In-source laser spectroscopy at ISOLDE and IRIS (Gatchina): New results and the problem of hyperfine structure anomaly A. Barzakh Petersburg Nuclear Physics Institute, Gatchina, Russia on behalf of Windmill-ISOLTRAP-RILIS collaboration

In-source laser spectroscopy at ISOLDE and IRIS 1.Brief review of the last results in lead region (At, Bi, Au, Hg chains) 2.Reminder on the HFA problem and the recently proposed method of experimental HFA study 3.HFA in Tl: first attempt to measure HFA rather far from stability 4.HFA in Au and Bi: some problems 5.HFA in Fr: determination of HFA 6.Urgent theoretical and experimental task to be solved

Pre-2003: Charge radii in the l Pre-2003: Charge radii in the lead region ? ? 85 At ? Pre-2012: Charge radii in the l Pre-2012: Charge radii in the lead region preliminary results! ? ?

IRIS, Bi isotopes: radii big isomer shift: different deformation for g.s. and m.s. (intruder states) big odd-even staggering; start of departure from spherical trend?

HFA: Hyperfine structure anomaly atomic part: independent of A (b-factor)nuclear configuration part Theory: A.-M. Mårtensson-Pendrill, Phys. Rev. Lett. 74, 2184 (1995) notation: — RHFA notation: ε — HFA factorization: J.R. Persson, ADNDT 99 (2013) 62

DHFA: Ratio may have a different value for different isotopes because the atomic states with different n, l have different sensitivity to the nuclear magnetization distribution. Differential hyperfine structure anomaly Tl: we have studied state with p 1/2 valence electron; previously state with s 1/2 valence electron has been studied DHFA J. R. Persson, Eur. Phys. J. A 2, 3 (1998) J. S. Grossman, et al., Phys. Rev. Lett. 83, 935 (1999) J. Zhang, et al., PRL 115, (2015)

pure atomic value! Independent on A Differential hyperfine structure anomaly determination of RHFA without independent high-accuracy μ-measurements η(Tl; 7p 3/2, 6p 1/2 ) exp = -15.6(2) η(Tl; 7p 3/2, 6p 1/2 ) theor = -17 admixture of 6s6p7s configuration! η(Tl; 7s 1/2, 6p 1/2 ) exp = 4.4(15) η(Tl; 7s 1/2, 6p 1/2 ) theor = 3.1 Differential hyperfine structure anomaly DHFA RHFA μ correction

HFA in Tl: μ correction two orders of magnitude! A. E. Barzakh et al. Phys. Rev. C 86, (2012) reasonable agreement of theory (Mårtensson-Pendrill) and experiment

DHFA: Au RHFA in Au may be greater than 10%. To extract μ properly one needs in calculation/measurement of η-factor. Measurement of η is possible for 196,198,199 Au where precise independent μ-values are available (  RHFA).

DHFA: Bi M. R. Pearson, et al., J. Phys. G, 26 (2000) 1829 very strange behaviour; usually RHFA for identical nuclear configuration with close μ’s is of order ÷ Sharp increase of atomic factor for atomic open p-shell (6p 3  6p 2 7s)? Or some “nuclear physics”?

RHFA: Fr, experiment 1. RHFA for odd isotopes is of order % — comparable to the μ-errors (1%). Should be taken into account! 2. Marked difference in ρ (i.e. in Δ) for odd and even isotopes was found previously in: J. S. Grossman, et al., Phys. Rev. Lett. 82, 935 (1999). It was attributed to the larger radial magnetization distribution of the unpaired neutrons, i.e. to the change in m : 1. Precise hfs-data: 7s 1/2, 7p 1/2, 7p 3/2, 8p 1/2, 8p 3/2 (7p 1/2 : R. Collister, et al., PR A 90, (2014); J. Zhang, et al., PRL 115, (2015) & 7s 1/2 : A. Voss et al., PR C 91, (2015) ) 2. Atomic calculations (for 7s 1/2, 7p 1/2 states) (A.-M. Mårtensson-Pendrill, Hfi 127 (2000) 41: scaling Tl results!) η(Fr; 7s 1/2, 7p 1/2 ) theor =3.0 & ρ exp  experimental 210 Δ A

Calculation with MP-atomic constants and simple one-configuration approximation for nuclear part, with assumption m = c. RHFA: Fr, theory Odd-even Δ-staggering is fairly explained without assumptions of the larger radial magnetization distribution for neutrons. Deviations may be connected with the oversimplification of the nuclear part and/or with the nuclear configuration mixing for odd-odd nuclei. prediction: 210 Δ 201 (I=9/2)=-0.8% 210 Δ 201 (I=1/2)=+1.5%

