outline lecture 2 · outline lecture 2 • isotope shiftt: determination of nuclear charge radii...
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Outline Lecture 2
• Isotope Shiftt: Determination of Nuclear Charge Radii
• Example 1: Mg Isotopes
• Example 2: Halo Nuclei: Charge Radii of Be Isotopes and a
Test of NR-QED Calculations
Collinear-Anticollinear Approach
• Example 3: The Calcium Isotopes
Bunched Beams
State-Selective Charge Exchange
• Hyperfine Structure and Nuclear Deformation
• Example 4: The Cd Isotopes
Reminder: Mass and Field Shift
Isotope Shifts of Mg Isotopes
Isotope A=
Charge Radii of Mg Isotopes
Other „Regions of Inversion“
A. Brown, Physics 3, 104 (2010)
https://physics.aps.org/articles/v3/104
The Beryllium Isotopic Chain
Stable Nucleus
208Pb
11Li
Neutron Halo
I. Tanihata, Progr. Part. Nucl. Phys 35, 505 (1995)
6He 8He
11Li
11Be12Be
14Be
4He
fm2.10
30
R
ARR
Theory: Mass Shift in Be+
Atomic Theory:
Photomultiplier
ion beamEkin~60 keV
collinear
laser beam
fixed frequency
+
anticollinear
laser beam
fixed frequency
Doppler-tuning 10c
10a
„CONVENTIONAL SETUP“
Acceleration /
Deceleration
2
0
222
0ca 1
= (U,m), = (U,m),
DU/U 10-4
dIS (9Be,11Be) = 18 MHz
10c
NEW APPROACH
Completely
independent
of U !
Experiment: Frequency-Comb Based
Collinear-Anticollinear Laser Spectroscopy
Laser System for Collinear-Anticollinear
Measurements
A. Krieger et al., Appl. Phys. B 123, 15 (2017)
Laser System for Collinear-Anticollinear
Measurements
A. Krieger et al., Appl. Phys. B 123, 15 (2017)
Ion-Photon Coincidence
A. Krieger et al., Appl. Phys. B 123, 15 (2017)
Experimental D1 and D2 Transition Frequencies
Be Be
A. Krieger et al., Appl. Phys. B 123, 15 (2017)
pure p²
pure
(sd)²
75% admixture
of (sd)²-levels
2s1/2
1s1/2
1p1/2
1d5/2
1p3/2
1d3/2
2
4
2
62
4
12BeN=8
Extracting Nuclear Charge Radii
Rc-n 8 fm
Experimental D1 and D2 Transition Frequencies
A. Krieger et al., Appl. Phys. B 123, 15 (2017)
Isotope-dependent Fine-Structure Splitting
W. Nörtershäuser, PRL 115, 033002 (2015)
A. Krieger et al., Appl. Phys. B 123, 15 (2017)
Fine Structure Splitting from Even Isotopes
A. Krieger et al., Appl. Phys. B 123, 15 (2017)
Take Home
• For light Nuclei the Field Shift is a small contribution to the isotope
shift.
• It can be separated only if highly precise atomic structure calculations
(now possible up to 5 electrons) and highly accurate isotope shifts are
available
• Charge Radii in this region are strongly affected by nuclear clustering
• The charge radius of 12Be clearly shows the disappearance of the N=8
shell closure
• Accurate measurements of fine-structure splittings of few-electron
systems provide a test of Quantum Electrodynamics QED
Detection Techniques in Collinear Laser
Spectroscopy
Prinzip des Akkumulieren und Kühlens
z
End p
late
pote
nti
al Accumulate
Release
Reacceleration
potentialPMT
10µs gatee.g. 100ms accumulation
=10µs gate width
Background
suppression~104
URF
Laser beamPMT
Accumulation for
e.g. 100 ms
E.M
ané
et a
l, E
ur.
