross section for more than j electron capture is given as below.

σq =

q−1∑i=1

σq,q−1 =

q−1∑j=1

σjq = 2.6× 10−13 · jq

(I/eV )2 (2.44)


2.3 Optical Transitions

When an atoms transfer between two different states, photon absorption oremission occurs. In the case of excitation/de-excitation to higher/lower en-ergy level (E2/E1), the absorption/emission occurs. The photon emissionshave two processes such as spontaneous and stimulated emissions. The spon-taneous emission is the transition process from an excited state to a lowerstate by emitting photon after its lifetime τ . The stimulated emission is theprocess in which an excited atom is stimulated to fall to a lower energy levelby absorbing an incoming photon and then to emit a photon with the samefrequency as the absorbed one. The frequency of emitted photon (ν) in theseprocesses is written as below.

hν = E2 − E1 (2.45)

2.3.1 Einstein A Coefficients

Transition rates of spontaneous emissions are expressed by Einstein A coeffi-cients. The A coefficients have a dimension of s−1, which means the numberof the transitions per unit time. Now, specific two energy levels are consid-ered. The upper levels is expressed as n, and the lower is expressed as m.Assuming that a state in the level n as an initial state |i〉 and a state in thelevel m as a final state |f〉, A coefficient of the transition from |i〉 to |f〉 isgiven as below,

Anm =8πhν3

nm

c3

1

2πm2eν

2nm

e2

4πε0

1

gn

∑i

∑j

|〈i|eik·rε · ∇|j〉|2 (2.46)

where νnm, me, gn, k and ε mean frequency of emitted light, electron mass,the number of degeneracy of the level n, wave number vector which meanspropagation direction, and polarization vector showing vibration directionof electric field, respectively. The tern of exp(ik · r) in Eq. (2.46) can beexpanded as below.

exp(ik · r) = 1 + (ik · r) +1

2(ik · r)2 + · · · (2.47)

The transition probability significantly depends on which term in exp(ik · r)contributes.


2.3.2 Electric Dipole (E1) Transitions

In the case of k · r � 1, Eq. (2.47) can be written as exp(ik · r) ' 1 and amatrix element in A coefficient can be written as below.

〈i|eik·rε · ∇|j〉 ' ε · 〈i|∇|j〉

= ε · ime

~〈i|r|j〉

= −2πmeνnm~

ε · rnm (2.48)

Furthermore, the approximate expression above is called an electric dipoleapproximation (E1 transition), because an electric dipole moment can bewritten as D = qr = −er. In the case of isotropic radiation, the equationbelow holds.

|ε · rnm|2 =1

3|rnm|2 (2.49)

Hence, the A coefficient of the electric dipole transition is written as below.

Anm =8π

hc3(2πνnm)3 e2

4πε0

1

3gn

∑i

∑j

|rij|2 (2.50)

According to Eq. (2.46), A coefficients of the optically allowed transitionsare proportional to the cube of angular frequency ωnm = |En−Em|/~ whichmeans energy difference between two states. This shows that the larger theenergy difference is, the larger A coefficients are.

2.3.3 Magnetic Dipole (M1) Transitions

In the case where the electric dipole transition is forbidden, contribution ofthe second term in Eq. (2.47) should be considered (exp(ik · r) ' ik · r). Byconsidering wave number vector in z direction and polarization vector in x


of the atom Md is given as below.

Md = −e~µ0

2me

(L+ 2S) (2.55)

By adding a spin contribution into Eq. (2.54), the equation can be writtenas below.

me2πνnm~

1

ceµ0

(Md,y)ij (2.56)

Hence, A coefficient of the magnetic dipole transitions is given as below.

Anm =8π

hc3(2πνnm)3 e2

4πµ0

1

3gn

∑i

∑j

|(Md)ij|2 (2.57)

2.3.4 Selection Rule for E1 and M1 Transitions

By using four quantum numbers in Russell-Saunders coupling, selection rulesfor electric dipole transitions of LSJMJ −−L′S ′J ′M ′

J are given as follows.

1. ∆S = 02. ∆L = 0, ± 1 (L+ L′ ≥ 1)3. ∆J = 0, ± 1 (J + J ′ ≥ 1)4. ∆MJ = 0± 15. odd parity ↔ even parity

(2.58)

When these all five conditions meet, the electric transitions are allowed.L + L′ ≥ 1 means that in the case of L = L′ = 0 and ∆L = 0, thetransitions are forbidden. Furthermore, selection rules for magnetic dipoletransitions from light atoms are given as follows.

1. ∆S = 02. ∆L = 03. ∆J = 0, ± 1 (J + J ′ ≥ 1)4. ∆MJ = 0, ± 1 (In the case of ∆J = 0, only ∆MJ = ±1.)5. even parity ↔ even parity, odd parity ↔ odd parity

(2.59)


2.3.5 Cascade Transitions

As described previously, transitions between two states with large energydifference are likely to occur. However, according to the selection rules,transitions between states with small energy difference can also occur. Thedecay process by sequential transitions is called cascade transition.

2.3.6 Yrast Transitions

As shown in Fig. 2.3, from a level with maximum orbital angular momentuml = n − 1, only transitions satisfying ∆n = ∆l = 1 can occur. These arecalled yrast transitions.

Figure 2.3: An example of cascade and yrast transitions.


2.4 Theoretical Calculation

2.4.1 Hartree-Fock Method

The Hartree-Fock method is a self-consistent method for solving a manyelectron problem by using the central field approximation. Eq. (2.60) meansthe Hamiltonian for many electrons.

H =∑i

(− ~2

2m∇2

ri− Ze2

(4πε0)ri) +

∑∑i>j

e2

(4πε0)rij+∑i

σ(ri)Li · Si(2.60)

This system has a potential obtained by an iterative process until consecutivevalues for the potential agree with within a desired approximation. The Li

· S i term in Eq. (2.60) indicates a spin-orbit correction and becomes moreimportant for high Z elements. The Li means the orbital angular momentoperator and the S i means the spin angular moment operator. σ(ri) is givenby the following equation.

σ(ri) =1

2m2c2

1

ri

dV (ri)

dri(2.61)

By using atomic units, Eq. (2.61) can be written as follows.

H =∑i

∇2ri− 2Z

ri+∑∑

i>j

2

rij+∑i

σ(ri)Li · Si (2.62)

The center of gravity energy of the electron configuration can be defined asfollows.

Eav =Σi〈ψi(i)||H||ψi(i)〉

number of basis functions(2.63)

Summing over all basis functions, the spin-orbit correction goes to zero (LScoupling) and Eq. (2.63) reduces as below.

Eav =∑i

〈ψi(i)| − ∇2ri|ψi(i)〉av +

∑i

〈ψi(i)| −2Z

ri|ψi(i)〉av

+∑∑

i>j

[ψi(i)ψj(j)|2

rij|ψi(i)ψj(j)〉av − 〈ψi(i)ψj(j)|

2

rij|ψj(j)ψi(i)〉av](2.64)


Rewriting in terms of the one electron radial wavefunction Pi(r),

EKinetic = 〈ψi(i)| − ∇2ri|ψi(i)〉av

=

∫ ∞0

P ∗i (r)[−−d2

dr2+li(li + 1)

r2]Pi(r)dr (2.65)

ENuclear = 〈ψi(i)| −2Z

ri|ψi(i)〉av

=

∫ ∞0

P ∗i (r)[−−2Z

r]|Pi(r)|2dr (2.66)

EInteraction =∞∑k=0

F k(ij)ck(limli , limli)ck(ljmlj , ljmlj)

−δmsimsj

∞∑k=0

Gk(ij)|ck(msimsj)|2 (2.67)

where ck is renormalized spherical harmonics and Pn,l(r) = rRn,l(r). Fk and

Gk can be written in terms of a more general Coulomb integrals Rk.

F k(ij) = Rk(ij, ij) (2.68)

Gk(ij) = Rk(ij, ji) (2.69)

Rk(ij, tu) =

∫ ∞0

∫ ∞0

P ∗i (r)P ∗j (r′)rk<rk>+1

Pt(r)Pu(r′)drdr′ (2.70)

where the symbols i, j, u and t represent arbitrary nl combinations and r<and r>+1 are the maximum and minimum of the radial distances r and r′.This allows the minimum center of gravity energy to be obtained from theone electron wavefunctions. F k and Gk correspond to direct and exchangeCoulomb interaction energies.


2.4.2 Cowan’s Suite of Atomic Structure Codes

The Cowan’s suite of atomic codes was developed by R. D. Cowan [59] andconsists of four fortran programs (RCN, RCN2, RCG and RCE). This codecan obtain atomic energy levels and spectra for a multi-electron atom bysolving the Schrodinger equation in a multi-configuration with relativisticcorrections treated perturbatively. In this section, brief descriptions of eachprogram will be given.

RCN code

The RCN code calculates one-electron radial wavefunctions for each speci-fied electron configuration by using the Hartree-Fock approximation method.The output consists of the center-of-gravity energy (Eav) of a specific configu-ration, the radial Coulomb integrals (Fk and Gk), and the spin-orbit integral(ζ) needed to calculate the energy levels for each configuration.

RCN2 code

The RCN2 code calculates the configuration-interaction Coulomb integrals(Rk) between each interacting configuration pair, and the electric-dipole (E1)and/or electric quadrupole (E2) radial integrals between each configura-tion pair. By scaling Fk, Gk, Rk and ζ, accurate solutions to the atomicSchrodinger equation in close agreement with experimental results can beobtained.

RCG code

The RCG code build energy matrices for each possible value of the totalangular momentum J and diagonalizes each matrix to obtain eigenvaluesand eigenvectors. The output consists of the energy levels, eigenvectors,transition wavelengths, oscillator strengths, radiative transition probabilitiesand radiative lifetimes.

RCE code

The RCE code can be used to change the radial energy parameters Eav,Fk, Gk, ζ and Rk to obtain higher accuracy results by iterative proceduresthrough a least square fitting of experimental energy levels.

Chapter 3

Experimental apparatus

3.1 Electron Cyclotron Resonance Ion Source

An electron cyclotron resonance ion source (ECRIS) was developed by Gelleret al. in the Commissariat a l’energie atomique (CEA) [60, 61]. Electronsin magnetic field are resonantly accelerated by microwaves at the frequencycorresponding to the electron cyclotron resonance, and successively ionizeneutral atoms or molecules by electron impact. The plasma is stored bymirror and sextupole magnetic fields. Ion beams can be obtained by elec-trostatically extracting the produced ions. The ECRIS has disadvantages inproduction of metastable ions and wide energy width of extracted ion beamsdue to plasma potential, but a major advantage in being able to supplyinghigh intensity ion beams stably. Currently, the ECRISs are also used in ionincident systems of heavy ion accelerators. The principle of the ECRIS isdescribed below.

A charged particle in magnetic field moves in a spiral due to the Lorentzforce. By using the charge q, magnetic flux density B in tesla, mass of thecharged particle m and velocity component perpendicular to the magneticfield lines v⊥, the equation of motion is written as below.

mdv⊥dt

= qv⊥B (3.1)

37

Chapter 3. Experimental apparatus 38

Hence, a frequency ω of this spiral motion can be written as below.

ω =v⊥2πr

=qB

2πm(3.2)

This frequency is called a cyclotron frequency. In the case of electrons,by using m = me and q = e, an electron cyclotron frequency ωe is written asbelow.

ωe =eB

2πme

∼ 2.80B × 1010 Hz (3.3)

By applying the microwave with the same frequency as the electron cyclotronfrequency to electrons, their kinetic energies increase by absorbing it reso-nantly. This phenomenon is called an Electron Cyclotron Resonance (ECR).

The ECRIS produces multiply charged ions by colliding electrons heatedby ECR with the neutrals and ions. Thermal velocity of the electrons inan ECR plasma is much higher than ions because of extremely small massof an electron. Therefore, the electrons diffuse rapidly and neutral state ofthe plasma collapses. However, diffusion of the electrons is suppressed andinversely diffusion of the ions is accelerated due to Coulomb repulsion. Theelectrons and ions diffuse at the same velocity and the plasma can keep itsneutral state. That is to say, a storage of the electrons results in a storageof the plasma.

The ECR plasma cannot be stored by only static magnetic field. A com-bination of the mirror and sextupole magnetic fields make it possible for theECRIS to store the plasma in axial and radial directions, respectively. Themirror magnetic field has a fusiform-shaped magnetic configuration as shownin Fig. 3.1 which confines the plasma at the center.

Regarding the magnetic flux densities at the center of the mirror and bothends, the velocity of the charged particle passing through the central planeof the mirror field and the angle from the magnetic field line as B0, Bm, v0

and θ, respectively, the magnetic momentum µ and total kinetic energy ε aregiven as follows,

µ ≡ mv2⊥

2B(3.4)


Figure 3.1: Upper: Coil configuration and magnetic field lines, lower: mag-netic flux density distribution.

ε ≡(mv2

‖ +mv2⊥)

2(3.5)

where v‖ and v⊥ mean vcosθ and vsinθ, respectively. Assuming that µ andε conserve, the perpendicular component of the kinetic energy increases andthe parallel component decreases low due to the magnetic fields at the mirrorends being larger than that at the center. The particles are reflected at thepoint where of v‖ = 0 in the field of B < Bmax. This is the reason why thefield is called “mirror”, and the ratio of the maximum and minimum of thefield Rm = Bmax/Bmin is called mirror ratio. Regarding the pitch angle wherethe particles are reflected at the mirror ends as θL, the following is given bythe conservation law.

Rm =Bm

B0

=1

sin2θL

(3.6)

The particles with the pitch angle smaller than θL cannot be confined at thepoint of Bmax, because v‖ cannot be zero and they escape from the mirror.This θ make a circular cone in the velocity space.

