Charge radii measured by laser
spectroscopy around Z = 30
Jon Billowes
ISCOOL – COLLAPS Collaboration
Outline
• Charge radii measurements on stable isotopes
- atomic factor calibrations
• Radioactive isotopes measurements (ISCOOL – COLLAPS)
• Charge radii for Ga isotopes (published)
• Charge radii for Cu isotopes (to be published)
• Charge radii for Zn isotopes (preliminary results)
• Preparation considerations for Ni isotopes
Electron scattering on stable isotopes
Coulombic cross section modified by
a form factor:
Fourier transform of F(q) gives ρch(r)
For low momentum transfer (q)
Isotope shifts in atomic transitions
6p
Optical transitions (3 eV)
6s
Shift ~ 10-6 eV
n=3
e-
n=2
K X-rays (50 keV)
n=1
Shift ~ 0.1 eV
μ-
Muonic X-rays (1 MeV)
Shift ~ 5,000 eV
(Theory allows absolute
size measurement)
Nuclear charge distribution differences between isotopes
(combined analysis of electron scattering and muonic x-ray data)
Lines show upper and lower
limits of differences
Wohlfahrt et al Phys. Rev. C22 (1980) 264
Nuclear charge distribution differences between isotones
(combined analysis of electron scattering and muonic x-ray data)
Lines show upper and lower
limits of differences
(πf7/2)2
(πp3/2)2
Wohlfahrt et al Phys. Rev. C22 (1980) 264
“Kinks” at Z=28 and N=28
Wohlfahrt et al.,
Phys. Rev. C23 (1981) 533
ISOTONES
ISOTOPES
rms nuclear charge radii,
including radioisotopes,
for medium mass and
heavy elements
Angeli & Marinova
Atomic Data and Nuclear Data Tables 99 (2013) 69
Features:
• Kinks at closed neutron shells
• Regular odd-even staggering (sometimes
reversed due to nuclear structure effects)
• Obvious shape effects (Light Hg, N=60…)
• Radii of isotopes increase at ~half rate of
1.2A1/3 fermi (neutron rich nuclei develop
neutron skin)
Isotope shift = (normal + specific) mass shift + field shift
Approximate magnitudes for ΔA = 2
Element Transition
11Na
70Yb
Normal
Specific
Field
Doppler width
3s – 3p
550 MHz
200 MHz
-10 MHz
6s – 6p
20 MHz
‹ 20 MHz
-1500 MHz
Light element measurement techniques should be Doppler-free.
Evaluation of atomic F and M factors required.
1400 MHz
500 MHz
Fricke & Heilig Nuclear Charge Radii (Springer 2004)
Analysis of stable isotopes
Combined analysis
Result: Fi and Mi providing δ<r2> for all isotopes (including radioactive)
For optical / eμ King Plot analysis, at least three stable isotopes (two
intervals) needed
Zn, Ni – OK
Cu, Ga – only two stable isotopes, so only a single difference in mean square
charge radius.
Calibration options:
Calculations for F, M eg with multi-configuration Dirac-Fock (MCDF) methods.
Semi-empirical methods also available for F.
F normally under better control than M – so could adjust M to reproduce single
difference in MSCR from combined electron/muon measurements.
Fricke & Heilig Nuclear Charge Radii (Springer 2004)
Faults in recent (last two decades) experimental papers:
• Tendency to focus on features of laser systems; describe “again and again
origin of IS”; omit basic information on results.
• Convention on sign of IS – do papers follow their convention?
• Are error limits 1σ or 3σ?
• Transitions are chosen for ease of laser spectroscopy and not with respect of
usefulness for relevant physical result
• Quoted wavelength (nm but no digits after decimal point) may not identify
transition; give wavelength once and add complete description of transition.
“some papers omit wavelength and give only (many times) wavenumbers!”
• Give King plot with any previous work to demonstrate (or otherwise)
consistency. Explain anything outside quoted errors.
• Why change reference isotope from paper to paper? Use earlier literature.
• Avoid odd isotope as reference (eg risk of 2nd order hyperfine mixing)
Laser spectroscopy in Ni region (Z=28, 29, 30, 31)
Situation when this
programme started
Stable isotope
Previous studies by
laser spectroscopy
ISCOOL – COLLAPS measurements
Bunched-beam collinear laser spectroscopy
Gas-filled linear RFQ trap
CEC
Ion beam
cooler
Laser beam
Light collection region
5μs
(Laser resonance fluorescence)
+39.9 kV
40 kV
Reduces energy-spread of ion beam
Improves emittance of ion beam
+40 kV
On-line
ion source
Trap and accumulates ions – typically for 300 ms
Photons
during the 5µs when
Releases
ions inonly
a 15counted
µs bunch
ion beam passes photomultiplier tube.
