1. Charge radii measured by laser spectroscopy around Z = 30
Jon Billowes
ISCOOL – COLLAPS Collaboration

2. 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

3. 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)

4. Isotope shifts in atomic transitions
Optical transitions (3 eV)
Shift ~ 10-6 eV 6s
n = 3
n = 2
K X-rays (50 keV)
Shift ~ 0.1 eV
n = 1 e- μ-
Muonic X-rays (1 MeV)
Shift ~ 5,000 eV (Theory allows absolute size measurement)

5. 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

6. 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

7. “Kinks” at Z=28 and N=28 ISOTONES ISOTOPES Wohlfahrt et al.,
Phys. Rev. C23 (1981) 533
ISOTONES
ISOTOPES

8. 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)

9. Approximate magnitudes for ΔA = 2
Isotope shift = (normal + specific) mass shift + field shift
Approximate magnitudes for ΔA = 2
Element Transition Normal Specific Field Doppler width
11Na s – 3p MHz MHz MHz MHz
70Yb s – 6p MHz ‹ 20 MHz MHz MHz
Light element measurement techniques should be Doppler-free.
Evaluation of atomic F and M factors required.

10. 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)

11. 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.

12. 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)

13. Laser spectroscopy in Ni region (Z=28, 29, 30, 31)
Situation when this programme started
Stable isotope
Previous studies by laser spectroscopy

14. ISCOOL – COLLAPS measurements
RILIS
COLLAPS
ISCOOL
HRS
GPS
1.4 GeV p+
PSB
ISCOOL – COLLAPS measurements

15. Bunched-beam collinear laser spectroscopy
Gas-filled linear RFQ trap
CEC
Ion beam cooler
Laser beam
Light collection region
(Laser resonance fluorescence)
5μs
+39.9 kV
Reduces energy-spread of ion beam
40 kV
Improves emittance of ion beam
Trap and accumulates ions – typically for 300 ms
+40 kV
On-line ion source
Releases ions in a 15 µs bunch
Photons only counted during the 5µs when ion beam passes photomultiplier tube.
50 ms trapping = 104 reduction in background

16. Nuclear structure interest in Z=30 region
Migration of πf5/2 level
Spin measurements / confirmation
N=40 sub-shell effects
Test of shell model interactions (using spins, magnetic and quadrupole moments)
Radii of neutron-deficient isotopes
Gallium
56Ni core
JUN45
jj44b
40Ca core
GXPF1
GXPF1A
Matter radii

17. Gallium charge radii Atomic structure of gallium (Z=31)
RILIS ionization scheme in ion source
Fluorescence measurements
Atomic structure of gallium (Z=31)

18. 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

19. Differences in mean square charge radii for galliumZn
Lépine-Szily et al.,
Eur. Phys. J. A (2005)

20. Cu 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 nm (2S1/2 2P3/2) 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

21. Differences in mean square charge radii (Z = 28 – 32)Ga Zn Cu Ni

22. Copper mean square charge radii after droplet model subtraction

23. 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)

24. 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
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 3S1 state that is responsible)
The Zn beam can also lose quanta of 2.1 eV through inelastic collisions with Na atoms before or after neutralization.
3S1
1P1
481 nm
2.58 eV
3P2 Na
Resonant charge exchange
1S0 Zn

25. 68Zn
Offset frequency (MHz)

26. 69Zn
1/2 ground state
9/2 isomer

27. Non-optical measurements

28. Ga Zn
N=50
N=40 Cu

29. Considerations for Ni isotope measurements
Ionization potential
5P2
323.4 nm
many states
5D μs K 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.)

30. F and M atomic factors for Ni atom from low-lying states
(D.H. Forest, Birmingham, Private Communication)
Wavelength (nm) E (lower) E(upper) F (MHz fm-2) M (60-58) (MHz)
cm-1 cm-1
(47) (12)
(6) (1)
(206) (53)
(39) (10)
(98) (25)
(17) (4)
(174) (45)
(81) (20)
(30) (7)
(55) (13)
E (lower)
0 (d)8 (s)2
204.8, (d)9 s
E(upper) (d)8 sp
NMS (60-58) ~ 315 MHz
Transitions from ground state are weak: 61Ni not measured, so missing from King plot

31. 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)

33. 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
Ratio Aupper /Alower is independent of nuclear moment (ie same for all isotopes)
Experimental spectrum
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

34. Spins confirmed through ratio of hyperfine A factors