On the other hand, the magnetic field in radial direction exists due to the


sextupole magnets as shown in Fig. 3.2, and the particles are confined at thecenter by the same principle as in axial direction. By trapping the electronsdue to the principle above, the ECRIS can confine the plasma and producemultiply charged ions. The ions are extracted as a beam by applying highervoltage to a plasma chamber than an extraction anode.

Figure 3.2: Magnetic field produced by the sextupole magnets.

The ions with desired mass-to-charge ratio are selected with an analyzingmagnet for the charge-state separation. The multiply charged ions move in acircle by receiving Lorentz force. At this time, the centrifugal force matcheswell with the Lorentz force and an equation below holds,

Mv2

R= Qv ×B (3.7)

where M , v, R, Q(= qe) and B mean ion mass, ion velocity, orbital radius,ion charge and intensity of the magnetic field. The kinetic energy of the ionis written by using an acceleration voltage V as below.

1

2Mv2 = QV (3.8)

By solving the two equations above, the following equation for the ion sepa-


ration is obtained,

M

Q=m

q

u

e=B2R2

2V(3.9)

where u, m, e and q mean atomic mass unit, mass number, elementary chargeand valence of ion, respectively. By converting the units into atomic units,the equation can be useful.


3.2 Kingdon Ion Trap

A Kingdon trap was invented by K. H. Kingdon, which can trap chargedparticles by some electrostatic fields [62]. It has very simple structure asshown in Fig. 3.3 and do not require radio frequency voltages and ion cool-ing. Therefore, it can easily confine the ions with a high kinetic energy ofabout 10 keV/q. By applying lower voltage to a wire than to a cylinder, alogarithmic potential is created in the trap. The ions with appropriate angu-lar momentum can be trapped in the radial direction by moving around thewire. In the axial direction, the ions can be trapped by a harmonic potentialproduced by two end-caps.

Figure 3.3: A schematic drawing of a Kingdon trap consisting of a wire,cylinder and two end-caps.

Now, we consider that the wire and cylinder are infinitely long and theideal logarithmic potential is created. As shown in Fig. 3.4, the inner diame-ter of the wire, diameter of the cylinder and voltages applied to the wire and


cylinder are represented as a, b, VW and VC, respectively.

Figure 3.4: Infinitely long concentric cylinders.

According to the Gauss’ law, an electric field E is written as below,

E =λ

2πε0r(3.10)

where λ and ε0 are a linear charge density of the wire and vacuum permit-tivity. The electric potential is obtained by integrating the electric field asbelow.

V (r)− VW = −∫ r

b

Edr

= − λ

2πε0r

∫ r

b

dr

r

= − λ

2πε0rln (r/b) (3.11)

In the case of r = a, V (r) = VC holds and λ is written as below.

VC − VW = − λ

2πε0rln (a/b) (3.12)


λ = −2πε0rVC − VW

ln (a/b)(3.13)

As shown above, the potential at r, V (r) can be written as below.

V (r) = (VC − VW)ln (r/b)

ln (a/b)(3.14)

Representing the charge of the trapped ions as qe, the mean kinetic energyEk can be obtained by using virial theorem.

Ek =qe(VC − VW)

2 ln(a/b)(3.15)

From the above, the mean square velocity of the ions with a mass of m canbe written as below.

vrms =

√qe(VC − VW)

m ln (a/b)(3.16)

The real Kingdon trap has the two end-cap electrodes and they createthe harmonic potential. Therefore, the potential in the trap is a sum of theharmonic and logarithmic potentials. By determining the wire direction andits radial direction as z- and r-axes, the sum of the potentials φ(r, z) can bewritten as below,

φ(r, z) = (VC − VW)ln (r/b)

ln (a/b)+κVEC

z20

(z2 − r2

2

)(3.17)

where κ, 2z0 and VEC indicate geometrical factor, interval between the end-caps and voltage applied to the end-caps. By using this potential, motionequations of the trapped ions can be written as follows.

md2r

dt2=mθ2

r− qe∂φ(r, z)

∂r(3.18)


md2z

dt2= −qe∂φ(r, z)

∂z(3.19)

Moreover, conservation of angular momentum leads to the following.

md

dt

[r2

(dθ

dt

)]= 0 (3.20)

The mean square velocity vrms of the trapped ions is constant regardlessof the ion trajectories. This is a characteristic feature of the Kingdon trap.Furthermore, multiply charged ions with the high kinetic energy injectedexternally can be easily trapped by using this ion trap. However, an ioncooling is impossible due to the presence of the wire at the minimum of thetrap potential.

An example of the trapped ion trajectory in the ideal logarithmic poten-tial is shown in Fig. 3.5. In this figure, xy-plane is defined as a plane parallelto the end-caps. The wire is located at the center of the xy-plane and z-axis is defined as the wire axis. Only ions with adequate kinetic energy andangular momentum can be trapped by turning around the wire.

Figure 3.5: Ion trajectory in the ideal logarithmic potential.


3.3 Ion Trapping Experiments

3.3.1 ECRIS at Sophia Univ.

In order to perform a performance test of the developed Kingdon trap, weused a compact ECRIS (NANOGAN 10 GHz, Pantechnik) at Sophia Uni-versity. The cross sectional diagram of the ECRIS and main parameters areshown in Fig. 3.6 and Tab. 3.1. During applying the microwave, a plasmachamber and permanent magnet are cooled by a compressor.

Figure 3.6: Cross sectional diagrams of the NANOGAN.

3.3.2 Production of Multiply Charged Argon and Oxy-gen Ions

Multiply charged Ar and O ions were produced by injecting neutral Ar andmixed gas of O2 and He (1:1) into the ECRIS. The ion beam intensities ofArq+ (q = 5–7) and O6+ ions measured at the most downstream were 0.5–6 nA, which depended on the charge state. Fig. 3.7 and 3.8 show typicalmass spectra of Ar and O ions produced by the NANOGAN. Vertical andhorizontal axes show the voltage applied to the charge separator and the ionintensity, respectively. In the case of the oxygen ion production, neutral Hegas is injected to the plasma chamber as support gas. Therefore, a peak ofO4+ ions in mass spectra overlaps with that of He+ ions because of the samemass-to-charge ratio.


Table 3.1: Main parameters of the ECRIS at Sophia Univ.

Plasma chamber Material CuDiameter 26 mmLength 140 mm

Permanent magnet Multipolarity HexapoleMaterial Nd-Fe-BField strength ∼0.357 T (on the surface)

Microwave amplifier Frequency 10 GHzMax. power 100 W

Max. acceleration voltage 20 kVBackground pressure Without operation ∼5×10−4 Pa

During operation ∼5×10−2 Pa

Figure 3.7: Typical mass spectra of Ar ions produced by the NANOGAN.

3.3.3 Beamline at Sophia Univ.

A schematic drawing of a beamline at Sophia Univ. is shown in Fig. 3.9. Theions produced by the NANOGAN were extracted by an electric potential of6.0 or 8.0 kV and separated by the charge separator depending on mass-to-


Figure 3.8: Typical mass spectra of O ions produced by the NANOGAN.

charge ratio. The ion beam with a desired charge state was focused by aneinzel lens and adjusted by two pair of deflectors. Just before injected into theKingdon trap, the ions were decelerated by an electrostatic lens fixed on thetrap. A Faraday cup was installed at the most downstream of the beamlineto measure ion beam intensity. The charge separator and trap chamber have4.0 and 1.5 mm apertures, respectively, for differential pumping.

3.3.4 Kingdon Ion Trap

In order to observe long-lived forbidden transitions following charged ex-change, we developed the Kingdon trap. A schematic drawing of it is shownin Fig. 3.10. It consists of a central wire electrode with a diameter of100±10 µm, a cylinder electrode with an inner diameter of 50±0.1 mm,and two end-cap electrodes. The distance between the end-caps is also50±0.1 mm. An electrostatic lens is fixed on the Kingdon trap to deceleratethe ion beam. All electrodes are made of stainless steel (SUS304) and themaximum floating voltage is 10 kV. The cylinder electrode has four 18 mmapertures: two for ion beam passing, another for ion detection and the otherfor photon detection. In order to reduce the disturbance of the electric fieldfor ion trapping, they are covered with a mesh. Three apertures for the beam


Figure 3.9: A schematic drawing of a beamline at Sophia Univ. It containsthe ECRIS, analyzing magnet, beam transport optics, Kingdon trap andFaraday cup.

passing, ion detection and photon detection are covered with a gold-platedtungsten mesh which has a transmittance of about 93%. The only apertureat the most downstream is covered with a stainless steel mesh with 1 mminterval. The residual pressure in the trap chamber is maintained to be about4.4×10−7 Pa, which is measured with an ion gauge. By a partial pressuregauge, the main residual gas is identified to be molecular hydrogen. A liquidnitrogen trap is installed the trap chamber to remove impurities. The mainparameters of the Kingdon trap is summarized in Tab. 3.2.

High Voltage Push-Pull Switching Units

The ion tapping experiments require fast switching of high voltage appliedto the wire electrode. For this, we used a high voltage push-pull switching


Figure 3.10: A schematic drawing of the developed Kingdon trap. The lowerfigure shows the side view from the ion beam axis. The extraction lens istypically biased at -2.0 kV and used for the time-of-flight measurement ofextracted ions from the trap. The distance between the wire and the entranceof the lens is 48.5 mm.

units (Behlke, GHTS 100), which consists of a DC/DC converter, control andprotection circuit, and switching module. The switching module is made of alarge number of series and parallel connected MOSFET with intrinsic diodes.By combining two high voltage power supplies with a function generator,square wave voltage can be generated with amplitudes up to 10 kV.


Table 3.2: Main parameters of the Kingdon trap.

Cylinder electrode Material SUS304Inner diameter 50 mmLength 50 mm

Wire electrode Material SUS304Diameter 100 µ m

End-cap electrodes Material SUS304Distance 50 mm

Max. floating voltage 10 kVPressure Without operation 4.4×10−7 Pa

Table 3.3: Main parameters of the high voltage push-pull switching units.

Max. Operating Voltage Range 10 kVMax. Peak Current 15 AMin. Pulse Width 100 nsTypical Transition Time 15–106 ns depending on load capacitanceMax. Pulse Width No limit, pulse width up to DC possibleMax. Switching Frequency 15 kHzControl Signal Voltage 2–10 V

3.3.5 Time-of-Flight Mass Spectrometer

During the storage of the multiply charged ions, lower charge state ions areproduced by charge exchange collisions with residual H2 gas in the ion trap.

Xq+ + H2 → X(q−1)+ + H+2

→ X(q−1)+ + H+ + H

X(q−1)+ + H2 → X(q−2)+ + H+2

→ X(q−2)+ + H+ + H

The projectile and product ions are still trapped in the trap and extractedfrom the trap at the same time. When a microchannel plate is installed closeto the trap, the detection efficiency is high. However, the some ion species


are almost simultaneously detected due to the short flight distance, whichmakes it impossible to measure the precise trapping lifetime of the projectileions. Therefore, the distance between the cylinder electrode and the MCP,the flight distance, is extended from 8 mm to 302 mm to discriminate thedetection signals of the extracted ions. In order to increase the detectionefficiency, an extraction lens is installed close to the cylinder electrode. Aschematic drawing of the TOF measurement system is shown in Fig. 3.11.

Figure 3.11: TOF measurement system.

In order to identify the TOF spectra, we performed the trajectory simulationof Arq+ ions by using SIMION 8.0. The xy-plane was defined as the sameplane parallel to the end-caps, and the direction along the wire was definedas the z-axis as shown in Fig. 3.12. The acceleration voltage of the trappedions is defined as a difference between the potentials during the storage andthe extraction, which were calculated at each mesh point in the trap. Theions were isotropically ejected from the each mesh point in x2 + y2 ≤ 202,y ≤ 0 and z = 0. About 7000 Arq+(q = 1–7) ions were ejected. The TOFspectrum was obtained by recording the time between the ion ejection anddetection by the MCP. Figure 3.13 shows the simulated TOF spectrum ofArq+(q = 1–7) ions. Horizontal axis shows TOF and vertical axis shows ionintensity.


Figure 3.12: 3D electrode geometry of ion trap system by SIMION 8.0.

Figure 3.13: A sum of each TOF spectrum of Arq+ ions simulated bySIMION 8.0.


3.4 Forbidden Transition Measurements

3.4.1 TMU-ECRIS

Photon count rates of forbidden transitions are expected to be much lowerthan those of resonance transitions due to their long lifetimes of milliseconds.In order to realize the forbidden transition measurements, high intensityion beam is required. Therefore, the measurements have been performedby the ECRIS at Tokyo Metropolitan University [63]. A cross sectionaldiagram of the TMU-ECRIS and main parameters are shown in Fig. 3.14and Tab. 3.4. A plasma chamber and ion extraction chamber are evacuatedby turbo-molecular pumps, respectively. Water-cooling is adopted to coolthe plasma chamber and conductivity of the coolant water is kept lower than2.0 µS/cm by using an ion-exchange resin. The ECRIS has three lenses toextract multiply charged ions effectively. Figure 3.15 shows a cross-sectionaldiagram of the extraction lenses.

Figure 3.14: A cross sectional diagram of the TMU-ECRIS.


Figure 3.15: A cross-sectional diagram of an ion extraction lenses installedat the TMU-ECRIS.

3.4.2 Production of Multiply Charged Oxygen Ions

H-like O ions were produced by introducing O2 gas into the plasma chamberthrough a gas introduction system. Figure 3.16 shows a typical mass spec-trum of oxygen ions produced by the TMU-ECRIS. Ion beam intensity wasmeasured by a Faraday cup. Horizontal axis shows the control current of thecharge separator and vertical axis shows the ion intensity. The beam inten-sity of O7+ ions reaching the most downstream of the spectroscopy beamlinewas approximately 1–10 nA.