DHFA: Fr, 7p 3/2 vs 7p 1/2 excluded from mean Ratio s Δ p 3/2 / s Δ p 1/2 should be independent on A due to atomic-nuclear factorization Mean: s Δ p 3/2 / s Δ p 1/2 =-3.65(42) η(7p 3/2,7p 1/2 )=10.3(1.3) with η(7s,7p 1/2 )=3.0 HFA for p 3/2 state is ten times greater than for p 1/2 state! (cf. similar increase in Tl; some configuration mixing in Fr too?) This systematics also points to the necessity to remeasure a(7p 3/2 ) for 207,221 Fr to check dropdown points on this plot

RHFA: Ra, experiment Data for a(7s 1/2 ) and a(7p 1/2 ) in Ra II were used; η(Ra II; 7s 1/2, 7p 1/2 ) was fixed to η(Fr; 7s 1/2, 7p 1/2 )= 3 Direct measurement: 213 Δ 225 (7s 1/2 )=-0.8(4)% Extracted from ρ: 213 Δ 225 (7s 1/2 )=-0.80(27)% η(Ra II; 7s 1/2, 7p 1/2 ) exp =3(3) S.A. Ahmad, et al., Nucl. Phys. A483, 244–268 (1988) W. Neu, et al., Z. Phys. D 11, 105–111 (1989)

HFA: urgent theoretical & experimental tasks Atomic theoryExperiment Au Large-scale atomic calculations of η(6s 2 S 1/2, 6p 2 P 1/2 ) and b-factors for 6s 2 S 1/2, 6p 2 P 1/2 states Determination of a(6p 2 P 1/2 ) for 196,198,199 Au with the accuracy less than 2÷3 MHz (  η with the accuracy of 5÷10%). Tl Determination of a(7s 2 S 1/2 ) for 203,205 Tl with the accuracy less than 0.5 MHz (  η with the accuracy of 10÷15%). Bi Large-scale atomic calculations of b-factors for 6p 3 4 S 3/2, 6p 2 7s 4 P 1/2 states Check the unusual behaviour of ρ(6p 3 4 S 3/2, 6p 2 7s 4 P 1/2 ) for 205,213 Bi At Large-scale atomic calculations of b-factors for 6p 5 2 P 3/2, 6p 4 7s 4 P 3/2 (46234 cm -1 ), 6p 4 7p (?) (J=3/2, cm -1 ) states Experiments with better resolution to determine ρ’s with better accuracy Fr Large-scale atomic calculations of η(7s, 7p 1/2 ), η(7s, 7p 3/2 ) and b-factors for 7s, 7p 1/2, 7p 3/2 states Measurements of a(7p 3/2 ) for 207,221 Fr to check dropdown points (and for some other isotopes with unrealistic s Δ p 3/2 : 205,210 Fr )

Fr & Ra: η determination Ratio of the electron density at the nucleus for s 1/2 and p 1/2 states: 1/(αZ) 2 =2.9 for Z=81(Tl). Bohr & Weisskopf one-electron formulas: η(Tl; s 1/2, p 1/2 ) BW =3.0 — fairly corresponds to Mårtensson many- body calculations: η(Tl; s 1/2, p 1/2 ) M =3.1. η(Fr; s 1/2, p 1/2 ) BW =2.51 (rather than 3.0 as quoted in: Hfi 127 (2000) 41 — should be checked!) η(Ra + ; s 1/2, p 1/2 ) BW =2.43

Au: μ determination Previously empirical Moskowitz-Lombardi rule was used for HFA estimation in Au (and, therefore, μ determination) : P. A. Moskowitz and M. Lombardi, Phys. Lett. 46B (1973) 334 However, it was shown recently that this rule is (at least) not universal: J. R. Persson, Hfi 162, 139 (2005). Therefore, all previously determined hfs-μ values should be revised taking into account experimentally measured DHFA(  RHFA).

DHFA calculation Atomic part: atomic many-body technique (relativistic “coupled-cluster” approach) by A.-M. Mårtensson-Pendrill Single shell-model configuration: (in Tl case: pure h 9/2 intruder state) A.-M. Mårtensson-Pendrill, Phys. Rev. Lett. 74, 2184 (1995) Odd-odd nuclei: