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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
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
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
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
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