3.4.3 Beamline at TMU

A schematic drawing of a beamline at TMU is shown in Fig. 3.17. In the Achamber between the ECRIS and analyzing magnet, a high speed deflector isinstalled to pulse the ion beam in order not to inject it into the trap duringthe ion trapping. The multiply charged ions extracted from the plasmachamber are separated by the analyzing magnet according to mass-to-chargeratio. In the B chamber between the analyzing magnet and switching magnet,adjustable two pair of slits, an einzel lens and a quadrupole lens are installed.


Table 3.4: Main parameters of the TMU-ECRIS.

Plasma chamber Material CuDiameter 50 mmLength 190 mm

Permanent magnet Pole number 6Material Nd-Fe-BMagnetic field Intensity ∼1.0 T (on the surface)

Solenoid coils Max. current 600 AMax. power 36 kW×2Max. field intensity ∼1.2 T (on the axis)

Microwave amplifier Frequency 14.25 GHzMax. power 500 W (Initial:1.5 kW)

Max. acceleration voltage 20 kVBackground pressure Without operation ∼5×10−7 Pa

During operation ∼2×10−6 Pa

Figure 3.16: A typical mass spectrum of oxygen ions produced by the TMU-ECRIS.


Figure 3.17: A schematic drawing of the TMU beamline. In the presentwork, a spectroscopic beamline was used.

After passing through the above, the ion beam is directed to an beamline forspectroscopy by the switching magnet. Just after the switching magnet, theFaraday cup is installed and used for ion beam adjustment. The pressure inthe beamline is kept to be about 10−7 Pa without operation.

3.4.4 Silicon Drift Detector

We used a window-less silicon drift detector (Princeton Gamma-Tech Instru-ments, Sahara SDD) to observe soft X-ray emissions derived from chargeexchange reactions. The SDD is one of energy dispersive X-ray detectors.Radiation produces electron-hole pairs in the valence band on a pn junction


surface. The number of them is detected by a charge-sensitive preamplifier.X-ray incidence surface is made from an uniform electrode, and has a seriesof ring electrodes, an anode and a field effect transistor (FET) on the re-verse. The anode and FET is located at a center of the rings and collect thecharge carriers. The ring electrodes generate a potential gradient and driftthe charged carriers to the center anode. Incident X-ray energy can be mea-sured by using a feature of proportion between the detected current valueand the X-ray photon energy. The “drift” makes it possible to significantlyreduce the anode size, which leads to very small capacitance between theanode and FET. By integrating the FET at a center of the ring, floating ca-pacitance also reduces greatly. Due to these improvements, a large detectionarea and high energy resolution are achieved.

Our SDD has a detection area of 100 mm2 and an energy resolution ofabout 140 eV for Mn Kα. The window-less SDD achieves detection efficiencyof nearly 100% and this allows measurements of absolute values of crosssections. Moreover, the peltier cooling is used for noise removal instead ofthe liquid nitrogen cooling, which makes the detector small and lightweight.X-ray emissions following charge exchange reactions were detected and thesignals were recorded by a fast multichannel analyzer (MCA, System 8000).The SDD included a preamplifier and amplifier, and was directly connectedto the SDD. A specification of the SDD is listed in Tab. 3.5.

Table 3.5: Specification of the SDD.Energy resolution at 5.9 keV 137 eVCrystal thickness 0.3 mmActive area 100 mm2

Bias voltage -180 VShaping time 1.5 µs


3.5 Spectroscopy of Inner-Shell Excited Li-

like C, N and O Ions

3.5.1 Production of Inner-Shell Excited Li-like Ions

It is well known that He-like ions produced by the ECRIS include metastable1s2s 1,3S states and the metastable beam fraction is at least a few percent ofthe total beam. We took advantage of this feature in order to produce inner-shell excited Li-like ions. In our experiments, the inner-shell excited Li-likeC, N and O ions were produced by charge exchange collisions of metastableHe-like ions with neutrals.

3.5.2 Spectroscopic Beamline at TMU

In spectroscopy experiments of inner-shell excited Li-like ions, the samebeamline as the forbidden transition measurements was used, but a soft X-raydetector being used was different. In this measurement, a grazing-incidencespectrometer was used, which was developed by Nakamura et al. A schematicdrawing of the beamline and grazing-incidence spectrometer being used inthis measurement is shown in Fig. 3.18.

3.5.3 Grazing-Incidence Spectrometer

Soft X-ray emitted from the inner-shell excited Li-like ions were measuredwith a grazing-incidence spectrometer (GIS) and a back-illuminated chargecoupled device (CCD) camera (Princeton Instruments, PIXIS-XO: 400B). Aschematic of the GIS and CCD camera is shown in Fig. 3.19. The soft X-rayemissions through an aperture of the collision cell were collected by a gold-plated cylindrical mirror. The emission region had width corresponding toa diameter of the aperture and this made the wavelength resolution of theGIS worse. Therefore, a slit was installed after the mirror. In this study,spectroscopy was performed with slit width of 50 µm and the resolution wasapproximately 0.015 nm. A laminar-type replica diffraction grating witha groove density of 1200 grooves/mm (SHIMADZU, 30-002) was irradiatedand then the CCD camera was exposed to the diffracted lights. The exposuretime was varied form 6 to 24 hours, which depended on emission intensities.

A flat-field type holographic grating was installed at the GIS used in this


Figure 3.18: A schematic drawing of the TMU beamline, collision systemand grazing-incidence spectrometer.

study. The relation between incident and diffraction lights is given as below,

d (sinα− sinβ) = mλ

β = sin−1

(sinα− mλ

d

)(3.21)


where d, α, β, m and λ indicate the groove spacing, incident angle, diffractionangle, diffraction order and wavelength, respectively. From the geometry ofthe GIS and CCD shown in Fig. 3.19, the following equation can be obtained.

tan (π/2− β) =x+ y

b

y = b tan(π

2− β

)− x (3.22)

Here, parameters of b, x, y are important, because detection points dependon their diffraction angles. They are determined by measuring the detectionpoints on the CCD pixels using transitions with well known wavelengths. Thewavelength of the diffracted light at position x is obtained by substitutingEq. (3.21) for Eq. (3.22) and deformation of it.

y = b tan

{π

2− sin−1

(sinα− mλ

d

)}− lpnp

λ =d

m

{sinα− cos

(tan−1 lpnp + y

b

)}(3.23)

where lp and np are the pixel length and pixel number of the CCD, and xcan be expressed as the product of lp and np. Eq. (3.23) shows a relationbetween λ and np, and this equation is used for a wavelength calibration.

The designed values of each parameter for the GIS is shown in Tab. 3.6.The calculated values in the experimental calibration of wavelengths are dif-ferent from the designed values with a few percents.

Table 3.6: Main parameters of the GIS and CCD.a : 237.0 mmb : 235.0 mm

Incident angle α : 87.0◦

Groove spacing d : 1/1200 mmWavelength region : 5–20 nm

Pixel size : 20×20 µmExposure area : 1340×400 Pixels


Figure 3.19: A schematic of the GIS and back-illuminated CCD camera.

Chapter 4

Ion Trapping Experiments

4.1 Experimental Procedures

The measurement procedures are described as follows. As shown in thetiming sequence of the trapping experiment (Fig. 4.1), the HCI beam wasinjected into the Kingdon ion trap while the wire electrode was held at ahigher potential. Then the wire potential was rapidly switched to a lowerpotential than the other electrodes. This wire voltage (VW ) is controlled bya high voltage push-pull switch (Behlke, GHTS 100). After a certain delay,the ion beam is switched off by deflecting a HCI beam using the upstreamdeflector. The deflection voltages are controlled by high-speed operationalamplifiers (APEX, PA97). The timing of the beam-off is the start for astorage time of HCIs. After a pre-determined storage time, the trappedHCIs are ejected by raising the wire potential. A fraction of the ejected ionsare detected by the MCP and the output signals are counted by the MCS.The data acquisitions were repeated 103–104 cycles depending on the storagetime, which was varied from 5 ms to 3 s. The above measurement sequenceis controlled by a master oscillator (Stanford Research, DG535).

First, the MCP was placed at 35 mm from the center of the ion trap.Although we cannot discriminate the charge state of trapped HCIs in thiscase, the detection efficiency is higher than the TOF measurement. Theoperating voltage in this measurement mode is indicated as extraction inTab. 4.1. In the TOF mode, we placed the MCP at a 329 mm distancefrom the trap center and the extracted ions are focused on the detector bythe ion extraction lens (see Fig. 3.10). The voltage of the extraction lens

63

Chapter 4. Ion Trapping Experiments 64

was typically set to -2.0 kV. The output pulse signals from the MCP werecounted by a fast multichannel scaler (Comtech, MCS6A).

A summary of typical operating voltages of the Kingdon trap is shownin Tab. 4.1. All of the operating voltages were sequentially adjusted andoptimized as the ion signal increased. It is noted that the axial and radialtrapping potential are determined by the temporally position of the injectedion into the Kingdon trap when the wire potential is quickly lowered bythe high voltage switch. Since the potential near the trap center is close tothe wire potential, the depth of the axial and radial trapping potential isconsidered to be ∼150 V and ∼130 V, respectively.

Figure 4.1: A timing chart of the ion trapping experiment. A master os-cillator generates trigger pulses for controlling the timing. The ion beam ischopped by the upstream deflector.


Table 4.1: A summary of typical operating voltage for Arq+(q = 5, 6) trap-ping experiments; VDL: deceleration lens, VR: ring electrode, VE: end capelectrodes, VW: wire electrode. The extraction voltage from the ECRIS is6 kV and the voltage of the ion extraction lens is set to -2.0 kV. Each rowcorresponds to the measurement mode: ion storage, ion extraction, time-of-flight (TOF) and ion beam monitoring by the Faraday cup. In the extractionmode, the charge states of the trapped ions are not discriminated by the de-tector.

Operation VDL [kV] VR [kV] VE [kV] VW [kV]Storage 5.17 6.27 6.29 6.14Extraction 5.17 6.27 6.29 6.50TOF 5.17 6.27 6.29 7.39Monitoring 0 0 0 0


Figure 4.2: A schematic of the ion trapping experiments and forbidden tran-sition measurements.


Figure 4.3: A schematic of the circuit for trapped ion and soft X-ray detec-tions.


4.2 Velocity Distribution of Trapped Ions

The velocity distribution of trapped ions is very important information incollision experiments using a Kingdon ion trap. In this section, velocitiesof Ar5,6+ ions trapped in ideal logarithmic potential and realistic potentialformed by the trap are discussed.

4.2.1 Ideal Logarithmic Potential

As described in Sec. 3.2, the Kingdon ion trap with the infinitely long wireand cylinder electrodes creates an ideal logarithmic potential written by

V (r) = (VR − VW)ln (r/a)

ln (a/b), (3.14)

and the mean kinetic energy of trapped ions is given by

Ek =qe(VR − VW)

2 ln (a/b), (3.15)

where a and b represent the radius of the ring and the wire electrode, respec-tively [69]. Using Eq. (3.15), the root-mean-square (rms) velocity of an ionwith the mass of m can be written by

vrms =

√qe(VR − VW)

m ln (a/b). (3.16)

As indicated in the above equations, the ideal Kingdon trap has the inter-esting property that the mean kinetic energy of trapped ions is the same forall stable trajectories regardless of initial conditions [69]. However, it is ob-vious that the above equations are not valid for trapped ions in the realisticKingdon ion trap.

4.2.2 Realistic Potential

In order to check the velocity distribution of trapped ions, we performedtrajectory calculations of trapped Arq+(q = 5, 6) ions by numerical simula-tions [70]. In Fig. 4.4 (a), a typical trajectory of a trapped Ar6+ ion is shown.The electrodes were arranged the same as with the actual Kingdon trap and


some lenses for ion deceleration and ectraction. The direction along the wireelectrode is defined as the z-axis. The mesh electrodes on the apertures ofthe ring electrode is also considered in the simulations. We set the samevoltages as in the first row of Tab. 4.1.

Starting positions (rs) of the ions are set to cross points on a 1 mmmesh within a 6 mm distance from the central wire on the xy-plane. Oneach mesh point, the positions are randomly set within a circle of a 0.5 mmradius. The emission cone angle at each source point is randomly set towithin ±2 degrees with respect to the beam direction (y-axis) as shown inFig. 4.5. The source points on the xy-plane were also moved by ±3 mmalong the z-axis by the interval of 0.5 mm. This range was determined bythe incident beam diameter estimated by the numerical simulations. Sinceno stable trajectories are obtained in the case of rs > 6 mm, we need notextend the source positions anymore. The incident ion energy is varied from10 to 150 eV at each source point. It is noted that the initial incident energyis not important in determining the velocity distribution because the kineticenergy of a trapped ion changes continuously along the trajectory and hasa broad width. Actually, only the ions with a specific incident energy andangle can be trapped at a specific starting position.

In the present simulations, the total number of trials and the stable tra-jectories were on the order of 104 and 102, respectively (If the storage timeis longer than 100 ms, we define it as “stable”). When an ion is in a stabletrajectory, we record the kinetic energy every 100 µs during the flight time.Examples of stable trajectories are shown in Fig. 4.4. Finally we obtainedabout 105 samples of kinetic energies of single trapped ions.

As a result of the simulations, we found the following properties of thestable trajectories of trapped Ar6+ ion: (1) Energy distributions are very wideand are not dependent on the initial conditions. The peak energy is around80 eV without exception, and (2) there are some exceptional trajectories,where the energy width is very narrow (Fig. 4.4(b)). However, the peakenergy is still almost the same as the other stable trajectories.

These properties show that Eqs. (3.15) and (3.16) are qualitatively cor-rect. Thus, we conclude that the velocity distribution of the trapped ionscan be obtained by averaging many different stable trajectories, which werecalculated at different initial conditions.

