Charge radii measured by laser spectroscopy around Z = 30

Jon BillowesISCOOL – 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

Coulombic cross section modified by a form factor:

Fourier transform of F(q) gives ρch(r)

For low momentum transfer (q)

Electron scattering on stable isotopes

Isotope shifts in atomic transitions

n = 1

n = 2

n = 3

6s

6p

K X-rays (50 keV)

Shift ~ 0.1 eV

Muonic X-rays (1 MeV)

Shift ~ 5,000 eV (Theory allows absolute size measurement)

Optical transitions (3 eV)

Shift ~ 10-6 eV

e-

μ-

Nuclear charge distribution differences between isotopes(combined analysis of electron scattering and muonic x-ray data)

Wohlfahrt et al Phys. Rev. C22 (1980) 264

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)

(πf7/2)2

(πp3/2)2

Lines show upper and lower limits of differences

Wohlfahrt et al., Phys. Rev. C23 (1981) 533

“Kinks” at Z=28 and N=28

ISOTONES

ISOTOPES

Angeli & Marinova Atomic Data and Nuclear Data Tables 99 (2013) 69

rms nuclear charge radii, including radioisotopes, for medium mass and heavy elements

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 Normal Specific Field Doppler width

11Na 3s – 3p 550 MHz 200 MHz -10 MHz 1400 MHz

70Yb 6s – 6p 20 MHz ‹ 20 MHz -1500 MHz 500 MHz

Light element measurement techniques should be Doppler-free.

Evaluation of atomic F and M factors required.

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)

Stable isotope

Previous studies by laser spectroscopy

Situation when this programme started

ISCOOL – COLLAPS measurements

Ion beam cooler

Light collection region

(Laser resonance fluorescence)

Reduces energy-spread of ion beam

Improves emittance of ion beam

Trap and accumulates ions – typically for 300 ms

Releases ions in a 15 µs bunch

Laser beam

+40 kV

+39.9 kV

5μs

40 kV

Bunched-beam collinear laser spectroscopy

Gas-filled linear RFQ trap

On-line ion source

Photons only counted during the 5µs when ion beam passes photomultiplier tube.

50 ms trapping = 104 reduction in background

CEC

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

56Ni coreJUN45jj44b

40Ca coreGXPF1GXPF1A

Gallium

Matter radii

Atomic structure of gallium (Z=31)

Gallium charge radii

RILIS ionization scheme in ion source

Fluorescence measurements

Atomic factors

MCDF calculations (S. Fritzsche, Comput. Phys. Commun. 183, 1525 (2012))

F = +400 MHz.fm-2 – stable as MCDF wavefunctions enlargedM = -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

Ga

Differences in mean square charge radii for gallium

Ge

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)

CuMeasurements on 324.8 nm (2S1/2 2P3/2) transition

Atomic factorsExtensive 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

Ga

Cu

Differences in mean square charge radii (Z = 28 – 32)

Ge

Zn

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)

3P2

1P1

3S1

1S0

Zn

Ionization potential

Na

Metastable state populationDirectly – resonantCascade – 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.

Resonant charge exchange

481 nm2.58 eV

Atomic charge exchange

Zn+ + Na Zn* + Na+ + ΔE (ΔE = 0 : resonant charge exchange) ΔE is energy difference between final and initial electronic states

68Zn

Offset frequency (MHz)

69Zn1/2 ground state9/2 isomer

Non-optical measurements

Ga

Zn

Cu N=40 N=50

many states

Ni

3F, 3D

Ionization potential

Na

K5D3 13 μs

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.)

5P2

Considerations for Ni isotope measurements

323.4 nm

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

294.3 204.8 34163.3 210(47) -820(12)298.1 879.8 34408.6 321(6) -494(1)298.4 0 33500.9 -1117(206) 1301(53)299.4 204.8 33590.2 356(39) -1075(10)300.2 204.8 33500.9 306(98) -838(25)300.4 879.8 43164.3 241(17) -835(4)301.9 0 33112.4 -1405(174) 1543(45)303.2 0 32973.4 -882(81) 1166(20)303.8 204.8 33112.4 170(30) -635(7) 305.1 204.8 32973.4 269(55) -902(13)

E (lower)0 (d)8 (s)2

204.8, 879.8 (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

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

Interval depends on Alower

Intervals depend on Aupper , Bupper, and I, J, F

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

and I, J, F

J=3/2

J=1/2

324.8 nm

Example for I=5/2

Spins confirmed through ratio of hyperfine A factors