166610/fulltext01.pdf · list of papers this thesis is based on the following papers, which are...

... and the circus leaves town.

List of Papers

This thesis is based on the following papers, which are referred to in the textby their Roman numerals.

I J. Ljungvall, M. Palacz, J. Nyberg (2004) Monte Carlo simula-tions of the Neutron Wall detector system. Nuclear Intrumentsand Methods in Physics Research A 528 741-762

II J. Ljungvall, J. Nyberg (2005) A study of fast neutron interactionsin high-purity germanium detectors. Accepted for publishing inNuclear Intruments and Methods in Physics Research A

III J. Ljungvall, J. Nyberg Neutron interactions in AGATA and theirinfluence on gamma-ray tracking. Submitted to Nuclear Intru-ments and Methods in Physics Research A

Reprints were made with permission from the publishers.

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Gamma-ray and neutron detection . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Gamma-ray interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Neutron interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Stopping of charged particles . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Scintillator detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.1 Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4.2 Light collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4.3 Discrimination of neutrons and γ rays . . . . . . . . . . . . . . . 122.4.4 Fast-timing using scintillator detectors . . . . . . . . . . . . . . . 13

2.5 High-purity germanium detectors . . . . . . . . . . . . . . . . . . . . . . 152.5.1 Segmented HPGe detectors . . . . . . . . . . . . . . . . . . . . . . . 162.5.2 Timing with HPGe detectors . . . . . . . . . . . . . . . . . . . . . . 16

3 Pulse-shape calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 Monte Carlo simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Geant4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Gamma-ray tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.1 Forward tracking of γ rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2 Backtracking of γ rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.3 Single interaction validation . . . . . . . . . . . . . . . . . . . . . . . . . . 335.4 Other issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

6 The Neutron Wall detector system . . . . . . . . . . . . . . . . . . . . . . . . . 356.1 Monte Carlo simulation of the Neutron Wall . . . . . . . . . . . . . . 396.2 Short summary of the results of paper I . . . . . . . . . . . . . . . . . . 40

7 Neutrons in HPGe detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417.1 Experimental setup and data acquisition system . . . . . . . . . . . . 417.2 Monte Carlo simulation and pulse-shape calculation . . . . . . . . 447.3 Pulse-shape analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457.4 Short summary of the results of paper II . . . . . . . . . . . . . . . . . 45

8 AGATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498.1 Monte Carlo simulations of AGATA . . . . . . . . . . . . . . . . . . . . 508.2 Short summary of the results of paper III . . . . . . . . . . . . . . . . . 52

9 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

vii

10 Summary in Swedish: Karakterisering av Neutronväggen och av neu-troninteraktioner i germaniumdetektorsystem . . . . . . . . . . . . . . . . . 55

11 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

viii

1 Introduction

This thesis has been written in the context of nuclear structure physics. In thisresearch field the low-energy excitation of atomic nuclei are studied with theaim of developing models that describe the structure of the nuclei. The modelsare mainly phenomenological due to mathematical difficulties with the strongforce and the inherent complexity of the many-body problem present for allnuclei but the very lightest. The most fundamental model is the shell modelthat correctly predicts the so-called magic numbers of nucleons (2, 8, 20, 28,50, 82, 126,...) by including a spin-orbit term in the nuclear potential [1]. Fornuclides with proton and neutron numbers located far from the magic num-bers collective models have been successful in describing nuclear structureproperties of high-spin states along the yrast line and above.

As the ratio of neutrons to protons starts to deviate from that of nuclideslocated in the valley of stability, several interesting phenomena, which are notfully described by the present models, can be observed. In heavy neutron-rich nuclei the least bound 10-30 neutrons may form a “skin” of very dilutednuclear matter. Theoretical predictions give evidence for shell quenching inextremely neutron-rich nuclei. The modification of the shell structure couldarise due to a change in the shape of the nuclear potential, affected by the di-luted matter, which reduces the strength of the spin-orbit coupling. A similarphenomenon is that of a “halo” of neutrons found in a few light neutron-richnuclei. On the proton-rich side, around the proton-drip line and for nucleiwith N = Z, there are several open questions. Is there a new type of T = 0pair correlations? Can interactions between bound states and the proton con-tinuum states change the nuclear structure? Of considerable interest is alsothe proton decay mode of nuclei at or beyond the proton-drip line where theCoulomb barrier increases the life time of the nuclide from 10−18 s to µs oreven ms. There are also considerable astrophysical interests in both proton-and neutron-rich nuclei because of their roles in the rp- and r-processes, re-spectively.

Other interesting phenomena are displayed by nuclei at extreme angularmomentum. An example is super-deformation (SD), where the nuclei haveellipsoidal shapes with an axis ratio of about 2 : 1. The study of such nucleiwill e.g. help the understanding of the interplay between collective and single-particle motion. Also the paths and mechanisms for how SD rotational bands

1

decay to non SD states are poorly understood and need to be further studied.Quantum mechanical concepts such as tunnelling and quantum chaos are ex-pected to play important roles in the decay out of SD states. At even higherangular momentum there are theoretical predictions of hyper-deformed stateswith a 3 : 1 axis ratio. Nuclei with such deformations would probe very exoticsingle-particle states.

Theoretical calculations predict an “island of stability” for super-heavy nu-clei (Z ≥ 120). Without microscopical nuclear structure effects such heavynuclei cannot exist. The production and study of these nuclei will amongother things increase the understanding of the single-particle levels for verylarge proton and neutron numbers.

The most common method of producing proton-rich nuclei is to fuse to-gether two stable neutron-deficient nuclei. This is done by accelerating one ofthe nuclei to an energy of a few MeV per nucleon and then letting it collidewith the other nucleus. The energy most be large enough to overcome theCoulomb barrier between the two nuclei. The resulting compound nucleuscarries a large excess of energy and angular momentum which is disposed ofby the emission of particles such as neutrons, protons, and α particles. As theexcitation energy decreases, γ-ray emission can compete with particle emis-sion and the remaining excess energy and angular momentum will be disposedof by the emission of γ rays. The γ rays emitted by the residual nucleus carrythe information of interest. The method described above is an example of in-beam γ-ray spectroscopy using heavy-ion fusion-evaporation reactions and isone of the most powerful tools for studies of the high-spin structure of nu-clides located far from the line of β stability. A unique identification of theresidual nuclides, produced in the reaction after the decay of the compoundnucleus, is of utmost importance, in particular while exploring unknown re-gions of the chart of nuclides. A commonly used method, for identificationof the residual nuclides, is to detect all, or at least as many as possible, of theemitted light particles. The Z and A of the residual nuclides can then simplybe determined by subtracting the summed Z and A of all detected particlesfrom the Z and A of the compound nucleus. The cross sections for productionof proton-rich nuclides decrease typically by an order of magnitude or morefor each emitted neutron.

The most efficient detection systems for this type of studies are arrays ofhigh-purity germanium (HPGe) detectors with ancillary detectors for particledetection. An example of such an array is the γ-ray spectrometer EUROBALL[2, 3], supplemented by the Neutron Wall [4], a 1π neutron detection arrayconsisting of closely packed liquid scintillation detectors, and EUCLIDES[5], a 4π silicon ball for the detection of light charged particles. With a closelypacked array of neutron detectors, like the Neutron Wall, the needed efficientand clean determination of the number of emitted neutrons is complicated by

2

the ability of the neutrons to scatter between many detectors and give rise toa signal in several detectors. A better understanding of such multiple scat-tering processes is important in order to identify methods for improving thediscrimination between one neutron channels and channels where more thanone neutron is emitted. About half of this thesis is based on a Monte Carlosimulation of the Neutron Wall detector array using Geant4 [6]. The resultsof the simulation were compared with the results of two EUROBALL exper-iments, with the aim of understanding the scattering process and, if possible,identify better methods for identification of scattered neutrons.

For the production and study of very proton- and neutron-rich nuclei theuse of radioactive heavy-ion beams is essential. In Europe there are currentlythree facilities, which can deliver accelerated radioactive heavy-ion beams forin-beam experiments. These are REX-ISOLDE at CERN, SPIRAL at GANIL,and FRS at GSI. The two first facilities use the Isotope Separator OnLine(ISOL) technique to produce the radioactive beam, whereas FRS uses frag-mentation of relativistic heavy-ions.

Independently of the technique used to create the radioactive heavy-ionbeams, their intensity is several orders of magnitude lower than what is ob-tainable with stable beams and hence the nuclide production rates are verylow. As a consequence the present state-of-the art γ-ray spectrometers, suchas EUROBALL, will not be powerful enough. This is also the case for studiesof weakly populated super- and hyper-deformed structures found at extremeangular momenta and produced by intense stable beams. Guided by this needand the development of segmented HPGe detectors and digital electronics[7, 8, 9, 10, 11, 12], the idea of γ-ray tracking was born [13]. The segmenteddetectors combined with pulse-shape analysis give information regarding theindividual interaction points of the γ rays, thus allowing for a reconstructionof the fully absorbed γ rays using γ-ray tracking algorithms. The importantdifference as compared to traditional γ-ray spectroscopy is that γ-ray track-ing based spectrometers can be constructed without Compton shields, thusincreasing the solid angle covered by the germanium detectors. The γ-raytracking algorithms also give the position of the first interaction point of a γray to within a few millimetres. This information can be used for making veryprecise Doppler corrections as compared to what is possible for example withEUROBALL. For experiments in which the produced and studied nuclideshave large kinetic energies in the laboratory frame of reference, γ-ray trackinggives a large improvement of the energy resolution. Two γ-ray tracking arraysare currently under development, namely the Advanced GAmma TrackingArray, AGATA [14] in Europe and the Gamma-Ray Energy Tracking Array,GRETA [15] in the USA. These future spectrometers promise an increase inperformance over existing detector arrays by several orders of magnitude forcertain experimental conditions.

3

This large performance increase opens up the opportunity to study veryweak reaction channels, e.g. in heavy-ion fusion-evaporation reaction exper-iments. It, however, still remains important to correctly identify the reactionchannels. The detection of evaporated particles will therefore continue to beimportant. For charged particles the same type of detector systems as wasused with the present generation of HPGe detectors arrays can be used. Forneutrons the situation is more complicated. The detection of neutrons requirelarge volumes of material in conflict with the γ-ray tracking concept, sincethe 4π HPGe detector coverage no longer would be possible. Another as-pect is the influence of neutron interactions on the γ-ray tracking, which willbe important to understand in particular in reactions with high neutron mul-tiplicities. Roughly half of this thesis deals with the interactions of neutronsin germanium-detector systems and how these interactions effect the perfor-mance of AGATA.

Basic research is not the only motivation for this thesis, which was partlyfinanced by the Advanced Instrumentation and Measurements (AIM) graduateschool at Uppsala University. Several of the methods used in the researchare applicable to solving a range of different problems outside the academicworld. This is the case e.g. regarding Monte Carlo simulations. Paper III in thethesis is related to γ-ray tracking, which is a concept that if successful couldbe used for medical imaging, safeguard applications, and in other researchareas such as γ-ray astronomy.

4

2 Gamma-ray and neutron detection

The detection of γ rays and neutrons, which are uncharged, requires the trans-fer of energy to a charged particle. The charged particle will then throughthe electromagnetic force lose energy to the detector material either via thecreation of charge carriers, as is the case for semiconductor detectors, or, asfor scintillator detectors, via excitations of the detector material followed bysubsequent decay by emission of light.

2.1 Gamma-ray interactions

Gamma rays in the energy range 0.01− 10 MeV interact with matter mainlyvia Rayleigh scattering, the photoelectric effect, Compton scattering, and pairproduction. In figure 2.1 the inverse mean free path for γ rays in germanium isshown separated into its different components. The three most important γ-ray interactions, which deposit energy, are the photoelectric effect, Comptonscattering, and pair production.

The photoelectric effect is the absorption of a γ ray by an atom combinedwith the ejection of an electron. The energy transferred to the electron is

Eelectron = Eγ −Ebinding, (2.1)

where Ebinding is the binding energy of the electron and Eγ is the energy of theγ ray. The recoil energy of the atom can be neglected. The ejected electronleaves a hole in the electron shell of the atom. This hole is filled by electronsde-exiting either via x-ray emission or via the emission of Auger electrons.There is no simple expression for the cross section of the photoelectric effect,but it varies as Zn, where Z is the atomic number of the material and n is aconstant with a value between 4 and 5. The energy dependence of the crosssection goes as E−3

γ and has discontinuities at the energies corresponding tothe binding energies of the electrons of the atom. In germanium the K edge islocated at about 10 keV.