All of kinetic energy histgrams of the stable trajectories were summed upand the kinetic energy distribution was obtained. As shown in Fig. 4.6, itwas then converted to the velocity distribution of Ar6+ ions. By fitting this


Figure 4.4: Left: A typical stable trajectory of Ar6+ ion on the xy-planeobtained by a numerical simulation. This figure is top view and the wireelectrode exists in the center of the trajectory. In this trajectory, the kineticenergy distribution is broad. Right: An example of a stable trajectory witha narrow energy width. Both trajectories were accumulated for more than100 µs.

histogram to the Lorentzian function, the peak velocity is determined to be2.0(0.4)×104 m/s, where the error is evaluated by the HWHM of the velocitydistribution. With these values, the binary collision energy between trappedAr6+ ions and H2 is evaluated to be 4.0+3.3

−3.0 eV in the center-of-mass system.We performed the same simulations for Ar5+ ions. The simulation study issummarized in Tab. 4.2. For comparison, we also calculate the mean kineticenergy and the rms velocity using Eqs. (3.15) and (3.16). These values areconsistent with the simulation results within the errors.


Figure 4.5: Starting position of ions are randomly set within a circle of a0.5 mm radius. The emission cone angle at each source point is randomlyset to within ±2 degrees with respect to the beam direction (y-axis).

Table 4.2: A summary of the simulation study of trapped Arq+(q = 5, 6) ions.The first row (”storage”) in Tab. 4.1 is applied to the voltage conditions. Ep

represents the peak values of the energy distribution. The peak velocity vpis calculated from Ep. Using Eqs. (3.15) and (3.16) we also calculate themean kinetic energy (Ek) and the rms velocity (vrms) in the ideal logarithmicpotential.

Ion Ek (eV) vrms (m/s) Ep (eV) vp (m/s)Ar5+ 52.3 1.59×104 68.1 1.8(0.3)×104

Ar6+ 62.8 1.74×104 82.0 2.0(0.4)×104


Figure 4.6: Velocity distributions of stable trajectories of trapped Arq+(q =5, 6) ions obtained by numerical simulations. The horizontal and vertical axisshow the velocity and the normalized intensity, respectively. The solid curveshows the fitted Lorentzian function to the data points.


4.3 Trapping Externally Injected Argon Ions

Figure 4.7(a) shows a time spectrum of the ejected ions after 3 ms storagetime when Ar7+ ion beam was incident to the Kingdon trap. An inputDC beam current of 1.5 nA was obtained from the ECRIS, resulting in 1.8ions detected per cycle. In this measurement, the ion signals contain allcharge states of the trapped ions. A broad time spectrum suggests that thevelocity distribution of the trapped ions is broad. This is consistent with thesimulation result in Fig. 4.6.

Figure 4.7(b) shows the number of the ejected ions as a function of storagetime. Each data point was accumulated over 3 cycles. The decay data is fittedby a double exponential function with two different time constants. The fastcomponent was possibly caused by motional instability of high-q ions inducedby collisions with background molecules. On the other hand, the slow decaycomponent suggests that the reaction product ions are still trapped after thefollowing charge-exchange reactions:

Ar7+ + H2 → Ar6+ + H+2 ,

→ Ar6+ + H+ + H.

Moreover, the sequential reactions, Arq+(q < 7) + H2, should also be consid-ered. In the next section, we demonstrate experimentally that product ionsare actually detected.

We evaluate the trapping efficiency of the Kingdon trap for the injectedions from the ECRIS as follows. The total number of the incident Ar7+ ionsis estimated to be about 1.3×109 ions per second for a DC beam currentof 1.5 nA. Using the simulated incident velocity of the ions (2.8×105 m/s),the transit time of the effective trapping length (2b = 50 mm) is estimatedto be about 0.18 µs. Thus the number of Ar7+ ions in the trap region isabout 2.4×102 ions. The total number of the detected ions can be expressedby Ndet = εtNtrap, where Ntrap is the number of trapped ions and εt is theion transport efficiency from the Kingdon trap to the MCP. The trappingefficiency η can be written by η ≈ Ntrap/(2.4 × 102). Since the number ofdetected ions is Ndet =1.8 ions per cycle as mentioned above, the trappingefficiency η is obtained by η ≈ 8×10−3/εt. In the optimistic case of εt ≈10%,we obtain η ≈8×10−2.


Figure 4.7: (a) A time spectrum of the ejected ions when Ar7+ ion beamwas incident to the Kingdon trap. The storage time was set to 3 ms. Thedata is the sum of 1000 cycles. (b) A decay curve of the trapped ions as afunction of the storage time. The solid curve shows the fitting curve by adouble exponential function with time constants of 1.8(0.2) s and 41(16) ms.The residual pressure was approximately 4.4×10−7 Pa.


4.4 TOF Measurements

Figure 4.8(a) shows the TOF spectra of ejected ions after 5 ms storage timewhen Ar6+ ions were injected into the Kingdon trap. We succeeded in dis-criminating the charge-state of trapped Arq+ ions, where the charge-state isidentified by comparing the experimental TOF spectrum to the simulatedspectrum. Since we introduced an extra ∼1.24×10−5 Pa of H2 gas, thereaction-product ions of Ar5+, H+

2 and H+ were also observed. As shown inFig. 4.8(b) and (c), the intensity of the reaction products gradually increasesas the storage time increases.

In the earlier study using the Kingdon ion trap, Church et al. reportedthat no product ions with lower charge state were stored after charge-transfercollisions between Arq+ and Ar [71]. Since the momentum transfer betweena target Ar and Arq+ at each collision is much larger than that in the presentwork, the product ions were possibly lost. However, the conditions in whichthe product ions are trapped after charge-transfer collisions were not clear.We observed the slow component of the decay curve of the trapped ionsin Fig. 4.7. This slow decay can not be explained by the charge-transferrate, therefore, we concluded that the TOF measurement is indispensablefor determination of the trapping lifetime of HCIs in the Kingdon ion trap.

Figure 4.9 shows the decay of trapped Arq+(q = 5, 6) ions as a function ofthe storage time in H2 gas at a pressure of 1.24×10−5 Pa. These data are wellfit by a single exponential function. The decay rates of Ar5+ and Ar6+ ionsare determined to be 28(6) s−1 and 67(6) s−1, respectively. Using the peakvelocity vp in Tab. 4.2 and the number density of H2, which was determinedby the ionization gauge with the relative sensitivity α of H2 to N2 (α = 0.44),the charge-transfer cross sections for Ar5+–H2 and Ar6+–H2 are determinedto be 5.2(2.6)×10−15 cm2 and 1.1(0.5)×10−14 cm2, respectively. The values inthe parenthesis show the errors estimated from the uncertainties of the decayrate, vp in Tab. 4.2, and the number density of H2 (nH2). The uncertainty ofnH2 was assumed to be within 40%. As shown in Tab. 4.3, the present crosssection values are consistent with previous experimental data and the valuesestimated using some scaling formula.


Figure 4.8: TOF spectra of ejected ions after (a) 5 ms, (b) 20 ms and (c)50 ms storage time when Ar6+ ions were injected into the Kingdon trap. Thenumber of switching cycles for obtaining the spectrum is 10000. The pressureof H2 gas is 1.24×10−5 Pa.


Figure 4.9: A plot of the extracted Ar5+ and Ar6+ ions as a function ofstorage time at H2 pressure of 1.24×10−5 Pa. The data are well fitted bysingle exponential functions. The decay rate of the Ar5+ and Ar6+ ions aredetermined to be 28±6 s−1 and 67±6 s−1, respectively.


Table 4.3: A summary of charge-transfer cross sections of Arq++H2 reactionsat present binary collision energies in the center-of-mass system (Ecm). Thecross sections σexp are previous values. σK is calculated from the scalingformula by Kimura et al. [58]. σMS is obtained by the well-known scaling for-mula by Muller and Salzborn [57]. σL represents the Langevin cross section.The cross sections are presented in the unit of ×10−15 cm2.

Ion Ecm (eV) this work σexp σMS σK σL

Ar5+ 3.3+2.8−2.5 5.2(2.6) - 4.94 5.46 4.17

Ar6+ 4.0+3.3−3.0 11(5) 13[72] 6.11 6.55 4.56

10[73]

4.5 Trapping Lifetime of Externally Injected

O6+ Ions

As a performance test of the ion trap system, we also measured a trappinglifetime of externally injected O6+ ions produced by the ECRIS at a residualpressure of approximately 4.6×10−7 Pa. Figure 4.10 shows a decay curve ofthe number of O6+ ions detected by the MCP as a function of storage time.By fitting it with an exponential function we obtained a trapping lifetime ofO6+ ions, of 279(14) ms, which is sufficient to observe the forbidden transitionof O6+ ions with a transition lifetime of 0.95 ms.


Figure 4.10: A plot of the number of O6+ ions detected by the MCP as afunction of storage time at H2 pressure of 4.6×10−7 Pa. The data was fittedby an exponential function, and a trapping lifetime of O6+ ions of 279(14) mswas obtained.


4.6 Conclusion

The Kingdon ion trap has been developed with the aim of future labora-tory observation of the X-ray forbidden transitions of metastable O6+ ions.We have succeeded in trapping externally injected Arq+(q = 5, 6) ion beam.The kinetic energy and velocity distributions are investigated by numericalsimulations and the results are consistent with previous analytical expres-sions. As a performance test, we measured trapping lifetimes of the multiplycharged ions under a constant number density of H2 and determined thecharge-transfer cross sections of Arq+(q = 5, 6)–H2 collision systems at bi-nary collision energies of a few eV. Moreover, we also observed a trappinglifetime of O6+ ions at a residual H2 pressure of approximately 4.6×10−7 Paand achieved the lifetime of 279(14) ms which is much longer than a lifetimeof the forbidden transition of interest.

Chapter 5

Forbidden TransitionMeasurements


For the forbidden transition measurements, the ion trap system was installedat the TMU-beamline (Fig. 3.17). The ion trap chamber was located behindthe collision chamber and a silicon drift detector (SDD, Princeton Gamma-Tech Instruments, Inc. Sahara Silicon Drift Detector) was installed at thechamber in order to detect the soft X-rays from the trapped metastable ions.Our SDD is a window-less type, so transmission efficiency need not be takeninto account.

A DC O7+ ion beam current of about 5 nA was obtained from the TMU-ECRIS and injected into the collision cell filled with He gas. The O7+ ions andO6,5+ ions produced by single and double electron captures were injected intothe Kingdon ion trap. By applying to the adequate voltage to the electrodes,the O7+ ions were reflected and O5+ ions produced by double electron capturepassed through the ion trap. We achieved the confinement of only O6+ ionsproduced by single electron capture and ruled out the possibility of detectionof soft X-rays from other ions. During the ion trapping, a fraction of thesoft X-ray emission from the metastable O6+ ions was observed with theSDD. The lifetime of the forbidden 1s2 1S0–1s2s 3S1 transition in O6+ ions is0.95 ms [64, 65], so the observation time for the soft X-rays in a cycle wasset to be 2 ms. Just after the start of the ion trapping, ions in unstabletrajectories are quickly lost in collisions with the trap electrodes. These

81

Chapter 5. Forbidden Transition Measurements 82

collisions cause background emission over broad energy range during theobservations, so the detection of the soft X-rays started after a delay of 100 µsto reduce the background. This delay also prevented observations of the inter-combination 1s2 1S0–1s2p 3P2 transition with a lifetime of 3.0 µs [66]. Aftera pre-determined storage time, the trapped ions were ejected by raising thevoltage applied to the central electrode and a fraction of them was detectedby the MCP. Detection efficiencies of the soft X-rays and the ejected ions werelimited mainly by the solid angles subtended by the detectors. Details of thetrapping timing chart and experimental circuits are shown in Fig. 4.1–4.3.

To check the validity of the forbidden line spectrum, we also observedresonance 1s2–1snp (n = 2–4) transitions in O6+ ions produced by the SWCXof O7+ ions with He gas. In the resonance line measurements, the SDD wasinstalled at the collision chamber and soft X-rays from the collision cell wereobserved at the magic angle of 54.7◦ from the ion beam axis [47].

5.1.1 Energy Calibration of SDD

The energies of observed emission spectra were calibrated by quadratic func-tion using well known transition energies. At first, the Mn Kα and Mn Kβlines from iron-55 which is a radioactive isotope of iron were used for roughcalibration. Moreover, 1s–2p transitions of H-like C and O ions were used formore precise calibration in soft X-ray region. The emission lines used for thecalibration are listed in Tab. 5.1 According to the calibration, we obtained alinear function of

E = 2.135× n+ 2.402

where E and n mean the soft X-ray energy [eV] and SDD channel.

Table 5.1: Relation between SDD channel and X-ray energies for each emis-sion used for the energy calibration.

Elements SDD channel X-ray energy/eVC VI 1s–2p 171 367.5O VIII 1s–2p 305 653.6Mn Kα 2741 5890Mn Kβ 3016 6490


5.2 1s2–1s2s 3S (M1) Transition Measurements

Figure 5.1 shows transition energies and lifetimes of He-like O6+ ion. By usingthe Kingdon ion trap, we trapped O6+ ions produced by charge exchange ofO7+ ions with He gas at a collision energy of 42 keV and observed soft X-rayspectrum with the SDD. Figure 5.2 shows the observed spectrum during theion trapping. A peak energy of 560 eV was obtained by fitting the spectrumto a Gaussian function and it corresponds to the 1s2 1S0–1s2s 3S1 transitionin O6+ ions. The background signals were caused by the detector itself andcollisions of trapped ions with the trap electrodes. As the background signalsare a sum of these effects, the forbidden line spectrum has an asymmetricstructure.

Figure 5.1: A schematic level diagram of the n = 1, 2 in levels of He-likeO6+ ion. The main paths of resonance, inter-combination and forbiddentransitions, their associated transition energies and lifetimes are shown.