50 ms trapping = 104 reduction in background
Nuclear structure interest in Z=30 region
• Migration of πf5/2 level
Gallium
• Spin measurements / confirmation
• N=40 sub-shell effects
• Test of shell model interactions
(using spins, magnetic and
quadrupole moments)
40Ca
core
GXPF1
GXPF1A
56Ni
core
JUN45
jj44b
• Radii of neutron-deficient isotopes
Matter radii
Gallium charge radii
RILIS ionization
scheme in ion source
Fluorescence
measurements
Atomic structure of gallium (Z=31)
Atomic factors
MCDF calculations (S. Fritzsche, Comput. Phys. Commun. 183, 1525 (2012))
F = +400 MHz.fm-2 – stable as MCDF wavefunctions enlarged
M = -431 GHz.u – but no final convergence
(NMS = +396 GHz.u)
M adjusted to allow better fit to muonic data for 69,71Ga: M = -211(21) GHz.u
Differences in mean square charge radii for gallium
Ge
Ga
Zn
A. Lépine-Szily et al.,
Eur. Phys. J. A 25 227 (2005)
Copper (Z=29) isotope shifts
(M.L. Bissell, T. Carette et al., to be published)
Main interest: is there an effect at N=40 subshell?
(parity change across N=40 reduces first-order M1
and E2 excitations, so moments do show a “magic”
behaviour)
Cu
Measurements on 324.8 nm (2S1/2
2P )
3/2
transition
Atomic factors
Extensive MCDF calculations (T. Carette and M. Godefroid)
F = -779 MHz.fm-2
M = 1368 GHz.u (compare with NMS = 506 GHz.u)
These values approx consistent with muonic atom 65,63Cu mscr difference
Differences in mean square charge radii (Z = 28 – 32)
Ge
Ga
Zn
Cu
Ni
Copper mean square charge radii after droplet model subtraction
Preliminary results for Zn charge radii
Charge radii – Liang Xie (Manchester)
Spins and moments – Calvin Wraith (Liverpool)
Poster “Spins and moments of odd-Zn isotopes and isomers
measured by collinear spectroscopy” Xiaofei Yang (Leuven)
Atomic charge exchange
Zn+ + Na  Zn* + Na+ + ΔE
(ΔE = 0 : resonant charge exchange)
ΔE is energy difference between final and initial electronic states
Ionization
potential
Na
3S
1
1P
1
481 nm
2.58 eV
3P
2
Resonant charge exchange
1S
Zn
0
Metastable state population
Directly – resonant
Cascade – from 3S1 state
Atoms neutralised via a non-resonant higher
excited state form a slower atomic beam. The
laser resonance of the 481 nm transition will have
a small satellite component on the low-velocity
side (corresponding to a 2.58 volt shift if it is the
3S state that is responsible)
1
The Zn beam can also lose quanta of 2.1 eV
through inelastic collisions with Na atoms before or
after neutralization.
68Zn
Offset frequency (MHz)
69Zn
1/2 ground state
9/2 isomer
Non-optical measurements
Ga
Zn
Cu
N=40
N=50
Considerations for Ni isotope measurements
Ionization
potential
5P
2
323.4 nm
many
states
5D
3
13 μs
Na
3F, 3D
Ni
Population of 5D3 by charge-exchange with Na at 30 keV ~4%
Population of 3D2,3 states after cascade ~14%. Nothing observed in 3D1
(Paul Mantica, MSU, Private Comm.)
K
F and M atomic factors for Ni atom from low-lying states
(D.H. Forest, Birmingham, Private Communication)
Wavelength (nm)
E (lower) E(upper)
cm-1
cm-1
F (MHz fm-2) M (60-58) (MHz)
294.3
298.1
298.4
299.4
300.2
300.4
301.9
303.2
303.8
305.1
204.8
879.8
0
204.8
204.8
879.8
0
0
204.8
204.8
210(47)
321(6)
-1117(206)
356(39)
306(98)
241(17)
-1405(174)
-882(81)
170(30)
269(55)
E (lower)
0
204.8, 879.8
(d)8 (s)2
(d)9 s
E(upper)
(d)8 sp
34163.3
34408.6
33500.9
33590.2
33500.9
43164.3
33112.4
32973.4
33112.4
32973.4
-820(12)
-494(1)
1301(53)
-1075(10)
-838(25)
-835(4)
1543(45)
1166(20)
-635(7)
-902(13)
NMS (60-58) ~ 315 MHz
Transitions from ground state are weak: 61Ni not measured, so missing from King plot
A and B hyperfine factors of low-lying states in Ni atom
(Childs & Goodman, Phys.Rev. 170 (1968) 136)
Energy (cm-1)
A (MHz)
B (MHz)
0
-215.040
-56.868
204.786
-454.972
-102.951
879.813
-171.584
-56.347
1332.153
-299.311
-42.063
Isotope shits for odd isotopes
– need nuclear spin I
J=3/2
Intervals depend on Aupper , Bupper,
and I, J, F
324.8 nm
J=1/2
Interval depends on Alower and I, J, F
Example for I=5/2
Experimental
spectrum
Ratio Aupper /Alower is independent of
nuclear moment (ie same for all
isotopes)
If the wrong value of I is used to fit the hyperfine structure then:
• May be impossible to fit structure (position or number of peaks)
• Deduced ratio Aupper /Alower is wrong
• Deduced relative peak intensities are wrong (Racah coefficients)
• Isotope shift is wrong
Spins confirmed through ratio of hyperfine A factors