For γ rays with an energy above a few hundred keV, Compton scattering, thescattering of a γ ray against an electron, starts to effectively compete with thephotoelectric effect. Assuming an unbound electron, four-vector conservation

5

-ray Energy [MeV]γ-110 1 10

[1/c

m]

µ

-510

-410

-310

-210

-110

1

10

210

310

410 Total cross section

Rayleigh cross section

Compton cross section

Photoelectric cross section

Pair production cross section

Pair production cross section

Figure 2.1: The attenuation coefficient µ (= inverse of the mean free path) for dif-ferent γ-ray interaction processes in natural germanium. The pair production in thenuclear field is shown with a solid line while a dashed line is used for pair produc-tion in the field of the electron. The mean free paths have been calculated using crosssections from reference [16].

in the rest frame of the electron gives(Eγ ,pγ

)+(

mec2,0)

=(

E ′γ ,p′γ

)+(√

m2ec4 + p2

e ,pe

), (2.2)

where Eγ and E ′γ are the energies of the incoming and outgoing γ rays, me

the rest mass of the electron, c the velocity of light, and pγ and pe the linearmomentum of the photon and electron, respectively. Solving for E ′

γ and usingα = Eγ/(mec2) gives

E ′γ =

Eγ

1+α (1− cosθ), (2.3)

where θ is the angle between the incoming and outgoing γ ray. The differen-tial cross section for Compton scattering is

dσc

dΩ=

r2e

2[1+α(1− cosθ)]2

1+ cos2 θ +

α2(1− cosθ)2

1+α(1− cosθ)

(2.4)

and it gives the probability for a γ ray to scatter into the solid angle elementdΩ. The constant re = 2.8179 fm is the classical electron radius. This cross

6

section was first calculated by Oskar Klein and Yoshio Nishina and is there-fore called the Klein-Nishina formula [17].

In figure, 2.1 Rayleigh scattering can be seen to have the second highestcross section below 90 keV. Rayleigh scattering is a special case of Comptonscattering where the photon interacts with all the electrons of the atom. Theatom will then neither be excited nor ionised and the γ ray will keep virtu-ally all of its energy after the scattering despite having changed its direction.Rayleigh scattering is important in applications where the path, also called thetrack, of the γ ray is considered.

For γ-ray energies above 1.022 MeV pair production is possible. This ef-fect has to take place in the presence of a nucleus or an electron to conservethe linear momentum. As can be seen in figure 2.1 the cross section of pairproduction in the field of a nucleus is several orders of magnitude larger thanfor pair production in the field of an electron. The large mass of the nucleuswill ensure that almost no energy is lost to the recoil and all of the γ-ray en-ergy will end up as mass and kinetic energy of the electron and positron. Thepositron will eventually annihilate with an electron and create two γ rays withenergies of 511 keV.

2.2 Neutron interactionsSince neutrons are uncharged particles they are detected indirectly via scatter-ing against a charged particle or via nuclear reactions, creating charged par-ticles or γ rays. Neutron scattering is therefore an important part of neutrondetection. A description of the theory and formalism for neutron scattering isnot within the scope of this work but can be found in, for example, reference[18].

For elastic scattering the conservation of momentum and energy gives thefollowing relation for the energy transferred to the nucleus, assuming non-relativistic energies and using the laboratory frame of reference:

Enucleus =4mM

(m+M)2 En cos2 θ , (2.5)

where θ is the angle of the recoiling atom, m the neutron mass, M the massof the nucleus, and En the neutron energy. For En = 2 MeV and M = 69GeV, corresponding to a neutron scattering against a 74Ge atom, the maximumrecoil energy is Enucleus = 110 keV. For inelastic scattering, with the neglectionof the recoil energy due to the emitted γ rays, equation 2.5 is modified to

Enucleus =2m2MEn cos2 θ±2

√m4MEn cos2 θ(MEn cos2 θ−Eex(m+M))−m2Eex(m+M)

m(m+M)2 , (2.6)

7

where Eex is the excitation energy of nucleus before the emission of the γ rays.The above expressions puts a limit on the allowed scattering angle,

cos2 θ ≥ (m+M)Eex

MEn. (2.7)

Equation 2.7 gives two possible intervals for the scattering angle, namely

0 ≤ θ ≤ cos−1

√

(m+M)Eex

MEn

(2.8)

and

cos−1

−

√(m+M)Eex

MEn

≤ θ ≤ π. (2.9)

The two possible scattering-angle intervals correspond to the plus and minussigns in equation 2.6. For neutron capture there is no outgoing neutron andthe momentum is fully absorbed by the recoiling nucleus. The error fromneglecting the momentum of the emitted γ ray is small. Making the aboveassumptions the energy of the recoiling nucleus will be

Enucleus =m

M∗ En, (2.10)

where M∗ is the mass of the nuclide produced in the neutron capture. Theexcitation energy of the nucleus after neutron capture is then given by

Eex = [(m+M)−M∗]c2 +En

(1− m

M∗ En

). (2.11)

The quantity within the brackets is about 8 MeV for most stable isotopes. Asa result neutron capture has no energy threshold. For inelastic scattering andneutron capture the excitation energy Eex is disposed of by emission of γ rays.

The cross sections of neutron interactions have been measured for a widerange of energies and materials and collected into large databases. For neu-trons with an energy up to 20 MeV an example of such a data base is ENDF/VI[19]. In the left panel of figure 2.2 the cross section for neutrons in germa-nium for the different processes are shown. In the right panel the differentialcross section for elastic scattering of neutrons on germanium is shown for afew neutron energies.

8

0 2 4 6 8 10 12 14 16 18 2010×

[bar

n]σ

Cros

s Se

ctio

n

-210

-110

1

10

[MeV]nE5 10 15 20

[deg.]cmsθ0 20 40 60 80 100 120 140 160 180

[mb]

Ωdeσd

10

210

310

= 0.5 MeVnE = 1 MeVnE = 2 MeVnE = 4 MeVnE = 8 MeVnE

Figure 2.2: Cross sections of neutron interactions in germanium. In the left panel thefollowing cross sections are shown, counting from the top: total, elastic scattering, to-tal reaction, and inelastic scattering cross section, which is a part of the reaction crosssection. In the right panel the angular distributions for elastic scattering of neutronsare shown for the energies 0.5, 1, 2, 4, and 8 MeV. The cross sections are from Geant4,see section 4.1.

2.3 Stopping of charged particles

Particles travelling through an absorber mainly lose energy to the electrons inthe absorber material. Some of these electrons can get a substantial energyand will in effect act as secondary particles that have to be stopped. Theseelectrons are usually referred to as delta rays. The stopping of an ion is dif-ferent from the stopping of an electron. A heavy ion will not, unlike an elec-tron, be deflected by the interactions with the much lighter electrons in theabsorber material, but will instead travel in a relatively straight path in the ab-sorber. Another important difference is that an electron also will lose energyvia bremsstrahlung photons.

The specific energy loss, dE/dx, the energy loss per unit length, also calledthe stopping power, depends linearly on the electron density of the absorbermaterial and quadratically on the charge of the particle being stopped. Forlow-energetic particles, the specific energy loss is approximately proportionalto 1/E. As the energy decreases even further the specific energy loss for ionswill decrease, since they will pick up electrons and lower their charge. Whenincreasing the energy of the particle towards relativistic speeds the specific en-

9

ergy loss, divided by the density of the material, approaches a value around 2MeVcm2/g for many particle species, which are then called minimum ionisingparticles.

Heavy ions also lose energy by collisions with the nuclei in the absorbermaterial. The fraction lost to elastic collisions with the nuclei in the absorberincreases with decreasing energy of the ion. Germanium ions with a few tensof keV of energy lose as much as 80% of their energy via collisions with othernuclei when stopped in germanium.

As mentioned, the loss of energy to bremsstrahlung radiation is an impor-tant contribution to the specific energy loss for electrons. The total specificenergy loss is then the sum of losses via collisions with other electrons andthe loss due to the creation of bremsstrahlung radiation. The relative impor-tance of the two can be approximated with

(dE/dx)r

(dE/dx)c≈ EeZ

700, (2.12)

where the electron energy Ee is measured in MeV and Z is the atomic numberof the absorber material. For electrons with up to a few MeV of energy thecollisional losses will always dominate over radiative losses.

Bethe has derived several expressions for calculating the specific energyloss in a material, see e.g. reference [20], but today stopping powers are usu-ally calculated using computer codes such as SRIM [21].

2.4 Scintillator detectorsThe main principle behind a scintillator detector is the use of a light-sensitivesensor to detect the scintillation photons, which are produced by the chargedparticle when it is stopped in the scintillation material. The most importanttype of sensor used is the photomultiplier tube (PMT).

Scintillator materials can be divided into two large groups of materials, or-ganic and inorganic. Organic scintillators produce their light by the radiativedecay of molecular states, which are excited by the stopping of a chargedparticle. The excited states can either be singlet (spin=0) or triplet (spin=1)states. The life times of the singlet excited to singlet ground state decays aretypically in the nanosecond region, while the triplet excited to singlet groundstate decays have millisecond life times. In organic scintillator detectors it ismainly the light from the nanosecond decays that is utilised. Molecules intriplet states can interact pairwise to form one molecule in the ground stateand one molecule in an excited singlet state. This formation is much fasterthan the decay of the triplet states, but still slower than the decay of the sin-glet states, and therefore the triplet states will give rise to a slow component

10

in the light from the scintillator material. If the particle that is stopped has ahigh specific energy loss the density of molecules excited to triplet states willbe very high, and a larger slow component can be seen in the output from thescintillator. This mechanism is used, in particular with some liquid scintillatormaterials, for neutron-γ ray discrimination.

Inorganic scintillators are crystals which have electronic band structures.The mechanism of scintillation is the creation of an electron-hole pair fol-lowed by radiative recombination. The two main groups of inorganic scintil-lators are activated and unactivated scintillators. In activated scintillators sub-stances added to the crystal are responsible for the emission of photons. Thisis to be compared with unactivated inorganic scintillators where photons areemitted directly after recombination of the electron-hole pairs. Unactivatedscintillators are therefore in general much faster than activated scintillators,but this occurs at the cost of a much lower light yield. If one compares theactivated CsI(Tl) with the unactivated BaF2 one finds that the former has alight yield which is 10 times larger than the latter, but it is also some 1000times slower. Most inorganic scintillators emit light with several componentshaving different wave lengths and decay times.

2.4.1 QuenchingIn most detectors the response depends on the type of the interacting particle.It turns out that electrons always give the most light per deposited energy forscintillator detectors, whereas heavier particles give less light per depositedenergy. For scintillators this phenomenon is referred to as quenching, whichhas been rigorously studied. A good starting point for the interested could bethe PhD thesis of Magnus Hoek [22].

2.4.2 Light collectionThe connection between the scintillator material and the PMT is called thelight guide and is an important part of a scintillator detector. If the light col-lection depends on the interaction position the energy resolution of the systemwill be degraded. For large detectors with fast decay times the light collectionmight also effect the timing properties of the detector system.

One way to model the light collection properties is to use Snell’s law ofrefraction,

ni sinθi = nt sinθt , (2.13)

combined with Fresnel’s laws for reflection and refraction,

r‖ =sin2θi − sin2θt

sin2θi + sin2θt(2.14)

11

r⊥ = −sin(θi −θt)sin(θi +θt)

(2.15)

t‖ =4cosθi sinθt

sin2θi + sin2θt(2.16)

t⊥ =2cosθi sinθt

sin(θi +θt)(2.17)

R = r2⊥ + r2

‖ (2.18)

T = t2⊥ + t2

‖ . (2.19)

In these equations ni and nt are the refractive indices of the two materials.The reflection and transmission amplitude coefficients are r‖, r⊥, t‖, and t⊥,respectively, where the subscripts indicate the orientation of the electric fieldrelative to the plane of incidence of the light ray. The reflected and transmittedintensities are given by R and T , respectively. The angles θi and θt are theangle of the incoming and transmitted light ray relative to the normal of thereflecting surface.

In figure 2.3 the plastic detector used for investigations of neutron interac-tions in two HPGe detectors (see chapter 7) is shown as modelled for light col-lection simulations. The rectangular shape drawn with solid lines is a NE102Aplastic scintillator sheet with the size 100× 100× 3 mm3. The scintillator isconnected to a light guide, shown with dashed lines in figure 2.3. The PMT,mounted at the end of the cylindrical part of the light guide, was not includedin the simulation. By emitting 10000 light rays in random directions from30000 equidistant points in the modelled plastic sheet, and using equation2.13 to 2.19, the fraction of light intensity that reached the PMT side of thelight guide was calculated. The optical connection between the light guideand the PMT was assumed to be perfect. The result of the simulation is shownin the bottom panel of figure 2.4, while the top panel shows the measured lightresponse for the real detector. The agreement between the experimental andsimulated light response of the detector is good considering the simple modeland it is much better than the assumption of a homogeneous light collectionwould give.

2.4.3 Discrimination of neutrons and γ raysThe possibility of using pulse-shape analysis to separate signals due to in-teractions of γ-rays and neutrons makes liquid scintillator detectors a good

12

Figure 2.3: The plastic scintillator detector used for n-γ experiments as modelled forthe calculation of its light collection properties. For details on the detector see paperII and chapter 7.

choice for neutron detectors in an environment with high γ-ray background.The mechanism behind the pulse-shape difference for neutrons and γ rays isthat the much heavier and more ionising proton excites a larger fraction oftriplet states in the scintillator liquid compared to what electrons do. The pro-tons therefore give rise to a larger slow component, as described in section2.4. One way of doing pulse-shape analysis is to integrate the current outputfrom the PMT for two different time intervals. Signals from neutrons and γrays will have different ratios between the two measured charges. Anotherapproach is to use a bipolar amplifier, with a suitable shaping time, whichwill generate a signal that crosses zero at a time that depends on the fractionof the slow component in the output signal from the PMT. For high-energyneutrons both methods are equivalent but the higher signal-to-noise ratio ofthe second method makes it more suitable for neutrons emitted in fusion-evaporation reactions. This so-called zero-crossover method is used with theEUROBALL ancillary detector Neutron Wall, described in chapter 6. In fig-ure 2.5 a time-of-flight vs. zero-crossover plot for one of the Neutron Walldetectors is shown. The zero-cross time is later for neutrons than for γ rays,as can be seen. Events with prompt TOF and delayed ZCO are due to pile-up in the detector. Delayed TOF and prompt ZCO events are due to randomand isomeric γ rays as well as from inelastic scattering of neutrons againstmaterial located close to the Neutron Wall.

2.4.4 Fast-timing using scintillator detectorsThe short decay times for the light in most organic scintillators and someinorganic scintillators makes them very useful for fast-timing applications.Using a fast plastic scintillator together with a BaF2 detector and carefullytuned high quality electronics, a time resolution well below 1 ns (FWHM)

13

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0 10

20 30

40 50

60 70

80 90

100 0 10 20 30 40 50 60 70 80 90 100

0.8 0.9

1 1.1 1.2 1.3 1.4 1.5

Light yield [a.u]

x [mm]

y [mm]

Light yield [a.u]

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

0 10

20 30

40 50

60 70

80 90

100 0 10 20 30 40 50 60 70 80 90 100

0.8 0.85

0.9 0.95

1 1.05

1.1 1.15

1.2 1.25

1.3

Light yield [a.u]

x [mm]

y [mm]

Light yield [a.u]

Figure 2.4: The top figure shows the experimental normalised light yield as a functionof detector position. The measurements were made with the kind help of AndersHjalmarsson. The bottom figure shows the simulated response for the same detector.The light yields are normalised such that the light yield = 1 corresponds to the averageamount of collected light.

14

Figure 2.5: Separation of neutrons and γ rays using the time-of-flight (TOF) and thezero-crossover (ZCO) parameters from the Neutron Wall pulse-shape discriminatorelectronics. The data shown is from a EUROBALL experiment (reaction 58Ni at 220MeV + 56Fe) performed at the Vivitron accelerator at IReS. The RF signal of thebeam-pulsing system was used as time reference in this measurement.

is obtainable [23]. A time resolution of about 2 ns (FWHM) can easily beachieved for a large dynamic range using constant-fraction timing. Such asetup was used in the experiment described in paper II.

2.5 High-purity germanium detectorsSemiconductor diode detectors are based on the electronic band structure incrystalline material with a valence band in which electrons cannot move anda conduction band in which the electrons can move. For semiconductors theenergy difference between the valence band and the conduction band is in theorder of one electron volt. Charged particles travelling through the crystal willcreate electron-hole pairs that can migrate in an applied electric field and theenergy deposited in the detector can be measured by collecting these chargecarriers. In the diode type of semiconductor detectors, a reverse bias is putover a p-n junction in the detector. The reverse bias should be large enoughto completely deplete the detector, i.e. empty it of free charge carriers, and itshould be large enough to saturate the drift velocity of the electrons and theholes. For a more elaborate discussion see references [20, 24].

15

The crown jewel of semiconductor detectors for γ-ray spectroscopy is thehigh-purity germanium (HPGe) detector. Made of the purest material avail-able, the HPGe detector offers an energy resolution of about 0.2 % at a γ-rayenergy of 1 MeV. The actual energy of a γ ray can be measured with evengreater precision. An uncertainty of one part in 105 for the peak position canbe achieved [20]. This remarkable performance is a result of the high qualitycrystals available that ensures a complete charge collection. A low statisticalcontribution to the energy resolution is given by the small energy needed tocreate an electron-hole pair in germanium (2.96 eV) combined with a Fanofactor of about 0.1 [20].

2.5.1 Segmented HPGe detectorsSince the late 1980s HPGe detectors with segmented contacts have been de-veloped. This development has lead to HPGe detectors that have positionsensitivity in the sense that the position of an energy deposition within thedetector can be determined. The position resolution is not limited to knowingin which segment energy was deposited, but advanced pulse-shape analysisof the detector output signals can be used to further improve the position sen-sitivity. In the determination of the interaction position the so-called mirrorpulses are of great interest. These are transient pulses in the segments close tothe segment where there was a deposition of energy. In figure 2.6 examples ofsuch mirror pulses are shown for one of the AGATA prototype detectors. Thesegment in which the charge was deposited is shown in the centre, togetherwith its eight closest neighbours. Mirror pulses are clearly visible in most ofthe neighbouring segments. One of the ideas of how to extract position infor-mation from the pulse shapes is to use calculated pulse shapes and performa fit of these to experimental data. This is a complicated problem and mucheffort is currently being put into it.

2.5.2 Timing with HPGe detectorsThe intrinsic timing properties of a large volume germanium detector is notas good as for fast scintillator detectors. This has two origins. First of allthe charge collection time is usually in the range of hundreds of nanoseconds.Secondly, the shape of the pulse from the detector varies depending on wherein the detector the γ ray interacted. The expected time resolution (FWHM)for a large volume HPGe detector is in the order of 10 to 100 nanoseconds,depending on the energy deposited at the interaction point. For small pulses,i.e. low-energy depositions, the dependence of the pulse’s shape on the po-sition of the interaction becomes particularly difficult. The reason for this isthat low-energy signals can only be detected as they approach their maximum

16

Figure 2.6: Charge and mirror pulses from an AGATA prototype detector. Pictureprovided by Andrew Boston, University of Liverpool.

amplitude and, thus, the variation in rise time for large volume germaniumdetectors will deteriorate the time resolution.

17

3 Pulse-shape calculations

The pulse-shape formation in any detector based on the motion of charge carri-ers can be calculated using the Shockley-Ramo theorem [25, 26], which statesthat the induced charge on an electrode due to moving charges can be calcu-lated as

dQ(t)dt

= e[Nh vh(rh) · W (rh)−Ne ve(re) · W (re)

], (3.1)

where W (re,h) = −∇ΦW (re,h) is the weighting field, Ne,h are the number ofcharge carriers for electrons and holes, and ve,h( re,h) are the charge carriervelocities, which are functions of the electric field E(r). The electric field iscalculated from the electric potential as E(r) = −∇Φ(r). Since the electricand weighting fields are two fundamental quantities, the calculation of pulseshapes for any semiconductor detector begins with solving the two differentialequations

∇2Φ(r) = −ρ(r)εGe

(3.2)

and

∇2ΦW (r) = 0 (3.3)

known as the Poisson and Laplace equations. They describe the electric andweighting potentials, respectively. In equation 3.2, ρ(r) is the free chargedistribution in the detector and εGe the dielectric constant for germanium. Theweighting potential ΦW (r) is not an electric potential but a “tool” used tocalculate the current on the collecting electrode. It is calculated by setting it toone on the collecting electrode and zero on all other contacts and then solvingthe Laplace equation. In figure 3.1 the equations and boundary conditionsused to solve the potentials are shown together with the calculated electricpotential for the coaxial detector used in the work described in paper II andchapter 7.

Once the electric field is calculated the charge carrier velocities have to bedetermined as a function of the position. A commonly used function [20] to

19

Ge∈DeN=-Φ2∇

=0Φ2∇

=0WΦ2∇

=0WΦ2∇

=0Φ

=1WΦ

=-4000 VΦ=0WΦ

VacdnΦd=

GednΦd

Ge∈

Figure 3.1: Equations and boundary conditions for the calculation of the electric po-tential Φ and the weighting potential ΦW . Also shown on the right hand side is theelectric potential as calculated for a closed-end coaxial detector.

describe the charge carrier velocity is

v(r) =µ0E(r)(

1+(E(r)/E0)γ)1/γ −µnE(r), (3.4)

where E0, γ , µn, and µ0 are experimentally adjusted parameters. A com-plication is the dependence of the charge carrier velocities in Ge crystalson the angle between the electric field and the crystal axis. This is knownas an anisotropy of the charge carrier velocity but will be referred to as theanisotropy for short. In figure 3.2 the magnitude of the charge carrier veloc-ity in germanium is shown for electrons and holes for electric fields orientedalong the < 100 >, < 110 >, and < 111 > crystal axes. As a consequenceof the anisotropy, the charge carrier velocity no longer has to be parallel withthe electric field. Before describing the models used for anisotropy in detail abrief explanation of the physics behind anisotropy is given.

The velocity of charge carriers in semiconductor detectors is limited by theacceleration of the charge carriers and the time between interactions of thecharge carriers with the surrounding crystal, the so-called relaxation time t.It has been shown that the effect of the crystal on the charge carriers can be

20

included in the effective mass m∗ [27] defined as,(1

m∗

)µν

=1h2

d2ε(k)dkµdkν

≡ ¯Γ, (3.5)

where ε(k) is the charge carrier energy as a function of its wave vectork. Thecharge carrier velocity is then given by

v = qt ¯ΓE (3.6)

and clearly does not have to be parallel with the electric field despite that theforce on the charge carriers is. The apparent breaking of the conservation oflinear momentum is absorbed by the crystal via interactions with the chargecarriers.

E [V/m]0 200 400 600 800 1000

310×

[m/s

]el

ectro

nv

0

20

40

60

80

100

120

310×

Electron drift velocity

Crystal direction <100>



E [V/m]0 200 400 600 800 1000

310×

[m/s

]ho

lev

0

20

40

60

80

100

310×

Hole drift velocity




Figure 3.2: Drift velocities for charge carriers in germanium as a function of appliedelectric field. The experimental data points shown for the holes are from reference[28]. Velocities for the directions < 100 > and < 111 > are calculated using equation3.4. The drift velocities for electrons and holes in the < 110 > direction have beencalculated using equation 3.8 and 3.12, respectively.

For electrons in germanium, L. Mihailescu et al. [29] have developeda model of the anisotropy that has been used in this work. The model isbased on the fact that for the electric-field strengths used in semiconduc-tor detectors the electrons that transport charge are moving in the conduc-tion band energy minima, which are found along the four < 111 > direc-

21

tions of the crystal. At these minima, referred to as valleys, ε(k) is givenby

εe(k) = h2

2

(k2

x+k2y

m∗l

+ k2z

m∗t

), (3.7)

where the index e stands for electron, and m∗l and m∗

t are the longitudinaland transverse effective electron masses, respectively. Using equation 3.5 andinverting the reciprocal effective mass tensor, the effective mass tensor ¯γ0 isgiven by

¯γ0 =

m∗l 0 0

0 m∗l 0

0 0 m∗t

.

According to the model, the drift velocity can be written as

ve = A (E)∑j

n j

n

¯γ j E0(E0 ¯γ j E0

)1/2 , (3.8)

in which A (E) is a function of the electric field magnitude, E0 is a normalisedfield vector, ¯γ j is the effective mass tensor for the jth valley, and n j/n is thefraction of electrons in the jth valley. The effective mass tensor ¯γ j is calcu-lated from ¯γ0 by relating the four <111> directions in the Ge crystal to thecoordinate system used for the electric field according to

¯γ j = ¯R j−1 ¯γ0

¯R j, (3.9)

where ¯R j are the rotation matrices. The next relation needed is for the valleypopulation fraction n j/n. Mihailescu et al. use

n j

n= R (E)

(

E0 ¯γ j E0

)−1/2

(∑l E0 ¯γl E0

)−1/2 −14

+

14, (3.10)

where R (E) is a function of the electric field strength. Using equation 3.4to calculate the electron drift velocity along the <100> direction for a fieldstrength E, A (E) can be calculated for this field strength using equation 3.8,since the choice of direction assures that n j/n = 1/4. Calculating the elec-tron drift velocity in the <111> direction, using equation 3.4, for the sameelectric field strength, equation 3.10 can be solved for R (E). The elec-tron drift velocity ve can now be calculated for all directions of the electricfield.