5.3 1s2–1s2p 1,3P (E1) Transition Measurement

In Fig. 5.3, the resonance line spectrum from collisions of O7+ ions with Hegas is shown. The spectrum mainly consists of a dominant peak and twosmall peaks. They correspond to the transitions 1s2–1s2p (570 eV), 1s2–1s3p(666 eV), and 1s2–1s4p (698 eV), which can be distinguished by deconvolutionusing Gaussian functions with a full-width at half-maximum of 73 eV foreach line, which corresponds to the energy resolution of the SDD. The 1s2–1s2p transitions might include not only the resonance transition (1s2 1S0–1s2p 1P1), at 574 eV but also the inter-combination transition (1s2 1S0–1s2p 3P1), at 569 eV. The contribution of the inter-combination line cannot beneglected because of its lifetime of nanoseconds and almost similar populationof the 1s2p 3P1 state as that of the 1s2p 1P1 state. We observed a significantand reasonable difference of about 10 eV between each main peak in theforbidden and resonance line spectra.

According to the classical over barrier model [56] and the two-centeratomic orbital close coupling method by Liu et al. [74], the dominant electroncapture level in collisions of O7+ ions with He gas has the principal quantumnumber n = 4. By cascades from the upper to the lower states, the pop-ulations of both 1s2s and 1s2p states become large, and the main emissionlines following the charge exchange are caused by transitions from these twostates to the 1s2 ground state.


Figure 5.2: Soft X-ray emission spectra measured with the SDD during O6+

ion trapping in collisions of O7+ ions with He gas. A peak energy of 560 eVwas obtained by fitting the spectrum to a Gaussian function.


Figure 5.3: Soft X-ray emission spectra measured with the SDD in collisionsof O7+ ions with He gas. This shows that of resonance and inter-combinationtransitions. Dotted lines are the results of the deconvolution using Gaussianfunctions.


5.4 Conclusion

By combining an ion trapping technique with ion beam collision experiments,we made it possible to observe the long-lived forbidden transitions followingcharge exchange collisions of a highly charged ion beam having a velocity ofa few keV/u with neutrals. We succeeded in the laboratory observation ofthe forbidden 1s2 1S0–1s2s 3S1 transition in O6+ ions following the SWCX ofO7+ ions with He gas for the first time.

Chapter 6

Spectroscopy of Inner-ShellExcited Li-like Ions


He-like C, N and O ions with charge number q were produced by the TMU-ECRIS. The 6 mm diameter ion beam with a kinetic energy of 15q keV wasinjected into a collision gas cell filled with various target gases, namely He,Ne, Ar, Kr, Xe, N2, O2 and CO2. The ionization potentials of Ar, Kr and Xeare almost the same as those of N2, CO2 and O2, respectively. The target gaswas admitted into the cell by a variable leak valve connected to gas cylinders.The gas pressure in the cell was kept at 3.0× 10−3–1.0× 10−2 Pa, which wasmeasured by a capacitance manometer. Moreover, a length of the cell is 5.0cm and typical charge transfer cross sections in present collision systems areof the order of 10−15 cm2. Therefore these conditions ensure single collisionsin the present measurements.

The collision cell has an aperture with a diameter of 6 mm to observephoton emissions with a solid angle of ∼7×10−3 sr. Soft X-ray spectrawere measured with a flat-field grazing-incidence spectrometer which con-sists of a gold-plated cylindrical mirror for light focusing, slit of width 50 µm,1200 grooves/mm diffraction grating (SHIMADZU, 30-002) and peltier cooledcharge-coupled device camera (Princeton Instruments, PIXIS-XO: 400B).The spectrometer was installed at the magic angles of 54.74◦ with respect tothe incident ion beam axis. In our experiments, the typical spectral resolu-tion was approximately 0.015 nm and the statistical uncertainty was about

88

Chapter 6. Spectroscopy of Inner-Shell Excited Li-like Ions 89

0.001 nm.The He-like ions produced by an ECRIS are generally in the ground

1s2 1S0 or excited 1s2s 1,3S states [48]. It is well known that the metastablebeam fraction is at least a few percent of the total beam and it depends onthe ion source parameters. According to theoretical calculations [67], transi-tion lifetimes of He-like C, N and O ions in the metastable 1s2s 3S1 state are2.052×10−2, 3.932×10−3 and 9.551×10−4 s and these ions reach the collisioncell with almost no de-excitations. Moreover, a fraction of C4+ ions in themetastable 1s2s 1S0 state also reach the cell under our experimental condi-tions due to its relatively long lifetime of 3.030×10−6 s [66, 68]. Therefore,the C4+ ion beam was a mixture of the 1s2 1S0 and 1s2s 1,3S0, and the N5+

and O6+ ion beams were mixtures of the 1s2 1S and 1s2s 3S1 states. Theirtypical beam currents were approximately 1.5 µA.

6.1.1 Soft X-ray Emission Spectra

A sample of an observed CCD image for the soft X-ray measurement is shownin Fig. 6.1. The photons were dispersed corresponding to their energies, i.e.wavelengths, in the horizontal axis and same wavelength photons spreadin the vertical axis. The toroidal mirror equipped in the GIS converged thelights in both horizontal and vertical direction, so thus photons detected nearcenter for vertical direction on the CCD. The emission spectrum was givenby integration for the converged region and in subtraction of the backgroundusing the non-converged region. Since cosmic rays were also detected, thosepixels of the CCD were substituted by means of the weighted average usingother pixels around the pixels. If it is difficult to make a judgment whetheran emission line or a noise, the judgment has done by confirming the intensityon the CCD image.

6.1.2 Second Order Diffraction

Due to the principle of the diffraction using the grating, a pseudo emissionline may be observed at the wavelength of 2λ when a strong emission linewas observed at λ. This must be taking into account in emission line identi-fications.


Figure 6.1: A sample of the CCD image in collisions of C4+ ions with Xe.

6.1.3 Wavelength Calibration

The wavelengths of observed emission spectra were calibrated by Eq. (3.23)using well known transition wavelengths. The emission lines of He-like C,N and O ions and those second order diffractions for the soft X-ray regionwere used. Table 6.1 shows the calibrated parameters of the GIS and thetransitions used for the calibration are listed in Tab. 6.2. In the presentmeasurements, the Doppler shift should be taken into account and the wave-length shifts of soft X-ray observed from He-like and Li-like C, N and O ionsare shown in Tab. 6.3. The 1s2 1S–1snp 1P transitions of He-like ions andthe 1s22s 1S–1s2s2p 4P transitions of Li-like ions are listed. In the case ofsame elements, there is almost no difference between the shifts in He-like andLi-like ion measurements.

Table 6.1: Calibration parameters of the GIS.d : 840.5 mmα : 86.99 degnl : 19.95 µmy : 16.43 mmb : 233.2 mm


Table 6.2: Emission lines for the wavelength calibration in the soft X-rayregion. λ× 2 means the observed second order diffraction.

C VI–NeIons Transitions Wavelength / nmC V 1s2 1S0–1s3p 1P1 3.497C V 1s2 1S0–1s2p 1P0 4.027C V 1s2 1S0–1s2p 3P1 4.073C V 1s2 1S0–1s3p 1P1 3.497×2C V 1s2 1S0–1s2p 1P0 4.027×2C V 1s2 1S0–1s2p 3P1 4.073×2

N VII–NeN VI 1s2 1S0–1s3p 1P1 2.490N VI 1s2 1S0–1s2p 1P0 2.879N VI 1s2 1S0–1s2p 3P1 2.908N VI 1s2 1S0–1s3p 1P1 2.490×2N VI 1s2 1S0–1s2p 1P0 2.879×2N VI 1s2 1S0–1s2p 3P1 2.908×2

O VIII–O2

O VII 1s2 1S0–1s3p 1P1 1.863O VII 1s2 1S0–1s3p 1P1 1.863×2

Table 6.3: The Doppler shifts of soft X-ray from He-like ions used in thecalibration and the shifts of soft X-ray from Li-like ions observed in thepresent measurements.

Projectile C V C VI N VI N VII O VII O VIIIIon energy / keV 60 75 75 90 90 105Wavelength / nm 4.218 4.027 2.997 2.879 2.238 1.863Shifted wavelength / nm 4.210 4.019 2.991 2.873 2.234 1.659Doppler shift / nm 0.008 0.008 0.006 0.006 0.004 0.004


Figure 6.2: Result of the wavelength calibration in the soft X-ray region.


6.2 Collision Processes

In collisions of metastable He-like ions with neutral targets, the followingprocesses should be considered as dominant reactions.

Pq+(1s2s) + T → P(q−1)+(1s2snl) + T+ (6.1)

→ P(q−2)+(1s2snln’l’) + T2+ (6.2)

→ P(q−1)+(1s2pnl) + T+ (6.3)

→ P(q−2)+(1s2pnln’l’) + T2+ (6.4)

→ P(q−1)+(1s2snl) + T2+ + e- (6.5)

Each process above is referred to as single electron capture (6.1), double elec-tron capture (6.2), single transfer-excitation (6.3), double transfer-excitation (6.4)and transfer ionization (6.5). Transfer-excitation electron capture is accom-panied with projectile excitation [75, 76, 77, 78] and transfer ionization in-volves simultaneous double electron capturer and ionization. In this ex-periment, we consider that the single electron capture and single transfer-excitation contribute observed soft X-ray spectra because of the projectileC4+, N5+ and O6+ ion velocities of 0.449, 0.465 and 0.476 a.u.

According to the classical over-barrier model [56], principal quantumnumbers n of dominant electron capture levels can be easily estimated byusing the charge numbers of projectile ions and ionization potentials of neu-tral targets. Table 6.4 shows ionization potentials of targets and estimateddominant capture levels n for each collision system. In the case of moleculartargets, vertical ionization potentials are used here, because the present col-lision times of a few hundred attoseconds are much shorter than vibrationaltimes of the molecular targets.

6.3 Radiative Decay Processes

In this paper, we focus on radiative transitions of the inner-shell excited1s2s(1,3S)nl and 1s2p(1,3P)nl states, such as resonance, inter-combination1s–np transitions and two-electron one-photon (TEOP) transitions. TheTEOP transitions are simultaneous transitions of two electrons followed bysingle photon emission, which have been theoretically and experimentallystudied [79, 80].

In order to identify observed emission lines, we referred to calculated


Table 6.4: List of ionization potential values of neutral targets and principalquantum numbers n of dominant capture levels in collisions of He-like C, Nand O ions with He, Ne, Ar, Kr, Xe, N2, CO2 and O2 estimated by using theclassical over-barrier model. The potentials of the molecular targets showvertical ionization potentials.

Target He Ne Ar N2 Kr CO2 O2 XeIp (eV) 24.59 21.56 15.76 15.60 14.00 13.78 12.30 12.13

C4+ 2.4 2.5 2.9 3.0 3.1 3.1 3.3 3.4N5+ 2.8 3.0 3.5 3.6 3.8 3.8 4.0 4.0O6+ 3.3 3.5 4.1 4.1 4.4 4.4 4.6 4.7

results by Goryaev et al. [81] They had calculated radiative decay rates andtransition energies for doubly excited 1s2l2l’ and 1s2l3l’ states of Li-likeions with atomic numbers Z = 6–36 by using the MZ code based on the Z-expansion method. Furthermore, we calculated radiative transition energiesand gA values of 1s2lnl’ (n = 2–5) states of Li-like C, N and O ions by usingCowan’s suite of atomic structure codes [59]. Tabs. 6.5, 6.6 and 6.7 showsummaries of experimental and theoretical results.


Table 6.5: List of wavelengths, radiative rates, Auger rates and branchingratios of transitions of inner-shell excited C3+ ions. The currently observed,calculated and previously reported values are shown in units of nm and s−1.Line no. corresponds to emission line numbers in Fig. 6.3. ∆λ indicatesthe difference between the calculated and reported wavelengths. Numbers inparentheses indicate the powers of 10 by which the entries are to be multi-plied.