Ph
ys. J. A
42, 5
03
(2
00
9)
F. Herfurth, NIMA 469, 254 (2001)
A. Nieminen, Phys. Rev. Lett. 88, 094801 (2002)
Bunched Beam Detection
~104 background
suppression
Photon Detection with Time Tagging
-500 -450 -400 -350 -300 -250 -2000
10
20
30
40
20,5
21,0
21,5
22,0
22,5
tim
e [
µs]
0
1
2
3
4
5
counts
voltage [V]
43Ca
+
Measurement of Calcium Isotopes using
Bunched Beam Detection
R.F. Garcia Ruiz et al., Nature Physics 12 (2016) 594
Spectra of 49,51,52Ca+
R.F. Garcia Ruiz et al., Nature Physics 12 (2016) 594
Extracted Charge Radii
R.F. Garcia Ruiz et al., Nature Physics 12 (2016) 594
Large charge radius of 52Ca:
No signature for shell closure
at N=32
Towards 54Ca
Goal: cross N=32 and reach N=34
For both N values there is experimental evidence for new shell closures
Challenge: Production Rate of about 1 ion/sec
Technique: State selective charge exchange
Garcia-Ruiz et al., J.Phys. G 44, 044003 (2017)
40Ca+ + Na 40Ca + Na+
(beam) (gas) (beam) (gas)
Charge Exchange Cross Section
Garcia-Ruiz et al., J.Phys. G 44, 044003 (2017)
Ratio of charge exchange cross
sections for 3d and 4s levels in
Ca+
Off-Resonance: Ion stays in 4s level
Resonance: Ion is transferred to 3d level
ce(3
d)
/
ce(4
s)
Towards 54Ca
Garcia-Ruiz et al., J.Phys. G 44, 044003 (2017)
1g
2d
3s
1h
1g9/2
1g7/22d5/2
2d3/23s1/21h11/2
1h9/2
50
5864
687082
92
50
82
Spherical Shell Model
2
28
20
28
50
8
20
28
50
82Z
N
Be
Mg
Halo nuclei
Island of inversion
Monopole migration
Ca
99Cd
130Cd
Nuclear Chart
Cd
11/2- -Isomers
F. Buchinger et al., Nucl.Phys. A 462, 305 (1987)
Fourth Harmonic Generation of 215 nm
Hyperfine Structure
Spin
Hyperfine Structure
~ Alow
~ Alow
~Aup
SpinMagnetic Moment, I
site nuclear at fieldmagnetic )0(
,)0(
e
eI
H
JI
HA
~Aup
Quadrupole moment Qs
site nuclear at
gradient fieldelectric )0(
),0(
zz
zzs
V
VeQB
Hyperfine Structure
SpinMagnetic Moment, I
site nuclear at fieldmagnetic )0(
,)0(
e
eI
H
JI
HA
~ μ(129mCd)
~ μ(111mCd)
Qs
Elektrical Hyperfine Structure
Isotope Shift
Hyperfine Structure
Isotope Shift
Hyperfine Structure
Shift of Hyperfine State Einfluss des
Quadrupolmomentes auf Niveauenergien
Nucleus
Electron Orbital
Analyzing Hyperfine Structure
Peak Positions:
choose I, Nonlinear Least Squares Fitting Au, Al, Bu, Bl, 0, 2red
Isomers (t1/2 > ms)
are easily identified
lowlowlowlowupupupup0 BABA
2
)1()1()1(
2),,(lowup,
JJIIFFCFJI
JIJI
JJIICCFJI
)12)(12(2
)1()1()1(),,( 4
3
up,low
m
low
m
low
m
low
m
low
m
up
m
up
m
up
m
up
m
IS BABAm m
ISISIsomer d Isomer-Spin: I m Isomer-Shift:
MHz
Extraction of Nuclear Moments
nucleus of site at fieldmagnetic )0(
)0(
e
eI
H
JI
HA
Determination of nuclear moments requires hyperfine fields !
Relatively large theoretical uncertainties
nucleus the of site the
at gradient fieldelectric )0(
),0(
zz
zz
V
eQVB
f
fI
AA
Re
Re
f
fB
BQQ
Re
Re
Alternatives:
Reference nuclei (stable Isotopes) with accurately known moments
Simple Structure in Complex Nuclei
1g
2d
3s
1h
1g9/2
1g7/22d5/2
2d3/23s1/21h11/2
1h9/2
50
5864
687082
92
50
82
Capacity of 1h11/2 niveau:
12 neutrons
→ 6 quad. moments
But: 10 quad. moments
Neutron pairs shared
between the neighboring
levels.
Capacity of 1h11/2 niveau:
12 neutrons
→ 6 quad. moments
But: 10 quad. moments
Neutron pairs shared
between the neighboring
levels.
D.T. Yordanov et al, PRL 110 (2013) 192501
Take Home
• Bunched beam spectroscopy increased the sensitivity by about a
factor of 100
• Isomeric states are easily discovered by laser spectroscopy
• The electric hyperfine structure reveals the nuclear deformation
• The quadrupole moment and its sign can be extracted from the
spectra