For hole transport no implemented model was found in the literature, andtherefore the following model was developed. The goal was to create a model,

22

using the simplest possible description of the involved physics, that gives goodresults when compared to the experimental data. This was achieved by assum-ing that the hole drift velocity can be explained by the fractions of holes in theheavy and the light hole band, respectively. While physically not correct, dueto the much higher energy of the light compared to the heavy hole band, thismodel do reproduce experimental data for hole drift velocities. For holes thesurfaces of equal energy in the conduction bands are not ellipsoids, whichmeans that the reciprocal effective mass tensor will depend on the directionof the wave vectork. Here the assumption was made that the wave vector isparallel to the applied electric field. The hole energy functions are [27]

εh(k) = Ak2 ± [B2k4 +C2 (k2xk2

y + k2yk2

z + k2z k2

x)]1/2

, (3.11)

where the positive (negative) sign is for the light (heavy) hole band. Usingequation 3.5, to calculate the reciprocal effective mass tensor, we have

vh = qT (E)[F (E) ¯Γ

heavyh +(1−F (E)) ¯Γ

lighth

]E. (3.12)

Comparing equations 3.6 and 3.12, the factor T (E) in the latter equationcorresponds to t in the former and should thus be considered an electric-fielddependent relaxation time. F (E) is the fraction of the holes moving in theheavy hole band and it is also assumed to be field dependent. Equation 3.4 cannow, as in the case for electrons, be used to calculate the hole drift velocities inthe < 100 > and < 111 > directions. Using these velocities one can solve forT (E) and F (E) for the electric-field strength in question. A big differencefor holes as compared to electrons is that the reciprocal effective mass tensornow will change as the direction of the electric field changes.

As an illustration to how the charge carrier velocity depends on the electric-field direction, an electric field with a magnitude of 2 · 105 V/m has beenrotated in the [010] plane and the resulting electron and hole drift velocityhave been calculated. The results are plotted in figure 3.3.

Using the above described models for the charge carrier velocities, pulseshapes can be calculated using equation 3.1. A few calculated pulse shapes fortwo different detectors are shown in figure 3.4. For details on the detectors seepaper II. In table 3.1 numerical values are collected for the parameters relatedto the charge carrier drift velocities. To show the effect of the anisotropy fora coaxial detector, the time to the maximum amplitude for calculated pulseshapes is shown in figure 3.5. The signals due to holes correspond to an energydeposition close to the central contact whereas electron-induced signals aregenerated when the electrons move from the outer contact towards the centreof the detector. The variation in rise time for hole-induced signals is of theorder of 10 % while for electrons it is about 5 %.

23

[m/s]100v-100 -50 0 50 100

310×

[m/s

]10

1v

-100

-50

0

50

100

310×

V/m5E=2*10

electronv

holev

Figure 3.3: Anisotropy of the drift velocities for charge carriers in a Ge crystal in the[010] plane. The plotted velocity curves are (v2

100 + v2101)

1/2. The short double-sidedarrows indicate the direction of the electric field, which is always pointing outward.The other arrows indicate the direction of the charge carrier velocities.

Time [s]5 5.2 5.4 5.6

-610×

Cha

rge

[C]

-1.5

-1

-0.5

-0

-1510×

Planar detector

z=0 mm

z=6 mm

z=12 mm

Time [s]5 5.2 5.4 5.6

-610×

Cha

rge

[C]

-1.5

-1

-0.5

-0

-1510×

Coaxial detector

R=5 mm

R=18 mm

R=31 mm

Figure 3.4: Calculated pulse shapes for two different HPGe detectors.

24

Angle [rad]0 1 2 3 4 5 6

Tim

e to

max

imal

am

plitu

de [s

]

0.3

0.32

0.34

0.36

0.38

0.4-610×

Signal due to holes

Signal due to electrons

Figure 3.5: Rise times of signals originating from the inner-most and outer-most ra-dius due to holes and electrons, respectively, in a closed-end coaxial detector.

Electrons Holes Electrons Holes Unit

µ1000 4.018 6.87 µ111

0 4.242 7.72 [m2/V s]µ100

n 0.0589 0.00548 µ111n 0.0062 5∗10−5 [m2/V s]

E1000 49300 18146 E111

0 25100 13307 [V/m]γ100 0.72 0.695 γ111 0.87 0.642

Table 3.1: Charge carrier drift parameters. Parameters for electrons are from Mi-hailescu et al. [29], while the parameters for the holes are from fits of equation 3.4 tothe data of reference [28]. No error estimates of the parameters have been made.

25

4 Monte Carlo simulations

When simulating systems that include processes which are stochastic in theirnature, Monte Carlo simulation is a very useful tool. The name Monte Carlois from similarities with the gambling in Monte Carlo, Monaco. Chance de-cides the outcome of some event, may it be when rolling a dice or when se-lecting the exit channel in neutron scattering. It is a very rich and complexfield and is best illustrated using a simple example. Should one begin or bethe second player in Russian roulette? One can show that the probability forthe first player to survive is 5/11, that is, one should not begin! Although aMonte Carlo simulation is clearly not needed, this simple example will allowa demonstration of some key features of Monte Carlo simulation.

The simulation of Russian Roulette is very simple, let the players take turnuntil one of them is killed. Check which one was killed and increase one ofthe two counters np1 and np2 accordingly, repeat this N times, and calculatethe risk for the players as P1 = np1/N and P2 = np2/N. This problem can beused to illustrate one of the main consequences of Monte Carlo simulations,which is that the results from such simulations have to be interpreted usingstatistical methods. This is illustrated by performing three different simula-tions, each with a different number of trials, N, used, namely 100, 1000, and10000. According to theory, the statistical variation is proportional to thesquare root of the number of trails, so the accuracy of the simulations shouldbe ∆P2 = P2/

√N. The results are shown in figure 4.1 for the three different

simulations performed of the Russian roulette problem. Each of these simula-tions have been repeated a large number of times. The lesson to learn is thatincreasing the precision in Monte Carlo simulations is very computer-timeconsuming, since it only increases as the inverse square root of the number oftrails.

One important part of the Monte Carlo simulation is the generation of ran-dom numbers. A survey of this subject would be a bit out of context and theinterested is advised to read, for example, chapter 13 in reference [30] andreferences therein.

27

N 100Entries 1110214Mean 0.4568RMS 0.04943

2P0.3 0.4 0.5 0.6

Coun

ts

0

100

200

310× N 100Entries 1110214Mean 0.4568RMS 0.04943


2P0.3 0.4 0.5 0.6

Coun

ts

050

100150



2P0.3 0.4 0.5 0.6

Coun

ts

050

100150200


Figure 4.1: Precision in the determination of the chance of survival for the startingplayer in Russian roulette. The number of trials N are shown in the legends.

4.1 Geant4Geant4 [6] is a tool kit for Monte Carlo simulations of detector systems. Theacronym comes from GEometry ANd Tracking. It is designed to provide allfunctionality needed for detector-system simulations, including the geometryof the detector system, interactions of the particles, and the response of thedetectors. Based on C++, it is an object oriented software package wherethe user has the possibility to add capabilities as needed, for example a newphysical process or the response of some detector. Geant4 has been developedby scientists in RD44, a world wide collaboration with participants in morethan 10 experiments in Europe, Russia, Japan, Canada, and the USA. Thesource code of Geant4 is freely available together with installing instructionsand documentation.

The user of Geant4 has to provide some mandatory definition and so-calleduser actions. The user has to define the geometry, which is done by overridingmethods in the virtual class G4VUserDetectorConstruction. It is also here thatthe different materials used in the simulation are defined. The next manda-tory implementation is to override the methods of the virtual class G4VUser-PhysicsList, where the particles and physical processes are defined. The lastmandatory class to be implemented by the user is G4VUserPrimaryGenerator-Action, in which methods for creating the particles to be tracked are defined.There are also a set of user actions: G4UserRunAction, G4UserEventAction,

28

G4UserStackingAction, G4UserTrackingAction, and G4UserSteppingAction.These actions allow the user to interact with the tracking of particles throughthe detector system at different levels.

In this work Geant4 has, among other things, been used to simulate theinteraction of neutrons in different detectors. The models used for the neu-tron interactions rely on a neutron cross section data library called G4NDL.In this work version 3.7 of the library has been used. It contains cross sec-tion data derived from the evaluated neutron reaction data libraries Brond--2.1, CENDL2.2, EFF-3, ENDF/B-VI.0, ENDF/B-VI.1, ENDF/B--VI.5, FENDL/E2.0, JEF2.2, JENDL-FF, JENDL-3.1, JENDL-3.2,and MENDL-2. As a test, Geant4 was used to simulate elastic scattering andneutron capture in a germanium shell and the results were compared withthose obtained by a MCNPX [31] simulation of the same shell. MCNPX isa Monte Carlo code that has been used extensively for the simulation of neu-tron transport in matter. The results were very similar and gave confidencethat the low-energy neutron interaction models of Geant4 are comparable inperformance to those of MCNPX.

Although Geant4 is a powerful tool it contains bugs, which is commonwithin all large software projects. Within the low energy models of neutronscattering used be Geant4 several bugs were found. The first concerned anerror in the choice of exit channel for inelastic scattering. Instead of pro-ducing germanium isotopes in a Ge(n,n′γ)Ge reaction, gallium isotopes wereproduced. This was solved by removing the cross section files for the individ-ual germanium isotopes in the G4NDL cross section library and using insteadthe cross-section files for natGe. The second bug found is related to the con-servation of linear momentum in inelastic scattering. Numerical calculationssuggested that the energy of the recoiling nucleus was given in the wrong ref-erence frame when the recoil was stacked for tracking. More careful studies,however, gave the impression that is was the momentum of the neutron thatwas set to zero. As a consequence of this the recoil of the nucleus in thefinal state was just what it would have been in a two-body decay (ignoringthe recoils from the emitted γ rays). This gave very strange looking energydistributions of the recoiling nuclei. A modification of the file G4Neutron-HPInelasticCompFS.cc was made, so that the correct neutron momentum wasused in the simulations in paper II and paper III.

29

5 Gamma-ray tracking

The germanium detector development under recent years has opened up theopportunity to use a new concept for γ-ray spectrometers, so-called γ-raytracking. The idea is to use the Compton formula, equation 2.3, to recon-struct the tracks of incident γ rays from a set of interaction points. The devel-opment of γ-ray tracking algorithms has followed two main paths, althoughother types of algorithms also exist [32, 33, 34, 35]. Here the two main al-gorithms will be described. They have also been used in paper III and areidentical to those used in the work of Lopez et al. [35].

5.1 Forward tracking of γ raysInteraction points from one γ ray will mostly lie close to each other in AGATA.The physics behind this is the forward peaked Compton cross section, i.e. theCompton scattering angle for the first interaction is likely to be small. The firstand second interaction point will therefore, together with the position of theγ-ray source, span a small solid angle. As the γ ray continues to scatter andloses energy the mean free path decreases fast. The result of this is that evenif the last few scattering angles are large, interaction points belonging to thesame γ ray will stay within a region spanned by a relatively small solid angleas viewed from the source. The first step of forward tracking is therefore toput the interaction points into groups, so-called clusters. The angle betweenthe two lines formed by the first interaction point in a cluster, the candidateinteraction point, and the γ-ray source is calculated. If it is smaller than amaximum value, the candidate point is included in the cluster. Interactionpoints that are rejected as members of the cluster will in turn be the first inter-action point in a new cluster. This can be done for several different maximalangle differences and a collection of clusters, each containing some subset ofinteraction points, is created. In most cases an interaction is allowed to be amember of several clusters since at the end of the γ-ray tracking only the clus-ter with the highest figure-of-merit is accepted. The figure-of-merit is basedon the comparison of the interaction energy calculated using the Comptonscattering angle and the measured interaction energy. Probabilities for Comp-ton scattering and photoelectric effect as a function of the distance betweenthe interactions in a cluster are also included in the figure-of-merit.

31

The condition for an interaction i at point ri to belong to cluster o can beexpressed as

cos−1( |ri ·ro||ri||ro|

)≤ α, (5.1)

where ro is the coordinate of the first interaction point in cluster o and α isthe maximum angular difference between two interaction points in the clus-ter. The figure-of-merit for clusters with more than one interaction point iscalculated as a product of two factors. The first factor is the probability ofthe γ ray to have travelled first the distances between points i and i + 1 andthen between points i + 1 and i + 2, and so on. The second factor describeshow well the Compton scattering formula fits the interaction sequence whichis assumed. The total figure-of-merit, for k interactions in the track, can bewritten as

Ftot =

(k

∏i=1

FiD

k

∏j=2

F jE

)1/(2k−1)

, (5.2)

where

FiD = exp

(−ri−1→i

λ (E)

)exp(− ri−1→i

λtot(E)

), (5.3)

and

F jE = exp

(−C

(∆ jE)2

σ2E

), (5.4)

and i and j are indexes. In equation 5.3, λ (E) is the mean free path for Comp-ton scattering (i < k) or the photoelectric effect (i = k), λtot(E) the total meanfree path, and ri−1→i the distance between interaction points i−1 and i (inter-action 0 is the source position). The constant C in equation 5.4 has a value ofeither 1, if i > 0, or 2 if i = 0. The larger weight for i = 0 is due to the welldefined source position. The factor ∆i

E is the difference between the energy ofinteraction i calculated by using the Compton scattering formula and calcu-lated by assuming it to be interaction number i of the track. The uncertainty inthe determination of the interaction energy is given by σE , and is dominated bythe error propagation of the position uncertainty when calculating the interac-tion energy using equation 2.3. For each track the order of the interactions thatgives the best figure-of-merit is chosen and when an interaction is included inmore than one track the track with the best figure-of-merit is selected. For atrack to be accepted it has to have a sufficiently high figure-of-merit.

32

5.2 Backtracking of γ raysBacktracking is based on the large probability for the final interaction ofa fully absorbed γ ray, the photoelectric effect, to be in the energy range100− 250 keV. Starting from such an interaction one tries to track the γ rayfrom the last interaction to the first interaction, hence the name backtracking.The tracking procedure is as follows. Sort the interactions in order of increas-ing energy. Take the first interaction above 90 and below 600 keV. Find theinteraction closest to the first interaction. Check if the distance between thetwo interactions is consistent with the photoelectric effect. If not take as thesecond interaction the second closest interaction. Do this until an interactionthat is consistent with the photoelectric effect has been found. Next, use theCompton scattering formula to look for a third interaction that fits the two firstones. If no such interaction can be found, check if the two first interactionsare consistent with a γ ray emitted from the source. If not, select the next oneamong the energy sorted interactions as the first interaction and repeat it all.Do this until all interactions have been used in a track or have been discarded.As in the case of forward tracking the tracks are given a figure-of-merit, whichhas to be large enough for a track to be accepted. The figure-of-merit is cal-culated as

Ftot =

(k

∏i=1

FicosPi+1→iPi(Et)C

)(1/k)

, (5.5)

where Pi+1→i is identical to the second exponential factor in equation 5.3,Pi(Et)C is the probability for the γ ray to have undergone a Compton scatter-ing, and

Fcos = exp(−|cos(θe)− cos(θp)|

σθ

). (5.6)

In equation 5.6, θe is the Compton scattering angle as calculated from theinvolved interaction energies and θp is the Compton scattering angle as calcu-lated from the positions of the interactions. The uncertainty in the position ofthe interactions gives an uncertainty in the determination of cos(θp) which isreflected in the denominator σθ of the exponential.

5.3 Single interaction validationBoth forward tracking and backtracking have to treat the possibility that aγ ray is fully absorbed in a single interaction. There is a trade off betweenlarge efficiency at low energy and a good peak-to-total ratio when optimisingsingle-interaction validation. In this work and in the work of Lopez-Martens

33

et al. [35] the following has been used: For an interaction point to be regardedas the single interaction of a fully absorbed γ ray it has to be at least 4 cmfrom its nearest neighbouring interaction. The probability for the γ ray tohave reached the position where the absorption took place must also be largerthan a certain value. This value is chosen depending on if large efficiency atlow energy or large peak-to-total ratio is requested.

5.4 Other issuesThere are a few complications that are usually discussed in connection to γ-ray tracking. The first one is that the Compton scattering formula 2.3 assumesthe electron to be at rest before the scattering of the γ ray. This leads to anincorrect relation for the scattering angle as a function of the incoming andoutgoing γ-ray energies. It has been suggested that this effect is indeed acomplication for the backtracking algorithm but that it has less impact forforward tracking [36], while other authors suggest that it is a less importanteffect [35].

Another source of uncertainty is that the secondary electrons created by theinteracting γ rays may lose energy via bremsstrahlung and thus deposit someof the energy quite far away from where the interaction took place. For anideal detector system, with perfect energy and position resolution, it turns outthat this effect is the dominating cause for the uncertainty of calculating theCompton scattering angle and the reason why the momentum profile of theelectrons is less important.

A third possible complication are fast neutrons emitted in the nuclear re-actions. Interactions of such neutrons with the Ge detectors may disturb thetracking algorithms, an effect which is studied in detail in paper III.

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6 The Neutron Wall detector system

The Neutron Wall detector system was developed as an ancillary detector tobe used with the EUROBALL γ-ray spectrometer [2, 3]. It consist of 50 liq-uid scintillator detector segments, configured as 15 hexagonal detectors eachwith three segments and one pentagonal detector with five segments. Thereis a high degree of symmetry in the geometry of the Neutron Wall, as can beseen in figure 6.1, where every detector has 4 other equivalent detectors, andsome detector segments are also symmetrical around a plane going throughthe centre of the Neutron Wall, the centre of the detector segments, and thebeam line. Examples of such detector segments are number 1, 25, 30, and 48.These symmetry planes will later be referred to as mirror planes.

The detector system was designed to be mounted in the forward hemisphereof EUROBALL covering a solid angle of about 1π . The intrinsic detectionefficiency of the Neutron Wall for a neutron with an energy of a few MeV isabout 50 %, which corresponds to a detetection efficiency of 20− 30 % forneutrons emitted in a typical heavy-ion fusion-evaporation reaction. In figure6.2 and 6.3 photographs of the detectors and the fully mounted Neutron Wallat IReS in Strasbourg, France, are shown. For details about the design andperformance of the Neutron Wall see reference [4] and paper I.

One of the most difficult problems with a closely packed neutron detectorarray such as the Neutron Wall is scattering of neutrons between the detectorsegments. This gives rise to multiple signals from a single neutron and makesit difficult to determine the number of detected neutrons. For the Neutron Wallthe probability for a detected neutron to give a signal in more than one detectorsegment is 6− 7 %, see paper I. Large efforts have been devoted to learninghow to discriminate against scattered neutrons. These efforts are described indetail in paper I. It turns out that when trying to discriminate against scatteredneutrons it is important to consider the geometrical relations between the seg-ments that have fired. Due to the high degree of symmetry of the geometryof the Neutron Wall the number of distinctly different geometrical relationsbetween the detector segments can be reduced. For an event with two firingdetector segments there are 50 · 49 = 2450 different combinations taken intoaccount the order in which the segments fire, but not the symmetries of theNeutron Wall. This number can be reduced by almost a factor of 10. Usingthe 7 different types of detector segments in the Neutron Wall, represented by

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Figure 6.1: Schematic figure showing the official numbering scheme of the NeutronWall detector segments as viewed from downstream of the target.

36

Figure 6.2: Photograph of the Neutron Wall detectors. Shown are a few of the indi-vidual hexagonal detectors and on the left side the pentagonal detector.

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Figure 6.3: Photographs of the Neutron Wall when mounted in the EUROBALL γ-rayspectrometer setup at IReS, Strasbourg. The upper photograph shows the lead platesused to shield the Neutron Wall from low energy γ and x rays. Shown in the lowerphotograph is the Neutron Wall as seen from downstream of the target.

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segments 1, 2, 3, 25, 26, 36, and 46, there are two different ways of formingtwo neutron events. If the first neutron hits one of the segments which is notcrossed by a mirror plane e.g. number 2, 3, or 36, all of the remaining 49segments will have a unique geometrical relation to the segment hit by thefirst neutron. The other case is that the first neutron hits a segment which islocated in a mirror plane, e.g. segment number 1, 25, 30, or 48. The secondneutron has then only 26 geometrically unique segments to hit. Summing upthe two different cases one gets 3 ·49+4 ·26 = 251 different combinations oftwo firing detector segments.

For three firing segments we begin with 50 ·49 ·48 = 117600 possible com-binations. To reduce this number we look at the three possible cases for threefiring detector segments when the order in which they have fired is consid-ered. If the two first neutrons hit segments lying in the same mirror plane,such as detector segments 1 or 30, the third neutron has 25 different segmentsto choose among. The next case is if the first neutron hits a detector segmentlying in a mirror plane, e.g. segment 1, and the second neutron hits a detec-tor segment that does not lie in a mirror plane, e.g. segment 43. The thirdneutron then has 48 different detector segments that it can hit. The last caseis that at least two of the neutrons hit segments not lying in a mirror plane.Together these cases give 4 · 3 · 25 + 4 · 23 · 48 + 3 · 49 · 48 = 11772 differentcombinations.

6.1 Monte Carlo simulation of the Neutron WallIn the Geant4 simulation of the Neutron Wall only the scintillator liquid andthe aluminium detector cans were included. No support structures or othersurrounding materials were included. The detector response of the liquid scin-tillators included an energy threshold and the quenching of the light output,but not the light collection properties of the system. The simulation is de-scribed in detail in paper I.

The user written part of the simulation consist of about 3000 lines of C++code divided into 18 files. These files are convenient divisions of the differ-ent definitions and actions needed for the simulation to work. Apart fromthe mandatory implementations (G4VUserDetectorConstruction, G4VUser-PhysicsList, and G4VUserPrimaryGeneratorAction) the user actions G4User-RunAction, G4UserEventAction, G4UserStackingAction, and G4UserStep-pingAction, which are used to control and extract results from the simulation,were also implemented. In the RunAction the output file is opened and closed.The light output from each detector segment is calculated in the EventActionusing information which is extracted in the SteppingAction. The Stacking-Action is used to remove low energy neutrons from the simulation to speedit up. In order to effectively handle the output from the simulation a ROOT

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[37] class containing members of the information from each event was im-plemented. This ROOT class was stored in a ROOT tree in the output file.To calculate the efficiency, the scattering probability, and the effect of differ-ent methods to discriminate against scattered neutrons several C++ programswere written.

6.2 Short summary of the results of paper IMethods using the correlation between the difference in time-of-flight, ∆TOF ,and the distance between the firing detector segments in the Neutron Wallwere tested. The most effective method proved to be one that uses a ∆TOFgate for each of the 251 unique combinations of two firing segments. Forthree neutrons the best method was to test each possible pair among the threefiring detector segments and reject the event if one pair was considered to bedue to a scattered neutron. The effect of discrimination is quantified using theenhancement ratio R. In words, this is the ratio between the loss in intensityof the wanted neutron channel, i.e. two or three emitted neutrons dependingon the reaction channel of interest, and the loss in intensity of the unwantedneutron channel, i.e. one or two neutrons. The R value should be as large aspossible. As with most discrimination processes there is a loss of interestingevents, which is equivalent to a reduction of the neutron detection efficiency.Another result of this work was the recognition of the importance of mis-interpreted γ rays as the origin of false neutron signals.

Methods based on the correlation of the total light output from the NeutronWall with the time-of-flight were also tried both on simulated and experimen-tal data in order to discriminate against scattered neutrons in two and threeneutron events. Results and detailed discussions are presented in paper I.

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7 Neutrons in HPGe detectors

The motivation behind paper II is related to the development of the next gen-eration of γ-ray spectrometers, which will be based on γ-ray tracking. Thegermanium detectors in these spectrometers will be segmented. This meansthat, if there is a pulse shape-difference between neutron and γ-ray inducedsignals, a neutron interacting in a segment, which was not hit by a γ ray, couldbe identified as a neutron. Such a difference in pulse shape would exist for sig-nals induced by elastic scattering of neutrons. If the γ rays emitted in inelasticneutron scattering does not interact in the same segment as the neutron did,inelastic neutron scattering could also induce such a signal. The pulse-shapedifference could e.g. arise from the much higher specific energy loss of therecoiling germanium ion as compared to an electron. Due to its high specificenergy loss the Ge ion will create a very dense charge carrier cloud in the ger-manium detector. In small silicon detectors a similar effect gives rise to theso-called plasma effect [38, 39, 40], which is a delay in the charge collectionprocess due to the screening of the electric field in the detector. If it would bepossible to discriminate between neutron and γ-ray induced pulses in AGATA,the loss in photo-peak efficiency due to neutrons could be minimised. AGATAcould also be used as a very efficient neutron detector and thus removing theneed of a dedicated neutron ancillary detector. Extensive experimental workhas been done, in parallel with simulations to facilitate the understanding ofthe experimental results. Although three different detectors were used, datafrom only two of the detectors were finally analysed. The used detectors weretwo closed-end coaxial germanium detectors and one planar germanium de-tector. For the planar detector measurements with two different bias voltageswere made, in order to investigate a possible dependence of the shape of theneutron induced pulses on the electric field strength.