Line no. λexp Lower Upper λcalc Acalc λrad rep [81] Arad rep [81] ∆λ AAug rep [81] BR [81]

1 3.637 1s22s 2S1/2 1s2s(1S)3p 2P3/2 3.624 2.24(+11) 3.636 8.89(+10) -0.012 8.64(+11) 8.67(-2)1s22s 2S1/2 1s2s(1S)3p 2P1/2 3.624 1.12(+11) 3.636 8.90(+10) -0.012 8.68(+11) 8.65(-2)

2 3.688 1s22s 2S1/2 1s2s(3S)3p 4P3/2 3.691 6.09(+6) 3.687 1.06(+7) 0.004 1.03(+8) 3.78(-2)1s22s 2S1/2 1s2s(3S)3p 4P1/2 3.691 1.21(+6) 3.687 3.22(+6) 0.004 3.73(+7) 1.57(-2)1s22s 2S1/2 1s2s(3S)3p 2P1/2 3.679 3.18(+11) 3.690 1.05(+11) -0.011 1.11(+12) 8.43(-2)1s22s 2S1/2 1s2s(3S)3p 2P3/2 3.680 6.36(+11) 3.690 1.05(+11) -0.010 1.11(+12) 8.41(-2)1s22p 2P1/2 1s2p(3P)3p 2S1/2 3.691 1.34(+11) 3.691 5.72(+10) 0.000 1.10(+12) 3.87(-2)1s22p 2P3/2 1s2p(3P)3p 2S1/2 3.691 2.69(+11) 3.691 1.14(+11) 0.000 1.10(+12) 7.73(-2)

3 3.716 1s22p 2P1/2 1s2p(3P)3p 2P1/2 3.721 8.19(+10) 3.713 6.46(+10) 0.008 6.09(+7) 3.97(-1)1s22p 2P1/2 1s2p(3P)3p 2P3/2 3.721 1.62(+11) 3.713 1.62(+10) 0.008 1.22(+7) 9.99(-2)1s22p 2P3/2 1s2p(3P)3p 2P1/2 3.722 3.97(+11) 3.713 3.15(+10) 0.009 6.09(+7) 1.94(-1)1s22p 2P3/2 1s2p(3P)3p 2P3/2 3.722 7.92(+10) 3.713 7.89(+10) 0.009 1.22(+7) 4.85(-1)1s22p 2P1/2 1s2p(3P)3p 4D3/2 3.726 1.94(+7) 3.714 1.64(+8) 0.012 2.70(+7) 7.89(-3)1s22p 2P1/2 1s2p(3P)3p 4D1/2 3.726 6.29(+7) 3.714 2.55(+8) 0.012 2.24(+5) 1.26(-2)1s22p 2P3/2 1s2p(3P)3p 4D3/2 3.727 7.55(+7) 3.714 6.13(+8) 0.013 2.70(+7) 2.95(-2)1s22p 2P3/2 1s2p(3P)3p 4D1/2 3.727 3.09(+7) 3.714 1.35(+8) 0.013 2.24(+5) 6.66(-3)

4† 4.006 ∗1s23p 2P3/2 1s2s(3S)4d 2D1/2 4.008 1.24(+9)∗1s23p 2P3/2 1s2s(3S)4d 2D3/2 4.008 2.51(+9)∗1s23p 2P1/2 1s2s(3S)4d 2D5/2 4.008 2.21(+9)

5‡ 4.030 1s23d 2D3/2 1s2p(1P)3d 2P3/2 4.031 3.42(+11) 4.020 8.12(+10) 0.011 9.07(+10) 8.65(-2)1s23d 2D5/2 1s2p(1P)3d 2P3/2 4.031 3.10(+12) 4.020 7.35(+11) 0.011 9.07(+10) 7.83(-1)1s23d 2D3/2 1s2p(1P)3d 2P1/2 4.031 1.72(+12) 4.020 8.17(+11) 0.011 9.17(+10) 8.68(-1)∗1s23s 2S1/2 1s2p(1P)3d 2P1/2 4.039 2.34(+11) 4.024 8.78(+10) 0.015 2.43(+10) 6.78(-1)∗1s23s 2S1/2 1s2p(1P)3d 2P3/2 4.039 4.78(+11) 4.024 8.93(+10) 0.015 2.37(+10) 6.84(-1)

6 4.046 1s23s 2S1/2 1s2p(1P)3s 2P1/2 4.044 4.84(+11) 4.045 6.36(+11) 0.001 5.52(+12) 1.03(-1)1s23s 2S1/2 1s2p(1P)3s 2P3/2 4.044 1.02(+12) 4.045 6.37(+11) 0.001 5.35(+12) 1.06(-1)1s23p 2P1/2 1s2p(1P)3p 2P3/2 4.051 4.82(+11) 4.047 1.09(+11) 0.004 7.98(+10) 1.05(-1)1s23p 2P3/2 1s2p(1P)3p 2P3/2 4.051 2.88(+12) 4.047 7.32(+11) 0.004 7.98(+10) 7.09(-1)1s23p 2P1/2 1s2p(1P)3p 2P1/2 4.051 1.14(+12) 4.047 5.65(+11) 0.004 9.45(+5) 5.92(-1)1s23p 2P3/2 1s2p(1P)3p 2P1/2 4.051 5.43(+11) 4.047 2.77(+11) 0.004 9.45(+5) 2.90(-1)1s23p 2P1/2 1s2p(1P)3p 2D3/2 4.052 4.82(+11) 4.048 6.20(+11) 0.004 2.10(+13) 2.85(-2)1s23p 2P3/2 1s2p(1P)3p 2D3/2 4.052 4.02(+11)1s23p 2P3/2 1s2p(1P)3p 2D5/2 4.052 4.33(+12) 4.048 7.08(+11) 0.004 2.08(+13) 3.28(-2)

7‡ 4.083 1s22s 2S1/2 1s2s(3S)2p 2P3/2 4.075 2.97(+11) 4.086 8.00(+10) -0.011 5.76(+13) 1.39(-3)1s22s 2S1/2 1s2s(3S)2p 2P1/2 4.075 1.52(+11) 4.086 7.71(+10) -0.011 5.78(+13) 1.33(-3)1s23d 2D5/2 1s2p(3P)3d 2F7/2 4.085 2.68(+7) 4.079 8.77(+10) 0.006 2.64(+10) 6.94(-1)1s23d 2D3/2 1s2p(3P)3d 2F5/2 4.085 5.47(+7) 4.079 8.33(+10) 0.006 2.36(+10) 6.64(-1)1s23d 2D5/2 1s2p(3P)3d 2F5/2 4.085 1.35(+8) 4.079 6.57(+9) 0.006 2.36(+10) 5.23(-2)1s23d 2D5/2 1s2p(3P)3d 2D5/2 4.103 4.74(+10) 4.085 1.01(+9) 0.018 4.23(+6) 9.46(-2)1s23d 2D3/2 1s2p(3P)3d 2D3/2 4.103 3.04(+10) 4.085 1.07(+9) 0.018 1.07(+9) 9.16(-2)∗1s23s 2S1/2 1s2s(1S)3p 2P3/2 4.091 1.08(+11) 4.086 3.55(+10) 0.005 8.64(+11) 3.46(-2)∗1s23s 2S1/2 1s2s(1S)3p 2P1/2 4.091 5.10(+10) 4.086 3.43(+10) 0.005 8.68(+11) 3.33(-2)

8 4.137 1s22s 2S1/2 1s2s(1S)2p 2P1/2 4.139 1.42(+12) 4.134 7.19(+11) 0.005 7.26(+12) 9.01(-2)1s22s 2S1/2 1s2s(1S)2p 2P3/2 4.139 2.86(+12) 4.134 7.16(+11) 0.005 7.51(+12) 8.70(-2)1s22p 2P1/2 1s2p(3P)2p 2P3/2 4.143 7.32(+11) 4.139 1.91(+11) 0.004 1.28(+10) 1.59(-1)1s22p 2P3/2 1s2p(3P)2p 2P3/2 4.143 3.93(+12) 4.139 9.96(+11) 0.004 1.28(+10) 8.30(-1)1s22p 2P1/2 1s2p(3P)2p 2P1/2 4.143 1.56(+12) 4.139 7.93(+11) 0.004 8.38(+6) 6.68(-1)1s22p 2P3/2 1s2p(3P)2p 2P1/2 4.143 7.73(+11) 4.139 3.94(+11) 0.004 8.38(+6) 3.32(-1)

9 4.218 1s22s 2S1/2 1s2s2p 4P3/2 4.227 7.47(+6) 4.213 4.64(+6) 0.014 7.30(+6) 3.85(-1)1s22s 2S1/2 1s2s2p 4P1/2 4.227 1.49(+6) 4.213 1.75(+6) 0.014 2.29(+6) 4.23(-1)

∗ Transitions with the asterisk symbol indicate TEOP transitions.† This line derives from the TEOP transitions.‡ These lines include the contribution of the TEOP transitions.


Table 6.6: List of wavelengths, radiative rates, Auger rates and branchingratios of transitions of inner-shell excited N4+ ions. Meanings of each symbolare described in Tab. 6.5. Line no. corresponds to emission line numbers inFig. 6.4.

Line no. λexp Lower Upper λcalc Acalc λrad rep [81] Arad rep [81] ∆λ AAug rep [81] BR [81]

1 2.505 1s22s 2S1/2 1s2s(3S)4p 2P1/2 2.503 2.87(+11)1s22s 2S1/2 1s2s(3S)4p 2P3/2 2.503 5.74(+11)1s22s 2S1/2 1s2s(3S)4p 4P3/2 2.506 1.84(+7)1s22s 2S1/2 1s2s(3S)4p 4P1/2 2.506 3.63(+6)

2 2.607 1s22s 2S1/2 1s2s(3S)3p 4P3/2 2.606 3.74(+7) 2.605 1.69(+8) 0.001 8.72(+8) 1.11(-1)1s22s 2S1/2 1s2s(3S)3p 4P1/2 2.606 7.37(+6) 2.605 5.55(+7) 0.001 3.14(+8) 6.79(-2)1s22s 2S1/2 1s2s(3S)3p 2P1/2 2.599 1.32(+12) 2.606 2.17(+11) -0.007 1.19(+12) 1.47(-1)1s22s 2S1/2 1s2s(3S)3p 2P3/2 2.599 6.59(+11) 2.606 2.17(+11) -0.007 1.20(+12) 1.47(-1)1s22p 2P1/2 1s2p(3P)3p 2S1/2 2.607 2.82(+11) 2.607 1.22(+11) 0.000 1.23(+12) 6.06(-2)1s22p 2P3/2 1s2p(3P)3p 2S1/2 2.607 5.66(+11) 2.607 2.42(+11) 0.000 1.23(+12) 1.21(-1)

3† 2.834 ∗1s23s 2S1/2 1s2s(3S)4p 2P1/2 2.828 1.68(+10)∗1s23s 2S1/2 1s2s(3S)4p 2P3/2 2.828 3.33(+10)∗1s23s 2S1/2 1s2s(3S)4p 4P3/2 2.832 6.65(+5)∗1s23s 2S1/2 1s2s(3S)4p 4P1/2 2.832 1.33(+4)

4‡ 2.919 1s22s 2S1/2 1s2s(3S)2p 2P1/2 2.909 3.24(+11) 2.915 1.66(+11) -0.006 6.46(+13) 2.56(-3)1s22s 2S1/2 1s2s(3S)2p 2P3/2 2.909 6.21(+11) 2.915 1.56(+11) -0.006 6.51(+13) 2.38(-3)∗1s23s 2S1/2 1s2s(1S)3p 2P3/2 2.918 2.28(+11) 2.915 6.53(+10) 0.003 4.98(+11) 7.97(-2)∗1s23s 2S1/2 1s2s(1S)3p 2P1/2 2.918 1.04(+11) 2.915 6.11(+10) 0.003 4.95(+11) 7.52(-2)∗1s23p 2P1/2 1s2s(1S)3d 2D3/2 2.914 2.78(+10) 2.916 2.28(+11) -0.002 3.69(+10) 6.21(-1)∗1s23p 2P3/2 1s2s(1S)3d 2D5/2 2.914 2.50(+10) 2.916 2.67(+11) -0.002 9.29(+10) 6.48(-1)∗1s23p 2P3/2 1s2s(1S)3d 2D3/2 2.914 3.30(+9) 2.916 4.65(+10) -0.002 3.69(+10) 1.27(-1)1s23d 2D5/2 1s2p(3P)3d 2D5/2 2.926 1.06(+11) 2.918 5.44(+9) 0.008 3.24(+7) 1.85(-1)1s23d 2D3/2 1s2p(3P)3d 2D3/2 2.926 6.80(+10) 2.918 5.58(+9) 0.008 1.44(+9) 1.83(-1)1s23d 2D5/2 1s2p(3P)3d 4D7/2 2.920 6.87(+7) 2.923 5.00(+7) -0.003 1.79(+8) 2.08(-1)1s23d 2D3/2 1s2p(3P)3d 4D5/2 2.920 4.78(+6) 2.923 6.52(+7) -0.003 1.15(+8) 3.24(-1)1s23d 2D5/2 1s2p(3P)3d 4D5/2 2.920 2.55(+7) 2.923 1.17(+7) -0.003 1.15(+8) 5.82(-2)1s23d 2D3/2 1s2p(3P)3d 4D3/2 2.920 2.06(+7) 2.923 4.70(+7) -0.003 3.26(+7) 5.22(-1)1s23d 2D5/2 1s2p(3P)3d 4D3/2 2.920 2.09(+7) 2.923 6.42(+6) -0.003 3.26(+7) 7.12(-2)

5 2.948 1s22s 2S1/2 1s2s(1S)2p 2P3/2 2.946 5.96(+12) 2.943 1.49(+12) 0.003 6.82(+12) 1.79(-1)1s22s 2S1/2 1s2s(1S)2p 2P1/2 2.946 2.97(+12) 2.944 1.48(+12) 0.002 7.27(+12) 1.69(-1)1s22p 2P1/2 1s2p(3P)2p 2P3/2 2.949 1.51(+12) 2.947 3.88(+11) 0.002 3.40(+10) 1.56(-1)1s22p 2P3/2 1s2p(3P)2p 2P3/2 2.949 8.26(+12) 2.948 2.06(+12) 0.001 3.40(+10) 8.30(-1)1s22p 2P1/2 1s2p(3P)2p 2P1/2 2.949 3.28(+12) 2.948 1.64(+12) 0.001 4.99(+7) 6.69(-1)1s22p 2P3/2 1s2p(3P)2p 2P1/2 2.950 1.61(+12) 2.948 8.12(+11) 0.002 4.99(+7) 3.31(-1)

6 2.997 1s22s 2S1/2 1s2s2p 4P3/2 3.001 4.59(+7) 2.995 2.39(+7) 0.006 3.97(+7) 3.75(-1)1s22s 2S1/2 1s2s2p 4P1/2 3.001 9.12(+6) 2.995 9.14(+6) 0.006 6.18(+5) 9.27(-1)

∗ Transitions with the asterisk symbol indicate TEOP transitions.† This line derives from the TEOP transitions.‡ This line includes the contribution of the TEOP transitions.


Table 6.7: List of wavelengths, radiative rates, Auger rates and branchingratios of transitions of inner-shell excited O5+ ions. Meanings of each sym-bol are described in Tab. 6.5. In this table, λexp means wavelengths of theobserved second-order diffracted lights and hence λexp/2 indicates true wave-lengths of the observed transitions. Line no. corresponds to emission linenumbers in Fig. 6.6.

