A. Barzakh Petersburg Nuclear Physics Institute, Gatchina, Russia

1. 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

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

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

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

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

6. Differential hyperfine structure anomaly 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. DHFA: Tl: we have studied state with p1/2 valence electron; previously state with s1/2 valence electron has been studied 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, 042501 (2015) DHFA

7. Differential hyperfine structure anomaly Differential hyperfine structure anomaly Differential hyperfine structure anomaly DHFA RHFA μ correction pure atomic value! Independent on A determination of RHFA without independent high-accuracy μ-measurements η(Tl; 7p3/2, 6p1/2)exp= -15.6(2) η(Tl; 7p3/2, 6p1/2)theor= -17 admixture of 6s6p7s configuration! η(Tl; 7s1/2, 6p1/2)exp= 4.4(15) η(Tl; 7s1/2, 6p1/2)theor= 3.1

8. HFA in Tl: μ correction two orders of magnitude! reasonable agreement of theory (Mårtensson-Pendrill) and experiment A. E. Barzakh et al. Phys. Rev. C 86, 014311 (2012)

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

10. DHFA: Bi very strange behaviour; usually RHFA for identical nuclear configuration with close μ’s is of order 10-3÷10-4. Sharp increase of atomic factor for atomic open p-shell (6p36p2 7s)? Or some “nuclear physics”? M. R. Pearson, et al., J. Phys. G, 26 (2000) 1829

11. RHFA: Fr, experiment 1. Precise hfs-data: 7s1/2, 7p1/2, 7p3/2, 8p1/2, 8p3/2 (7p1/2: R. Collister, et al., PR A 90, 052502 (2014); J. Zhang, et al., PRL 115, 042501 (2015) & 7s1/2: A. Voss et al., PR C 91, 044307 (2015)) 2. Atomic calculations (for 7s1/2, 7p1/2 states) (A.-M. Mårtensson-Pendrill, Hfi 127 (2000) 41: scaling Tl results!) η(Fr; 7s1/2, 7p1/2 )theor=3.0 & ρexp experimental210ΔA 1. RHFA for odd isotopes is of order 0.5-1% — 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 <r2>m:

12. RHFA: Fr, theory Calculation with MP-atomic constants and simple one-configuration approximation for nuclear part, with assumption <r2>m= <r2>c. 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: 210Δ201(I=9/2)=-0.8% 210Δ201(I=1/2)=+1.5%

13. DHFA: Fr, 7p3/2vs 7p1/2 excluded from mean Ratio sΔp3/2/ sΔp1/2 should be independent on A due to atomic-nuclear factorization Mean:sΔp3/2/ sΔp1/2=-3.65(42) with η(7s,7p1/2)=3.0 η(7p3/2,7p1/2)=10.3(1.3) HFA for p3/2 state is ten times greater than for p1/2 state! (cf. similar increase in Tl; some configuration mixing in Fr too?) This systematics also points to the necessity to remeasure a(7p3/2) for 207,221Fr to check dropdown points on this plot

14. RHFA: Ra, experiment Data for a(7s1/2) and a(7p1/2) in Ra II were used; η(Ra II; 7s1/2,7p1/2) was fixed to η(Fr; 7s1/2,7p1/2)= 3 Direct measurement: 213Δ225(7s1/2)=-0.8(4)% Extracted from ρ: 213Δ225(7s1/2)=-0.80(27)% η(Ra II; 7s1/2,7p1/2)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)

15. HFA: urgent theoretical & experimental tasks

16. Fr & Ra: η determination Ratio of the electron density at the nucleus for s1/2 and p1/2 states: 1/(αZ)2=2.9 for Z=81(Tl). Bohr & Weisskopf one-electron formulas: η(Tl; s1/2, p1/2)BW=3.0 — fairly corresponds to Mårtensson many-body calculations: η(Tl; s1/2, p1/2)M=3.1. η(Fr; s1/2, p1/2)BW=2.51 (rather than 3.0 as quoted in: Hfi 127 (2000) 41 — should be checked!) η(Ra+; s1/2, p1/2)BW=2.43

17. Au: μ determination Previously empirical Moskowitz-Lombardi rule was used for HFA estimation in Au (and, therefore, μdetermination) : 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). P. A. Moskowitz and M. Lombardi, Phys. Lett. 46B (1973) 334

18. 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 h9/2 intruder state) Odd-odd nuclei: A.-M. Mårtensson-Pendrill, Phys. Rev. Lett. 74, 2184 (1995)