7.1 Experimental setup and data acquisition systemIn figure 7.1 a schematic block diagram of the data acquisition system isshown. Arrows indicate the direction of the data flow. The Detectors, Analogelectronics, and TNT-1 boxes correspond to what is shown in the electronicsscheme in paper II. Added here are the CAMAC and the Standard PC boxes.A description of the detectors, the source, and the experimental setup is givenin paper II. In figure 7.2 a photograph of the experimental setup is shown.

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Figure 7.1: Schematic block diagram of the data acquisition system used in paper II.

Figure 7.2: A photograph of the experimental setup used for the experiments per-formed in paper II. Counting from left is the BaF2 detector, the 252Cf source, the leadshield, the plastic scintillator detector, and the closed-end coaxial germanium detector.

The TNT-1 was used for sampling the preamplifier pulses from the germa-nium detectors and for sampling the TAC used to measure the time-of-flightof the γ rays and neutrons. Sampling with 80 MHz, the TNT-1 is a two chan-nel 14 bit digital pulse-shape recorder constructed to sample the preamplifiersignals from large volume germanium detectors. The TNT-1 is implementedas a one slot wide NIM module, see figure 7.3. The dynamic range of each ofthe inputs is from −0.55 to 0.55 V, which for typical HPGe-detector pream-plifier signals corresponds to a deposited energy of 4−10 MeV. The data fromthe TNT-1 is read out via USB2 to a standard PC with a USB2 interface. Onboard the TNT-1 there is a field-programmable gate array (FPGA) to calculateenergy and time information from the preamplifier signal in real time. TheTNT-1 has several auxiliary NIM inputs and outputs to facilitate the integra-tion with other electronics. These inputs and outputs are user controlled andcan be used for trigger input and output, busy output, etc. The setup and con-trol of the TNT-1 is done by a JAVA based program running on the PC. Formore details about the TNT-1 see reference [41].

The CAMAC ADC was a 4 channel 13 bit peak sensitive ADC of modelORTEC AD413. It was used for readout of the energy from the two scintillatordetectors and the Ge time as measured with leading-edge time pick off.

Data was collected using either synchronised read out from the TNT-1and the CAMAC ADC unit or reading the TNT-1 and CAMAC data asyn-

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Figure 7.3: Photograph of the TNT-1. On the front panel the single ended LEMOinputs IN A and IN B are visible below the Acquisition LED used to indicate theoperational status of the unit. Also visible on the front panel are auxiliary NIM inputsand outputs. The USB2 connector and some analog and logic inspection outputs arelocated on the rear panel of the NIM unit.

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chronously. For the synchronised readout, a data acquisition program waswritten. In acquisition mode the program was polling the LAM signal of theCAMAC ADC to detect an event and start the readout from both the TNT-1and the CAMAC systems. The TNT-1 can produce a busy signal on one ofthe auxiliary outputs when it is in a readout phase and not accepting a trig-ger signal. This busy signal was used to block the complete data acquisitionsystem so that the TNT-1 and CAMAC data would stay synchronised. Thisprocedure worked well and the two data streams stayed synchronised for longperiods of time. To check the synchronisation the germanium detector energywas read out both using the TNT-1 and the CAMAC ADC. The control andreadout of the TNT-1 was done using standard USB2 library functions. Forcommunicating with the CAMAC system a standard SCSI interface was usedtogether with the sjy(LINUX) code developed at Fermilab.

In later stages of the experiment it was decided that the energy informationfrom the scintillator detectors was not required on an event-by-event basis.The synchronisation between the TNT-1 and the CAMAC system was there-fore no longer needed, and the JAVA based control software delivered with theTNT-1 was used both for control and data readout.

A set of data acquisition programs were written for use with the experi-mental setup. There were two different types of programs, either including orexcluding the control and readout of the TNT-1. In common for both types ofdata acquisition programs were the control and readout of the CAMAC ADCunit. The addition of the capabilities needed to control, and to read out datafrom, the TNT-1 was added to the data acquisition program be means of a C++class, purposely written to communicate with the TNT-1. The data acquisitionprograms contain simple ROOT based graphical user interfaces for setup andcontrol of the acquisition.

7.2 Monte Carlo simulation and pulse-shape calcula-tion

The Monte Carlo simulation of the experiment was implemented followingthe standard Geant4 procedure described in section 4.1. Flight times from theplastic scintillator to the germanium detector and position and energy depo-sitions of the interactions in the germanium detector were extracted from thesimulated events both for neutrons and γ rays, and stored in a ROOT tree.

For the calculation of simulated pulse-shapes, libraries with pulse shapeswere made, both for the 55 % closed-end n-type coaxial detector and for theplanar n-type detector. In these libraries, pulse shapes were stored for eachgrid point, with a spacing of 1 mm in the radial and longitudinal directionsand 5 degrees in the angular direction. The pulse-shapes were calculated asdescribed in chapter 3. The concentrations of impurities were given by the

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detector manufactures and used in the calculations of the electric fields. Thesimulated pulse shapes were made by taking the library pulse shape closest toeach interaction in the HPGe detector, scale it accordingly to the energy of theinteraction, and then sum up the individual pulse shapes. More details of thesimulation are found in paper II.

7.3 Pulse-shape analysisA C++ class that uses several ROOT features was written for the analysis ofthe waveforms read out from the TNT-1. The class reads TNT-1 data from afile on an event-by-event basis. For each event it determines the energy, thecoefficients for a straight line fitted to the base line, and rough time informa-tion using the Slope Counting Condition (SCC) algorithm [42]. The energywas determined using trapezoidal shaping [43]. The SCC algorithm simplycounts the number of slopes that are negative or positive within a time win-dow of some fixed number of samples, which gives a response when passingthe leading edge of the preamplifier output signal. To get the better definitionof the starting time of the preamplifier pulse the EBC2 algorithm [42] wasused. It works by calculating the crossing between the straight line fitted tothe baseline and a second degree curve fitted to a few data points around asampling point determined by the SCC algorithm. If the EBC2 algorithm can-not find a crossing point between the baseline and the second degree curve,the time at which the derivative of the second degree curve is zero is used asthe starting time of the pulse. All parameters used in the algorithms are easilychanged if needed.

Also determined, together with t0, the starting time of the preamplifierpulse, were the five rise times t10, t30, t60, t90, and t100. They were determinedas follows, exemplified for t30. From the sampling point with the largest am-plitude calculate the 30 % amplitude of the signal. Find the sampling pointclosest in value to this amplitude, then fit a second degree curve to a few sam-pling points around the selected point. Calculate t30 from the second degreecurve.

7.4 Short summary of the results of paper IINo difference between neutron and γ-ray induced pulse shapes was observedin this work. It was, however, concluded that germanium detectors, whichare used with a low energy threshold, as will be the case for the AGATAdetectors, will detect pulses from elastically scattered neutrons. The numberof registered interactions due to elastic scattering of neutrons increases fast asthe energy threshold is lowered. This effect is shown in figure 7.4. The pulse-

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Ge Energy [keV]0 20 40 60 80

Coun

ts

0

50

100

150

200

310×

Simulated Ge energy

Experimental Ge energy

Figure 7.4: Simulated and experimental Ge-energy spectrum for neutron inducedpulses. A 252Cf neutron source was used and γ rays were discriminated using time-of-flight techniques. The experimental energy threshold was 18 keV.

height defect for germanium recoils in germanium, which has been observedpreviously [44, 45, 46], was confirmed in this work.

Neutron time-of-flight discriminated pulse-height spectra were measured.They show the characteristic neutron induced peaks and distributions observedalready in earlier works. An example of such a spectrum is shown in figure7.5.

46

Energy [keV]0 100 200 300 400 500 600 700 800

Coun

ts

0

2000

4000

)γGe(n,72Ge(n,n’), 7369 keV,

Ge(n,n’)76563 keV, )γGe(n,73Ge(n,n’),74596 keV,)γGe(n,73Ge(n,n’),74609 keV,

Ge(n,n)

Ge(n,n’)72693 keV, F(n,n’)19110 keV, 197 keV,

Figure 7.5: Experimental Ge-energy spectrum for neutron induced pulses, the Gedetector used was an n-type 55 % closed-end coaxial. A 252Cf neutron source wasused and γ rays were discriminated using time-of-flight techniques. The experimentalenergy threshold was 18 keV.

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8 AGATA

Conventional HPGe-detector based γ-ray spectrometers have a large draw-back: to get high-quality spectra from such spectrometers the use of anti-Compton detectors is essential. These so-called Compton-suppression shields,usually made of BGO scintillator detectors, cover a large amount of solid an-gle, thus reducing the efficiency of the γ-ray spectrometer. Simulations of ashell consisting of 100− 200 individual Ge crystals, covering a solid angleof almost 4π , have shown that it would perform worse in terms of resolv-ing power than a Compton-suppressed array such as EUROBALL [47]. AGe shell based on segmented Ge detectors and combined with γ-ray trackingwould on the other hand have much better performance than the present γ-rayspectrometers. Extensive research and development work on γ-ray trackingarrays is currently carried out around the world, mainly in the framework ofthe AGATA [14] and GRETA [15] projects.

AGATA, the Advanced GAmma Tracking Array, will be a 4π γ-ray spec-trometer array based on segmented encapsulated HPGe crystals. The currentlychosen geometry consist of 180 germanium crystals mounted in triple clusterdetectors. With this geometry about 80% of the solid angle will be coveredby Ge detectors. Photos of a prototype crystal and a drawing of an AGATAtriple cluster detector are shown in figure 8.1. The germanium crystals used inAGATA are divided into 36 segments plus a core contact and are made usingthe encapsulation technology. In figure 8.2 the 180 crystal version of AGATAis shown as modelled in Geant4. The AGATA demonstrator with four to fivetriple clusters is currently being built and will be ready in 2007. The mainaim of the demonstrator is to prove that the γ-ray tracking technique worksin real experiments. The construction of the full AGATA 180 array will, if fi-nanced, start shortly after the tests performed with the demonstrator, and willbe completed not earlier than 2012.

Heavy-ion fusion-evaporation reactions, which are used to produce the nu-clides to be studied through γ-ray spectroscopy, are usually associated withemission of fast neutrons. The average energy of the emitted neutrons is typ-ically well below 5 MeV. For germanium arrays like the EUROBALL, theseneutrons lower both the photo-peak efficiency and the peak-to-total of theγ-ray spectrometer. This is mainly due to the γ-ray background from the in-elastic scattering of neutrons against nearby material, such as the detectors

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Figure 8.1: Photos of a prototype Ge crystal with a symmetric shape are shown onthe left side. On the right side CAD drawings of the segmented asymmetric crystal(bottom) and of the complete triple cluster detector unit with its cryostat (top) areshown.

themselves. At these neutron energies, however, the cross section for elasticscattering is much higher than the cross section for inelastic scattering. Thelargest fraction, about 90 %, of the neutron interactions in the detectors willtherefore be low-energy interactions. In classic γ-ray spectrometers such in-teractions would usually not be detected. The situation is different in a γ-raytracking array, where the energy threshold has to be very low in order to keepthe γ-ray tracking efficiency high. Because of this low energy threshold, elas-tically scattered neutrons might effect γ-ray tracking arrays more than arrayswhich do not use γ-ray tracking. This issue has been addressed in detail inpaper III. Another question addressed in paper III is if AGATA can be used asan effective neutron detector in parallel with working as a γ-ray spectrometer.

8.1 Monte Carlo simulations of AGATAThe Monte Carlo software used to simulate the response of AGATA to γ raysand neutrons was written by Enrico Farnea et al. [48] using the Geant4 pack-age. Since it is based on Geant4, the program is in most aspects similar tothe programs used in the simulation of the Neutron Wall and the simulationsdescribed in paper II.

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Figure 8.2: The picture shows the 180 crystal version of AGATA as modelled in theGeant4 simulation [48]. The three different shades correspond to the three slightlydifferent geometries of the asymmetric crystals. The crystals will be mounted in triplecluster detector units, which will house one crystal of each type.

Due to the finite range of secondary electrons and the possible emission ofbremsstrahlung photons from these electrons as they are stopped in germa-nium detectors, there is a lower limit to how well defined a γ-ray interactionis in terms of the position of the created charge carriers. In the Monte Carlosimulation of AGATA there is a choice to whether the simulation should trackthe electrons from γ-ray interactions or just deposit the energy given to theelectron at the position of the interaction. If the electrons are not tracked thefinite range of the electrons and the emission of bremsstrahlung photons areneglected. For paper III full electron tracking was used. The size of the elec-tron tracks are, however, small compared to the assumed position resolutionof the segmented detectors. Therefore, the use of full electron tracking doesnot make a large difference to the final result.

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The simulated interaction points are summed up if they are too close to beresolved by the detectors and the energy and position of the interactions aresmeared to emulate the resolution of the detectors. A detailed description ofhow the output from the Monte Carlo simulation is treated before and afterγ-ray tracking is given in paper III and reference [35].

8.2 Short summary of the results of paper IIINeutrons with a few MeV of kinetic energy have a probability of about 45 %to give a detectable signal in AGATA, assuming a low-energy threshold of5 keV. Depending on its energy, each detected neutron will give rise to 3 to11 interactions in AGATA. As discussed in paper II, it is not possible to sep-arate interactions due to neutrons and γ rays based on pulse-shape analysis.Attempts to use geometrical relations between the interactions to distinguishneutrons and γ rays, as described in paper III, were not successful.

The possibility of using γ-ray tracking to discriminate against γ rays frominelastic scattering of neutrons was also investigated. Gamma-ray trackingwas used to calculate the angle of the first Compton scattering of a track intwo different ways: by using the energies of the first interaction and of thecomplete track according to equation 2.3 and by using the positions of the twofirst interaction points and the centre of AGATA. For a correctly tracked fullyabsorbed γ ray emitted from the centre of AGATA the difference between thetwo calculated angles should be small. This approach did have some success.The reduction in peak intensity was a factor 2.5 larger for γ-ray peaks dueto inelastic scattering than for peaks due to γ-rays emitted from the centre ofAGATA. An increase in the peak-to-background ratio due to the rejection ofγ-ray tracks from not fully absorbed γ rays was also found.

For future spectrometers, based on γ-ray tracking, the obtained results im-ply that there will be a need for a neutron ancillary detector system. Thenegative influence of neutrons on the performance of γ-ray tracking arrays is,however, not larger than for classical γ-ray spectrometers. The latter result isof great importance for experiments on the neutron-rich side of the line of βstability, in which the neutron multiplicities of the nuclear reactions may bevery high.

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9 Conclusions and outlook

When the Neutron Wall was designed the most important goal was that ofhigh neutron detection efficiency with the constraint that it had to fit into themechanical structure of EUROBALL. The adopted design fulfils these goals,but suffers from neutron scattering between detector segments, which givesrise to multiple signals from single neutrons. The scattering makes it difficultto correctly determine the number of detected neutrons and discriminationmethods that decreases the neutron efficiency have to be applied to get cleanγ-ray spectra.

Despite a very good separation between γ rays and neutrons it was in paperI shown that the mis-interpretation of γ rays as neutrons is of great importancewhen one tries to determine the number of detected neutrons. Events with twoapparent neutrons detected, of which one is a mis-interpreted γ ray, cannot bediscriminated against by the methods used for rejecting scattered neutrons.

The simplest solution to both of these problems would be to make a NeutronWall with a larger distance to the target position. In this way the detector seg-ments would be larger and the probability for a neutron to scatter between twodetector segments would decrease. The larger distance would also improvethe time-of-flight separation of γ rays and neutrons. Such a solution, however,has its own problems, mainly connected to the light collection properties ofthe detectors. For improving the present detector system the thickness andmaterial of the shield used for absorbing x rays and low-energy γ rays shouldbe optimised using Monte Carlo simulations. A trade off between the absorp-tion of γ and x rays and the risk of producing γ rays and in particular neutronsthrough nuclear reactions in the shield will determine the thickness and mate-rial to be used.

The study of neutrons interacting in a HPGe detector, in order to find a wayto separate interactions due to neutrons and γ rays using pulse-shape analysis,gave several important insights benefiting the study of neutron interactionsin AGATA. Not only was the high detection efficiency of neutrons by elasticscattering against the atoms in Ge detectors confirmed, but very conclusiveresults regarding the pulse shapes due to neutron interactions were also found:they are identical to the pulse shapes due to γ-ray interactions.

From the investigation of the impact of neutrons on the performance ofAGATA it has been concluded that interactions due to elastically scattered

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neutrons will not disturb the γ-ray tracking algorithms. Thus, γ-ray spec-trometers based on γ-ray tracking will not be very sensitive to neutrons. Theneutrons will, however, create a γ-ray background due to the inelastic scatter-ing of neutrons from the germanium atoms in AGATA, and this can prove tobe a problem in experiments where a very low background is of importance.Using the information from γ-ray tracking it is, however, possible to reducethis neutron-induced background, but this is at the expense of a large loss inphoto-peak efficiency.

The last conclusion drawn from this work is that a dedicated neutron detec-tor system will be needed for AGATA. The full use of Monte Carlo simulationtechniques should be used in order to optimise the new neutron detector sys-tem for high efficiency while retaining a good ability to determine the numberof detected neutrons.

Looking into the future, γ-ray spectrometers based on γ-ray tracking willallow studies of nuclear structure phenomena presently out of reach. However,a lot of development remains before these new very powerful spectrometerscan be used in experiments.

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10 Summary in Swedish: Karakterisering avNeutronväggen och av neutroninteraktioner igermaniumdetektorsystem

Den del inom kärnfysiken som undersöker hur nukleoner (protoner och neu-troner) växelverkar i atomkärnor och vilka fenomen dessa växelverkningarger upphov till vid låga excitationsenergier, kallas kärnstrukturfysik. Kärn-strukturfysik krävs för att kunna förklara hur de tyngre grundämnen som finnsi naturen har kunnat skapas och är därför viktig för att vi ska kunna förklaravarför världen ser ut som den gör.

Nukleonerna i atomkärnor hålls ihop av den så kallade “starka kraften”.Den “starka kraften” har några egenheter som gör det svårt att beräkna egen-skaper hos atomkärnor med hjälp av de enskilda krafterna mellan alla nuk-leoner i atomkärnorna. Dessutom försvåras en matematisk beskrivning pågrund av det så kallade “mångkroppsproblemet”. På grund av dessa komplika-tioner utvecklas, och har utvecklats, modeller som baseras på intelligenta ap-proximationer som innehåller det essentiella i fysiken. Dessa modeller måste,liksom alla andra modeller, utvecklas och testas genom jämförelser med ex-perimentella data. För att ta fram dessa data krävs det väl utförda experiment,där mätutrustning vars beteende är mycket väl karaktäriserat används så attman kan särskilja fysik från mätresultat.

En stor del av vår kunskap inom kärnstrukturfysik har vi fått genom att kol-lidera atomkärnor som accelererats till en hastighet motsvarande några pro-cent av ljusets. Den höga hastigheten krävs för att atomkärnorna ska kunnakomma tillräckligt nära varandra så att den “starka kraften” kan sammanfogade två till en atomkärna. Den nya atomkärnan har för mycket energi ochrörelsemängdsmoment och för att göra sig av med dem sänder kärnan ut någoneller några protoner, neutroner, alfapartiklar och, när alla partiklar sänts iväg,gammakvanta. Ett gammakvantum är partikelbeskrivningen av gammastrål-ning och är i princip samma sak som den röntgenstrålning som används inomsjukvården. Det är oftast dessa gammakvanta som används för att studeraatomkärnan eftersom de storheter som kan utvinnas ur dem till stor del över-ensstämmer med de storheter som kan beräknas med hjälp av de teoretiskamodeller som används för att beskriva atomkärnor. Exempel på vad man kanbestämma med hjälp av dessa gammakvanta är energin hos exciterade till-stånd i atomkärnan eller hur deformerad atomkärnan är. De två exemplen

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är något olika då bestämningen av energin hos de exciterade tillstånden ärmodelloberoende i motsats till bestämmingen av kärnans deformation som ärmodellberoende.

För att kunna göra den typ av experiment som beskrivits och ha någon an-vändning för de data som experimenten producerar, måste man kunna be-stämma vilken atomkärna som sänder ut gammakvanta, vilka i sin tur måstedetekteras med hög effektivitet och noggranhet. Det finns många olika sätt attbestämma från vilken atomkärna de utsända gammakvanta kommer men ettav de sätt som är enklast att förstå är att addera alla protoner och neutronersom fanns i de två atomkärnorna som slogs ihop till en atomkärna och sedandra av det antal neutroner och protoner som sänds ut från den nya atomkärnanoch på det sättet räkna ut vilken atomkärna det är. I praktiken är det docklite svårare därför att det inte går att detektera alla de protoner och neutronersom sänds ut och just neutroner är särskilt svåra att detektera eftersom de inteär elektriskt laddade. Att detektera de utsända gammakvanta görs vanligenmed hjälp av germaniumdetektorer, som är en typ detektor med en mycketgod energiupplösning och som dessutom kan tillverkas stora nog för att gam-makvantet ska ha en stor sannolikhet att helt och hållet absorberas i detektorn.Om man samlar flera detektorer på samma ställe med avsikten att öka sanno-likheten att detektera ett gammakvantum brukar de tillsammans kallas för engammaspektrometer.

Mycket av den här avhandlingen handlar om neutroner, då den till en stordel bygger på karakteriseringen av neutrondetektorsystemet Neutronväggen(the Neutron Wall) som har utvecklats just för att räkna de neutroner somsänds ut i den typ av experiment som beskrivits ovan. Tillsammans med gam-maspektrometern EUROBALL och proton-alpha partikeldetektorn EUCLI-DES utgör den en mycket bra experimentuppställning för experiment inomkärnstrukturfysik. Neutronväggen består av 50 separata vätskescintillator ochhar för våra typer av experiment en effektivitet på ungefär 30 %, vilket mot-svarar att var tredje utsänd neutron detekteras.

När man gör experiment i syfte att skapa och lära sig mer om atomkärnormed för få neutroner blir just neutrondetektion en av de mest kritiska parame-trarna i experimentet. Skälet till det är enkelt men kanske något svårgenom-skådligt. Under experimentet skapas inte bara den sorts atomkärna man villstudera, utan även ett flertal andra sorter och eftersom sannolikheten att ska-pas, på den neutronfattiga sidan, ökar med antalet neutroner som finns i denfärdiga kärnar kommer de allra flesta atomkärnor som bildats att ha för månganeutroner. Det betyder i sin tur att de flesta gammakvanta som man detekterarkommer från fel atomkärna och med andra ord inte innehåller den informationman är intresserad av. Lösningen är att räkna de utsända neutronerna men detvisar sig vara svårare än man kan tro och det på grund av neutroners egen-het att studsa mellan flera detektorer i Neutronväggen och därmed detekteras

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flera gånger. Frågan blir alltså, var det två neutroner vi detekterade eller baraen som studsade omkring? Det här är ett välkänt problem för neutrondetek-torsystem som består av fler än en detektor och har studerats tidigare, menaldrig för Neutronväggen. Därför gjordes en karakteriseringen av den genomatt jämföra resultat från simuleringar med resultat från två olika experiment.Simuleringarna var av Monte Carlo-typ, vilket i korthet betyder att man an-vänder kända sannolikheter för att beräkna vad som sker. Dessa hade, förutomovan nämnda allmänna karakteriseringen, även som mål att hitta metoder föratt bättre kunna separera händelser (=detekterad reaktioner) där en neutrondetekterats två gånger från händelser där rätt antal neutroner detekterats. Demest användbara metoderna visade sig bygga på korrelationer mellan skill-naden i flygtid för de två neutronerna och avståndet mellan de två vätskescin-tillatorer som de detekterats i. För riktiga tvåneutronhändelser saknas en kor-relation mellan flygtid och avstånd medan för spridda neutroner är skillnadeni flygtid större om det är ett längre avstånd mellan de två vätskescintillator-erna. Genom att utnyttja den här korrelation kan man minska antalet felak-tiga händelser till några få procent av det ursprungliga antalet, samtidigt somnära hälften av de korrekta händelserna blir kvar. Generalisering till händelserdär man vill detektera reaktioner med tre utsända neutroner i en bakgrund avreaktioner med en eller två utsända neutroner låter sig göras med ett liknanderesultat. Dessa resultat är i överensstämmelse med tidigare liknande arbetenoch de vidarutvecklade metoderna gav ytterligare förbättringar. Ett av de vik-tigaste resultaten från arbetet är att gammakvanta som, av något skäl tolkatssom neutroner i vätskescintillatorerna ger upphov till händelser som ser utatt ha fler detekterade neutroner än de har och att dessa händelser ej går attsärskilja från korrekta händelser. Att dessa, väldigt få, felaktigt tolkade gam-makvanta spelar en väldigt stor roll för hur väl Neutronväggen kan uppfyllasin uppgift när man ligger på gränsen av dess prestanda var förvånande ochtidigare okänt.