Line no. λexp λexp/2 Lower Upper λcalc Acalc λrad rep [81] Arad rep [81] ∆λ AAug rep [81] BR [81]

1‡ 3.826 1.913 ∗1s22s 2S1/2 1s2p(3P)3s 2P3/2 1.910 8.45(+10) 1.910 5.97(+9) 0.000 3.01(+13) 1.96(-4)∗1s22s 2S1/2 1s2p(3P)3s 2P1/2 1.910 4.53(+10) 1.910 6.19(+9) 0.000 2.97(+13) 2.05(-4)1s22s 2S1/2 1s2s(1S)3p 2P3/2 1.916 1.35(+12) 1.917 3.44(+11) -0.001 2.93(+11) 3.95(-1)1s22s 2S1/2 1s2s(1S)3p 2P1/2 1.916 6.75(+11) 1.917 3.45(+11) -0.001 2.82(+11) 4.06(-1)

2 3.876 1.938 1s22s 2S1/2 1s2s(3S)3p 4P3/2 1.938 7.54(+9) 1.937 2.34(+9) 0.001 7.09(+9) 2.11(-1)1s22s 2S1/2 1s2s(3S)3p 4P1/2 1.938 1.31(+9) 1.937 9.07(+8) 0.001 2.86(+9) 1.83(-1)1s22s 2S1/2 1s2s(3S)3p 2P1/2 1.937 9.33(+11) 1.938 4.01(+11) -0.001 1.26(+12) 2.26(-1)1s22s 2S1/2 1s2s(3S)3p 2P3/2 1.937 1.87(+12) 1.938 4.00(+11) -0.001 1.27(+12) 2.25(-1)1s22p 2P1/2 1s2p(3P)3p 2S1/2 1.939 5.27(+11) 1.938 2.30(+11) 0.001 1.35(+12) 8.24(-2)1s22p 2P3/2 1s2p(3P)3p 2S1/2 1.939 1.06(+12) 1.938 4.56(+11) 0.001 1.35(+12) 1.63(-1)

3 3.901 1.950 1s22p 2P1/2 1s2p(3P)3p 2P1/2 1.951 6.17(+11) 1.949 2.55(+11) 0.002 3.54(+8) 4.12(-1)1s22p 2P1/2 1s2p(3P)3p 2P3/2 1.951 3.12(+11) 1.949 6.52(+10) 0.002 2.64(+8) 1.05(-1)1s22p 2P3/2 1s2p(3P)3p 2P1/2 1.952 2.91(+11) 1.950 1.21(+11) 0.002 3.54(+8) 1.96(-1)1s22p 2P3/2 1s2p(3P)3p 2P3/2 1.952 1.44(+12) 1.950 3.04(+11) 0.002 2.64(+8) 4.90(-1)1s22p 2P1/2 1s2p(3P)3p 4D3/2 1.954 4.55(+8) 1.950 1.26(+9) 0.004 3.31(+8) 1.34(-2)1s22p 2P1/2 1s2p(3P)3p 4D1/2 1.954 1.39(+9) 1.950 2.73(+9) 0.004 2.43(+5) 2.96(-2)1s22p 2P3/2 1s2p(3P)3p 4D3/2 1.954 1.66(+9) 1.950 4.26(+9) 0.004 3.31(+8) 4.51(-2)1s22p 2P3/2 1s2p(3P)3p 4D1/2 1.954 6.62(+8) 1.950 1.39(+9) 0.004 2.43(+5) 1.51(-2)

4 4.334 2.167 1s23d 2D3/2 1s2p(1P)3d 2F5/2 2.165 1.57(+13) 2.165 2.56(+12) 0.000 7.69(+12) 2.41(-1)1s23d 2D5/2 1s2p(1P)3d 2F5/2 2.165 1.29(+12) 2.165 2.50(+11) 0.000 7.69(+12) 2.35(-2)1s23d 2D5/2 1s2p(1P)3d 2F7/2 2.165 2.27(+13) 2.165 2.82(+12) 0.000 7.70(+12) 2.65(-1)1s23d 2D3/2 1s2p(1P)3d 2D7/2 2.167 1.52(+12) 2.166 2.85(+11) 0.001 1.12(+10) 8.40(-2)1s23d 2D5/2 1s2p(1P)3d 2D5/2 2.167 1.86(+13) 2.166 2.99(+12) 0.001 1.12(+10) 8.81(-1)1s23d 2D3/2 1s2p(1P)3d 2D3/2 2.167 1.21(+13) 2.166 2.96(+12) 0.001 2.83(+3) 8.74(-1)1s23d 2D5/2 1s2p(1P)3d 2D3/2 2.168 1.29(+12) 2.166 3.20(+11) 0.002 2.83(+3) 9.45(-2)1s23s 2S1/2 1s2p(1P)3s 2P1/2 2.167 5.33(+12) 2.167 2.40(+12) 0.000 7.44(+12) 2.40(-1)1s23s 2S1/2 1s2p(1P)3s 2P3/2 2.167 1.07(+13) 2.167 2.41(+12) 0.000 7.01(+12) 2.51(-1)1s23p 2P1/2 1s2p(1P)3p 2P3/2 2.169 9.87(+11) 2.168 2.43(+11) 0.001 7.05(+11) 5.75(-2)1s23p 2P3/2 1s2p(1P)3p 2P3/2 2.169 1.14(+13) 2.168 2.86(+12) 0.001 7.05(+11) 6.75(-1)1s23p 2P1/2 1s2p(1P)3p 2P1/2 2.169 4.30(+12) 2.168 2.12(+12) 0.001 9.93(+3) 5.96(-1)1s23p 2P3/2 1s2p(1P)3p 2P1/2 2.169 1.93(+12) 2.169 1.00(+12) 0.000 9.93(+3) 2.82(-1)1s23p 2P1/2 1s2p(1P)3p 2D3/2 2.169 9.81(+12) 2.169 2.42(+12) 0.000 2.73(+13) 8.09(-2)1s23p 2P3/2 1s2p(1P)3p 2D5/2 2.169 1.58(+13) 2.169 2.59(+12) 0.000 2.73(+13) 8.65(-2)

5‡ 4.371 2.185 1s22s 2S1/2 1s2s(3S)2p 2P3/2 2.181 1.25(+12) 2.184 2.80(+11) -0.003 7.09(+13) 3.93(-3)1s22s 2S1/2 1s2s(3S)2p 2P1/2 2.181 6.67(+11) 2.184 3.10(+11) -0.003 7.01(+13) 4.40(-3)∗1s23s 2S1/2 1s2s(1S)3p 2P3/2 2.185 4.28(+11) 2.184 1.11(+11) 0.001 2.93(+11) 1.28(-1)∗1s23s 2S1/2 1s2s(1S)3p 2P1/2 2.186 1.86(+11) 2.185 9.96(+10) 0.001 2.82(+11) 1.17(-1)∗1s23p 2P1/2 1s2s(1S)3d 2D3/2 2.184 7.20(+10) 2.185 4.30(+11) -0.001 6.46(+10) 6.23(-1)∗1s23p 2P3/2 1s2s(1S)3d 2D5/2 2.184 6.09(+10) 2.185 4.93(+11) -0.001 2.23(+11) 6.07(-1)∗1s23p 2P3/2 1s2s(1S)3d 2D3/2 2.184 8.65(+9) 2.185 8.82(+10) -0.001 6.46(+10) 1.28(-1)1s23d 2D5/2 1s2p(3P)3d 2D5/2 2.192 2.04(+11) 2.187 1.49(+10) 0.005 1.01(+8) 2.25(-1)1s23d 2D3/2 1s2p(3P)3d 2D3/2 2.192 1.33(+11) 2.187 1.53(+10) 0.005 2.56(+9) 2.29(-1)

6 4.416 2.208 1s22s 2S1/2 1s2s(1S)2p 2P3/2 2.203 1.10(+13) 2.202 2.76(+12) 0.001 6.42(+12) 3.01(-1)1s22s 2S1/2 1s2s(1S)2p 2P1/2 2.203 5.44(+12) 2.202 2.73(+12) 0.001 7.15(+12) 2.76(-1)1s22p 2P1/2 1s2p(3P)2p 2P3/2 2.206 2.74(+12) 2.205 7.01(+11) 0.001 8.02(+10) 1.52(-1)1s22p 2P3/2 1s2p(3P)2p 2P3/2 2.206 1.54(+13) 2.205 3.83(+12) 0.001 8.02(+10) 8.31(-1)1s22p 2P1/2 1s2p(3P)2p 2P1/2 2.206 6.12(+12) 2.205 3.04(+12) 0.001 1.90(+8) 6.70(-1)1s22p 2P3/2 1s2p(3P)2p 2P1/2 2.206 2.97(+12) 2.206 1.50(+12) 0.000 1.90(+8) 3.30(-1)

7 4.477 2.238 1s22s 2S1/2 1s2s2p 4P3/2 2.241 2.10(+8) 2.237 9.85(+7) 0.004 1.39(+8) 4.15(-1)1s22s 2S1/2 1s2s2p 4P1/2 2.241 4.16(+7) 2.237 3.78(+7) 0.004 6.12(+5) 9.82(-1)

∗ Transitions with the asterisk symbol indicate TEOP transitions.‡ These lines include the contribution of the TEOP transitions.


6.4 Soft X-ray Spectra for Each Collision Sys-

tem

C4+ Ion Experiments

Figure 6.3 shows soft X-ray spectra observed in collisions of metastable C4+

ions with rare gas and molecular targets. Many other emission lines werealso observed at much longer wavelengths which are due to collisions of theground 1s2 1S0 state. In this paper, we focus on only soft X-ray emissionderived from the metastable states. The observed spectral lines are labeledas 1–9 and detailed information of each line is listed in Tab. 6.5. In commonto all of the spectra, prominent emission lines at wavelength of 3.688(2),4.083(7‡), 4.137(8) and 4.218(9) nm were observed (superscripts indicate lineno. shown in Tab. 6.5 and Fig. 6.3). According to the calculated results, theycorrespond to the 1s–3p transitions of the 1s2s(3S)3p and 1s2p(3P)3p statesand the 1s–2p transitions of the 1s2s(1,3S)2p, 1s2p(3P)2p and 1s2p(3P)3dstates of C3+ ions. Moreover, the TEOP transitions of the 1s2s(1S)3p statesalso contribute to the line at 4.083(7‡) nm. Additionally, relatively weak lineswere also observed at wavelengths of 3.637(1), 3.716(3), 4.006(4†), 4.030(5‡)

and 4.046(6) nm especially on the Xe target. The emission lines at 3.637(1)

and 3.716(3) nm are due to the 1s–3p transitions following electron captureand transfer-excitation in collisions of the 1s2s 1S state, respectively. Theselines are derived from the mixing of the ion beams with singlet and tripletmetastable states and therefore they were observed only on the C4+ ionexperiments. Some of these weak lines were also observed on the He and Netargets, but on the other targets they were significantly weaker or negligible.

Before the experiments, we had expected that observed emission spectrawould depend on the ionization potentials of the different targets. In fact,the observed spectra on the rare gas targets show different spectral featuresdepending on the electron capture levels. On the other hand, the spectra withthe molecular gas targets show similar features, and differences between thespectra from collisions with the heavy rare gas and molecular targets arefound in spite of their similar ionization potentials. For example, the relativeintensities of each observed line depend on the choice of Ar, Kr or Xe targets,while those on the N2, CO2 and O2 targets are almost the same, as can beclearly seen in Fig. 6.3.

It is well known that the double electron capture is dominant in collisions


of C4+ ions with He target at collision energy less than 2.5 keV/u [82, 83].However, in the present collision energy of 5.0 keV/u, the single electroncapture dominants over the double electron capture and therefore the C3+

ions is a main emission source in this measurements.In the He target spectrum, the relative intensities of the 1s2s(3,1S)2p 2P

lines (line no. 7, 8) are higher than that of the 1s2s2p 4P line (line no. 9).Strohschein et al. published a paper showing enhancements for the metastable1s2s2p 4P state following single and double electron capture in collisions ofHe-like and H-like C ions with He and Ne targets [22], but the present spec-trum is different from their Auger emission spectrum. This might be dueto branching ratios of autoionization to radiation in each 1s2s2p state andthe observation efficiency of the 1s2s2p 4P transition. The lifetime of the1s2s2p 4P state of C3+ ions is approximately 10−6 s (Tab. 6.5). It is muchlonger than a flight time of the ions to pass by the detection area of our setup(∼6×10−9 s). Therefore, the observation efficiency of the 1s2s2p 4P state islower than those of other states with very short lifetimes. In the present C4+

+ He measurement, the line intensity of the 1s22s–1s2s2p 4P transition wasrelatively small and new lines were also observed at 3.716(3) and 4.030(5‡) nm.The former corresponds to the 1s–2p transitions of the 1s2p(1P)3s state andthe latter corresponds to the 1s–2p and TEOP transitions of the 1s2p(1P)3dstate.

For collisions with the Xe targets, additional emission lines at wavelengthsof 3.637(1), 4.006(4†) and 4.046(6) nm were observed in addition to the lines asobserved on the He target. Each line corresponds to the 1s–3p transition fromthe 1s2s(1S)3p state, the TEOP transition from the 1s2s(3S)4d state and the1s–2p transition from the 1s2p(1P)3s and 1s2p(1P)3p states, respectively.

The relative intensity of the TEOP line at 4.006(4†) nm increases withincreasing atomic number of the rare gas targets, which is equivalent todecreasing of the ionization potentials of these targets. This arises becausethe observed TEOP transition needs electron capture into a high energylevel, that indicates the 4d subshell. However, a significant difference in itsline intensity between the spectra on the Xe and O2 targets was observed inspite of their similar ionization potentials. This might be due to the spin-orbit interaction present in the heavy atomic gas targets. In the potentialcurve crossing model, the initial and final channels are approximated by the


polarization potential and Coulomb potential as below,

Vinitial(R) ≈ −α′q2

2R4(6.6)

Vfinal(R) ≈ +(q − s)s

R−Q (6.7)

where α′ is the polarizability volume, R is the internuclear distance betweenthe projectile ion and target atom, q is the charge of the projectile, s isthe number of the captured electrons, and Q is the energy balance for eachreaction. The spin-orbit interaction induces splitting fine structure. Forexample, the energy differences between outermost np5 2P3/2 and np5 2P1/2

levels for Ar+, Kr+ and Xe+ ions are 0.178, 0.666 and 1.306 eV. This leadsto different crossing points of the potential curves between initial and finalchannels in contrast with He and Ne.

In addition, differences of polarizabilities of the targets might induce thespectral changes. It has been demonstrated that relativistic effects increasepolarizabilities of heavy rare gases [84, 85]. In the present case, Xe has signifi-cant polarizability and there is a large difference between those of Xe and O2,namely 4.044 and 1.598 A3, respectively [86, 87]. Therefore, the differencesof the polarizabilities of the targets also induce the different electron capturelevels even if the targets have similar ionization potential values. There maybe other possible causes but the details are not understood yet.

N5+ Ion Experiments

Figure 6.4 shows emission spectra observed in collisions of metastable N5+

ions with several neutral targets. Prominent transitions are the same asthose observed in the C4+ ion experiments (line no. 2, 4–6 in Fig. 6.4). Theemission lines at 2.919(4‡), 2.948(5) and 2.997(6) nm are due to the 1s–2p ofthe 1s2s2p 2,4P, 1s2p(3P)2p and 1s2p(3P)3d states and the TEOP transitionsof the 1s2s(1S)3d. Unlike the carbon ion spectra, the 1s2s2p 4P line is thestrongest regardless of its long lifetime. This might be due to an increasingbranching ratio of the radiative 1s22s–1s2s2p 4P transition and a shorteningof the lifetime of the 1s2s2p 4P state. This branching ratio increases in theorder of C3+, N4+ and O5+ ions [88] and thus the relative line intensity of thequartet state increases in the same order. The emission line at 2.607(2) nmcorresponds to the 1s–3p transitions from the 1s2s(3S)3p 2,4P and 1s2p(3P)3p


states. The relative intensity of this line depends significantly on the targetgas because of the difference of the dominant electron capture levels.

Among the molecular targets, small differences on line intensity ratiosare found, but spectral differences are significant between the Xe and O2

gas targets. A weak emission line at 2.505(1) nm was observed only on theXe target, which is due to the 1s–4p transitions from the 1s2s(3S)4p state.Moreover, an emission line at 2.834(3†) nm was clearly observed on the heavyrare gas Xe collisions. This line corresponds to the TEOP transitions of the1s23s–1s2s(3S)4p. However, these two lines were not observed with the O2

target in spite of the similar ionization potentials.

O6+ Ion Experiments

Figure 6.5 shows observed spectra in collisions of metastable O6+ ions withHe and Xe targets in the wavelength region of 1.5–5 nm. The four first-orderdiffraction lines are resolved into seven second-order diffraction lines. In thepresent O6+ ion experiments, we focus on the second-order spectrum for clearseparation of lines. Hence, wavelengths of the observed lines are exactly twotimes longer than the true transition wavelengths.

Figure 6.6 shows soft X-ray spectra observed in collisions of metastableO6+ ions with eight neutral targets. Prominent emission lines at 4.371(5‡),4.416(6) and 4.477(7) nm are due to the 1s–2p transitions of the 1s2s(1,3S)2p 2,4P,1s2p(3P)2p and 1s2p(3P)3d states and the TEOP transitions of the 1s2s(1S)3dstates. Strong 1s–np (n ≥ 3) lines had been expected to be observed due tothe high dominant electron capture levels. In fact, for the rare gas targets,both the 1s–3p transitions were observed, but on the molecular targets, theyare almost negligible. This means that the dominant capture levels are thehighest angular momentum states and yrast transitions might be dominantin the molecular target cases.

Additionally, four emission lines at 3.826(1†), 3.876(2), 3.901(3) and 4.334(4) nmwere also observed for collisions on the rare gas targets. According to thetheoretical calculations, the first three lines correspond to the 1s–3p transi-tions of the 1s2s(1,3S)3p and 1s2p(3P)3p states, and the TEOP transitions ofthe 1s2p(3P)3s states. The fourth line corresponds to the 1s–2p transitionsof the 1s2p(1P)3l states. Unlike the C4+ and N5+ ion experiments, distinctTEOP lines derived from the 1s2s(3S)4l states were not observed. The emis-sion line at 4.334(4) nm were observed only on the rare gas targets and itsrelative intensity depends on the choice of targets.


Gu et al. observed the same emission line from O5+ ions at 2.1672 nmby using an EBIT and GIS and identified it as the 1s23s–1s2p3d and 1s23d–1s2p3d transitions with the wavelengths of 2.1600 and 2.1763 nm [89]. How-ever, our calculated results and the previously reported calculations [81]show that this line is due to only the resonance 1s–2p transitions from the1s2p(1P)3l states produced by the transfer-excitation, and this identificationis in better agreement with the experimental data.


Figure 6.3: Soft X-ray spectra in collisions of metastable C4+ ions with raregas (left) and molecular (right) gas targets at collision energy of 60 keV. Theresolved emission lines labeled as 1–9 are listed in Tab. 6.5.


Figure 6.4: Soft X-ray spectra in collisions of metastable N5+ ions with raregas (left) and molecular (right) gas targets at collision energy of 75 keV. Theresolved emission lines labeled as 1–6 are listed in Tab. 6.6.


Figure 6.5: Soft X-ray spectra in collisions of metastable O6+ ions with He(upper) and Xe (lower) targets at collision energy of 90 keV. These includeboth the first and second-order diffraction lines. The four first-order linesare separated into the seven second-order lines.


Figure 6.6: Soft X-ray spectra in collisions of metastable O6+ ions with raregas (left) and molecular (right) gas targets at collision energy of 90 keV. Inthe spectra, the observed second-order diffraction lines are shown in order toseparate the overlapped lines. The resolved emission lines labeled as 1–7 arelisted in Tab. 6.7.


6.5 Conclusion

We measured soft X-ray spectra in collisions of metastable He-like C, N,and O ions with He, Ne, Ar, Kr, Xe, N2, O2 and CO2 targets. Strongemission from the inner-shell excited Li-like ions was observed. Most of theobserved features correspond to resonance and inter-combination 1s–2p and1s–3p transitions following the electron capture and transfer-excitation. Inaddition, weak emission lines were also observed, whose intensities signifi-cantly depended on the choice of target. They are mainly due to the weak1s–3p transitions following transfer-excitation and 1s–4p transitions followingelectron capture.

Moreover, new characteristic emission lines from the TEOP transitions ofthe 1s2s(3S)4l states were also observed in collisions of C4+ and N5+ ions withthe heavy rare gas targets for the first time. The relative intensities of theselines increase as the atomic number of the rare gas targets increase. Thisarises because electron capture in the heavier rare gas targets occurs intohigher energy levels as a result of their lower ionization potentials. However,these TEOP transitions were not observed on the molecular targets in spiteof their having ionization potentials similar to those of the heavy rare gases.This difference between the spectra on the rare gas and molecular targetsmight be due to spin-orbit interaction in the heavy atomic gas targets. Inthe O6+ ion experiments, an emission line with the similar rare gas targetdependence was observed, which was not observed on the molecular targets.However, this is not only due to the TEOP transitions but also the 1s–2p transitions and the proportions of their relative contributions are notunderstood.

It is well known that a part of K-shell emission observed by astronom-ical observation satellites are caused by charge exchange reactions of solarwind H-like ions with neutrals in the heliosphere [3]. After the reactions,metastable He-like ions (1s2s 3S1) are produced. If the sequential chargeexchange occurs before they de-excite, inner-shell excited Li-like ions mightbe produced. X-ray emissions following this sequence of charge exchangecollisions can occur in the regions with high neutral gas density and can be anew tool for diagnostics of dense planetary atmospheres. Our experimentalresults will be useful for understanding such astronomical spectra. In orderto extract quantitative information from the spectra, absolute values of emis-sion cross sections are needed, but it is significantly difficult to measure themexperimentally. Therefore, theoretical calculations such as n, l state-selective


charge transfer cross sections and cascade calculations including both Augerand radiative transitions, are required for X-ray astrophysics. The presentdata will be also useful for verifying the validity of the calculations.

Chapter 7

Summary

In this thesis, we have succeeded in laboratory observation of forbidden tran-sitions following the SWCX of H-like O ions with He by using an ion trap.Moreover, we have investigated radiative decay processes of inner-shell ex-cited Li-like C, N and O ions produced by charge exchange collisions ofmetastable He-like ions. Details of each study are shown below.

Development of the Kingdon ion trap system

We developed the Kingdon ion trap with the aim of laboratory observationof X-ray forbidden transitions, and have succeeded in trapping externally in-jected Arq+(q = 5, 6) ions with kinetic energies of 6q keV. The kinetic energyand velocity distributions are investigated by numerical simulations and theresults are consistent with previous analytical expressions. As a performancetest, we measured trapping lifetimes of the multiply charged ions under aconstant number density of H2 and determined the charge-transfer cross sec-tions of Arq+(q = 5, 6)–H2 collision systems at binary collision energies of afew eV.

Laboratory observation of forbidden 1s2–1s2s 3S transition

By combining an ion trapping technique with ion beam collision experiments,we made it possible to observe the long-lived forbidden transitions followingcharge exchange collisions of multiply charged ion beams. At first, we mea-sured a trapping lifetime of externally injected O6+ ions accelerated up tosolar wind velocity of 2.6 keV/u and obtained the lifetime of about 280 ms,

109

Chapter 7. Summary 110

which is much longer than that of the forbidden 1s2–1s2s 3S transition ofmetastable O6+ ions. We succeeded in the laboratory observation of the for-bidden 1s2 1S0–1s2s 3S1 transition in O6+ ions following the SWCX of O7+

ions with He gas for the first time. The beam-based experiment has a greatadvantage in that it makes it possible to measure the absolute values of crosssections.

Spectroscopy of inner-shell excited Li-like ions

We measured soft X-ray spectra in collisions of metastable He-like C, N,and O ions with He, Ne, Ar, Kr, Xe, N2, O2 and CO2 targets. Strongemission from the inner-shell excited Li-like ions was observed. Most of theobserved features correspond to resonance and inter-combination 1s–2p and1s–3p transitions following the electron capture and transfer-excitation. Inaddition, weak emission lines were also observed, whose intensities signifi-cantly depended on the choice of target. They are mainly due to the satellite1s–3p transitions following transfer-excitation and 1s–4p transitions followingelectron capture.

Moreover, new characteristic emission lines from the TEOP transitions ofthe 1s2s(3S)4l states were also observed in collisions of C4+ and N5+ ions withthe heavy rare gas targets for the first time. The relative intensities of theselines increase as the atomic number of the rare gas targets increase. Thisarises because electron capture in the heavier rare gas targets occurs intohigher energy levels as a result of their lower ionization potentials. However,these TEOP transitions were not observed on the molecular targets in spiteof their having ionization potentials similar to those of the heavy rare gases.This difference between the spectra on the rare gas and molecular targetsmight be due to spin-orbit interaction in the heavy atomic gas targets.

Our success in the observation of the forbidden transition is a great stepforward for measurements of the absolute emission cross section values badlyneeded for astrophysics. Moreover, the spectroscopic data of the inner-shellexcited Li-like ions will provide guidelines not only for spectral analysis ofastrophysical plasmas but also for complicated calculations of electron cor-relation and spin-orbit interaction.

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Acknowledgement

First of all, I would like to express my deepest appreciation to my supervisorProf. H. Tanuma for his help, encouragement, and discussion during myentire Ph. D studies. I am owe many thanks to examiners of my thesis,Prof. H. Shiromaru and Prof. Y. Ezoe of Tokyo Metropolitan University,and Prof. N. Nakamura of The University of Electro-Communications forhelpful advices to this study from different standpoints of their speciality. Iwould like to thank Prof. K. Okada of Sophia University for their helpfuldiscussions and numerous advice on the development of the ion trap. I amalso grateful to Prof. G. O’Sullivan, Dr. J. Sheil and Dr. O. Maguire ofUniversity College Dublin for their support with the transition calculations.

I have to acknowledge financial supports from the Ministry of Education,Culture, Sports, and Technology (MEXT) and the TMU Strategic ResearchFunds.

Finally, I would like to thank my friends and my family for their continuedsupport, patience, and love during my doctoral life.

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List of Publications

1. N. Numadate, K. Okada, N. Nakamura and H. Tanuma, Developmentof a Kingdon ion trap system for trapping externally injected highlycharged ions, Review of Scientific Instruments 85, 103119 (2014).

2. N. Numadate, H. Shimaya, T. Ishida, K. Okada, N. Nakamura andH. Tanuma, Solar wind charge exchange in laboratory - Observationof forbidden X-ray transitions, Nucl. Instrum. Methods in PhysicsResearch B, 408, 114 (2017).

3. H. Tanuma, N. Numadate, Y. Uchikura, K. Shimada, T. Akutsu, E.Long and G. O’Sullivan, EUV emission spectra in collisions of highlycharged tantalum ions with nitrogen and oxygen molecules, Nucl. In-strum. Methods in Physics Research B, 408, 213 (2017).

4. N. Numadate and H. Tanuma, Radiative transitions of inner-shell ex-cited lithium-like ions produced in charge exchange collisions of metastablehelium-like ions with neutrals, Phys. Rev. A (Submitted).

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charge exchange collisions and spectroscopy of metastable

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