Gammaspårning är ett helt nytt koncept för gammaspektrometrar som byg-ger på att man med nya germaniumdetektorer kan, förutom den energi somett gammakvantum deponerat, bestämma position för energideponeringen idetektorn. Eftersom de processer som ger upphov till gammakvantas en-ergideponeringar i germaniumdetektorer är välkända kan man använda deninformationen för återskapa gammakvantas väg genom detektorn, därav nam-net gammaspårning. Dessa gammaspektrometrar, som ännu inte finns men ärunder utveckling, kan ses som ett ihåligt klot av germanium med en inner-diameter på cirka 20 cm och en ytterdiameter på cirka 30 cm. En simuleringvisade att ett sådant “germaniumskal” också skulle gå att använda som neutr-ondetektor om det finns någon möjlighet att säga hurvida en energideponeringi skalet kommer från en neutron eller ett gammakvantum, då sannolikheten föratt en neutron skulle deponera nog med energi för att upptäckas beräknades

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till 40 %. Den höga sannolikheten för neutroner att interagera i germani-umdetekorerna kan också tänkas påverka gammaspårningen på ett negativtsätt. För att grundligt reda ut hur neutroner kommer att interagera i framtidagammaspektrometrar samt om deras “germaniumskal” ska kunna användassom neutrondetektorer gjordes två studier, en för att fördjupa de kunskapersom finns om hur neutroner rent generellt interagerar i germaniumdetektoreroch en studie för att se hur neutronerna påverkar framtida gammaspektrome-trar och gammaspårningen i dessa.

Neutroners interaktioner i germaniumdetektorer har studerats ingående tidi-gare men då med andra foki. Oftast har man studerat de gammatoppar somfås i energispektra när neutroner studsar mot germaniumatomerna i detektorn,med resultatet att gammakvanta bildas, ungefär på samma sätt som i de ex-periment som beskrevs i början av sammanfattningen. Dessa gammatopparhar studerats för att använda germaniumdetektorer som neutronenergispek-trometrar eller bara för att lära sig känna igen de neutroninducerade gam-matopparna. I det här arbetet har fokus istället varit på de mycket mindresignaler som fås då neutroner studsar mot germaniumatomkärnor utan att nå-gra gammakvanta sänds ut. Fokus var lagt på dessa mycket mindre signaler dådet inte finns någon möjlighet att detektorerna kan se skillnad på ett gamma-kvantum utsänt från en germaniumatom eller ett gammakvantum utsänt frånden atomkärna man vill studera. Den enda möjligheten att kunna särskilja de-tektorsignaler från neutroner och gammakvanta är därför att den signal somgenereras när en germaniumatom knuffats till av en neutron skiljer sig frånden signal som bildas när en elektron knuffas till av ett gammakvantum.

En signal från en germaniumdetektor brukar ofta lite slarvigt kallas puls-form. Två olika germaniumdetektorer har bestrålats med neutroner från ettradioaktivt ämne som sänder ut neutroner och experimentalla pulsformer fråndessa båda detektorer har genom pulsformsanalys jämförts med beräknadepulsformer från simuleringar av experimenten. Simuleringarna gjordes för attkunna särskilja de olika effekter som påverkar pulsformerna genom att ute-sluta alla inverkningar på pulsformerna som kan tänkas bero på om det varen neutron eller ett gammakvantum som gett upphov till pulsen i detektorn.Tyvärr hittades inga skillnader på pulsformerna men arbetat gav trots det fleraviktiga resultat, varav ett av de viktigaste var att man i germaniumdetektor-system med en låg energitröskel kan förvänta sig att se många lågenergiinter-aktioner från neutroner.

Efter noggranna studier av hur neutroner interagerar i enskilda germani-umdetektorer fokuserades på neutroner i större detektorsystem. I det här fal-let Advanced GAmma Tracking Array (AGATA) som är Europas projekter-ade gammaspårningsspektrometer och som utvecklas i ett internationellt sam-arbete som inkluderar flera europeiska länder. Ett Monte Carlo-simulerings-program utvecklat i Italien har använts för att undersöka flera olika aspekter på

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neutroninteraktioner i AGATA. Sannolikheten för en neutron att detekteras iAGATA, neutroneffektiviteten, har bestämts för flera olika energitrösklar (en-ergitröskel=lägsta deponerade energi som ger en detekterbar signal) i ett neu-tronenergiområde som sträcker sig från 50 keV till 20 MeV. Det är ett ener-giområde som täcker in de neutroner som sänds ut vid den typ av experimentsom beskrivits här. Dessutom gjordes realistiska simuleringar där neutroneroch gammakvanta tillåtits att interagera samtidigt i AGATA, vilket inte gjortstidigare. Då simuleringsresultat innehöll interaktioner från både neutroneroch gammakvanta provades några olika idéer för hur geometriska relationermellan interaktioner skulle kunna användas för att identifiera neutroninterak-tioner.

Resultat från neutroneffektivitsberäkningarna bekräftade att sannolikhetenför att en neutron med en energi högre än 500 keV ska detekteras i AGATA ärrunt 45 %. Simuleringarna visade också att varje detekterad neutron gav upp-hov till mellan 3 och 11 extra interaktioner i AGATA. Hur dessa interaktionerpåverkar gammaspårning undersöktes också, vilket gav resultaten att sanno-likheten för att helt detektera ett gammakvantum i AGATA i medeltal sjönken procent per utskickad neutron. Dessutom ger neutronerna upphov till bak-grundssignaler som vid experiment där man för övrigt har en låg bakgrundkan ställa till med problem.

För att undersöka möjligheten att skilja på interaktioner från neutroner ochgammakvanta prövades två olika idéer, den första baserad på observationenatt neutroner ger fler lågenergiinteraktioner än gammakvanta medan den an-dra metoden baserades på den information som gammaspårningen ger om var-ifrån ett gammakvantum sänts ut. Båda metodera hade en viss känslighet meninte stor nog för att min i praktiken ska kunna använda AGATA till att räknaantalet neutroner som sänts ut i en kärnreaktion. Metod nummer två kan dockanvändas för att minska den bakgrund som neutronerna ger upphov till.

Resultat av simuleringarna av neutroner i AGATA kan sammanfattas medatt den nya generations gammaspektrometrar, som kommer att använda gam-maspårning, i stort sett reagerar likadant som de äldre gammaspektrometrarnapå neutroner, vilket är ett positivt resultat.

Gammaspårningens användbarhet begränsas inte till grundforskning inomkärnfysik. Förutom annan forskning, så som inom astronomi där gammas-trålning från rymden undersöks, kan gammaspårning också användas för av-bildning av radioaktiva föremål, det vill säga som så kallad gammakamera.Gammakamerans användningsområden är många, men det är för avbildningarinom sjukvården som intresset är störst.

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11 Acknowledgements

There are quite a few things that have to work out for a PhD thesis to be writ-ten, and most important are those things that have kept and keeps the authoralive:Kristina Örjan Jenny Hanna Kalle IngridBirgit Geer OlaMats Erik Fredrik Henrik Jennie Karl,thank you.

A good supervisor is also needed, and this I have had in Johan Nyberg. Iwould also like to thank Matthias Weiszflog for supervision during the firstfew years of my PhD studies. Finally I thank Anders Hjalmarsson for fruitfuldiscussions about Geant4.

Not all days are days made to get up early, go to work, and work hard. Veryfew are... So the presence of people willing to listen to my never ending nagabout just about everything has been crucial! A big

YEAH

to you all!

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References

[1] K. L. Heyde, The Nuclear Shell Model, 2nd Edition, Springer-Verlag, 1994.

[2] J. Simpson, Z. Phys. A 358 (1997) 139.

[3] W. Korten, S. E. Lunardi, Achievements with the EUROBALL spec-trometer, Scientific and Technical report 1997 - 2003, Tech. rep.,http://www-dapnia.cea.fr/Sphn/Deformes/EB/eb-report-final.pdf (2003).

[4] Ö. Skeppstedt, et al., Nucl. Instr. Methods A 421 (1999) 531–541.

[5] A. Gadea, et al., LNL Annual Report 1999 INFN (REP) 160/00., Tech. rep.(1999).

[6] J. Allison, et al., Nucl. Instr. Methods A 506 (2003) 250–303.

[7] J. Eberth, et al., MINIBALL A Ge Detector Array for Radioactive Ion BeamFacilities, Progress in Particle and Nuclear Physics 46 (2001) 389–398.

[8] T. Kröll, et al., Gamma-ray tracking with the MARS detector, Eur. Phys. J. A 20(2004) 205–206.

[9] M. Descovich, Improving the position resolution of Highly Segmented HPGeDetectors using Pulse Shape Analysis Methods, Ph.D. thesis, Oliver Lodge Lab-oratory, University of Liverpool (November 2002).

[10] K. Vetter, et al., Nucl. Instr. Methods A 452.

[11] D. Bazzacco, T. Kröll, Nucl. Instr. Methods A 463 (2001) 227.

[12] O. Wieland, et al., Nucl. Instr. Methods A 487 (2002) 441.

[13] I.-Y. Lee, Nucl. Instr. Methods A 422 (1999) 195–200.

[14] AGATA, http://www-w2k.gsi.de/agata/.

[15] GRETA, http://greta.lbl.gov/.

[16] M. Berger, et al., XCOM: Photon Cross Sections Database, http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html.

63

[17] O. Klein, Y. Nishina, Z. für Physik (52) (1929) 853–868.

[18] S. S. Wong, Introductory nuclear physics, 2nd Edition, Wiley Interscience, 1998.

[19] Evaluated Nuclear Data File (ENDF), http://www.nndc.bnl.gov/exfor/endf00.htm.

[20] G. Knoll, Radiation Detection and Measurement, 3rd Edition, John Wiley &Sons, 2000.

[21] J. Ziegler, J.F. Biersack, U. Littmark, The Stopping and Range of Ions in Solids,Pergamon Press, New York, 2003, http://www.srim.org.

[22] M. Hoek, Development and Use of Neutron Scintillator Systems for FusionPlasma Diagnostics, Ph.D. thesis, Chalmers University of Technology (1992).

[23] M. Moszynski, H. Mach, A method for picosecond lifetime measurements forneutronn-rich nuclei, Nucl. Instr. Methods A 277 (1989) 407–417.

[24] S. M. Sze, Semiconductor devices, Physics and Technology, John Wiley & Sons,1985.

[25] W. Shockley, J. Appl. Phys. 9 (1938) 635.

[26] S. Ramo, Proc. IRE 27 (1939) 584.

[27] C. Kittel, Introduction to Solid State Physics, 7th Edition, John Wiley & Sons,1996.

[28] L. Reggiani, et al., Phys. Rev. B 16 (1977) 2781.

[29] L. Mihailescu, et al., Nucl. Instr. and Meth. A 447 (2000) 350.

[30] M. Heath, SCIENTIFIC COMPUTING AN INTRODUCTORY SURVEY,McGraw-Hill, 1997.

[31] J. F. Briesmeister (Ed.), MCNP - A General Monte Carlo N-Particle TransportCode, Version 4C, Tech. Rep. LA-13709-M (April 2000).

[32] G. Schmid, et al., Nucl. Instr. Methods A 430 (1999) 69–83.

[33] J. van der Marel, B. Cederwall, Nucl. Instr. Methods A 437 (1999) 538–551.

[34] I. Piqueras, et al., Nucl. Instr. Methods A 516 (2004) 122–133.

[35] A. Lopez-Martens, et al., Nucl. Instr. Methods A 533 (2004) 454–466.

[36] L. Milechina, B. Cederwall, Nucl. Instr. Methods A 525 (2004) 208–212.

[37] ROOT, http://root.cern.ch/.

64

[38] P. Tove, W. Seibt, Nucl. Instr. Methods 51 (1967) 261.

[39] G. England, J.B.A. Field, T. Ophel, Nucl. Instr. and Meth. A 280 (1989) 291.

[40] W. Pausch, G. Bohne, D. Hilscher, Nucl. Instr. and Meth. A 337 (1994) 573.

[41] P. Medina, The TNT project, AGATA EDAQ Meeting, Padova, Sep 19-20 2002, http://nsg.tsl.uu.se/agata/padova-sep2002/slides/Medina/.

[42] W. Gast, et al., Digital Signal Processing And Algorithms For Gamma-RayTracking, IEEE Trans. Nuc. Sci. 48 (6).

[43] V. Jordanov, G. Knoll, Nucl. Instr. and Meth. A 345 (1994) 337.

[44] J. Lindhard, et al., Mat. Fys. Medd. Dan. Vid. Selsk. 33 (1963) 1.

[45] C. Chasman, et al., Phys. Rev. Lett. 21 (1968) 1430.

[46] L. Baudis, et al., Nucl. Instr. and Meth. A 418 (1998) 348.

[47] W. Korten, J. Gerl (Eds.), AGATA Technical Proposal, 2001.

[48] E. Farnea, D. Bazzacco, LNL Annual Report 2003, p. 158 LNL-INFN(REP)-202/2004 ISBN 88-7337-004-7, LNL Legnaro, see also http://agata.pd.infn.it/ (2003).

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