Ab initio electronic factors of the A and B hyperfine structure constants for the 5s25p6s<

Abstract

Large-scale ab initio calculations of the electronic contribution to the electric quadrupole hyperfine constant B were performed for the 5s 2 5p6s 1,3 P o 1 excited states of neutral tin. To probe the sensitivity of B to different electron correlation effects, three sets of variational multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations employing different strategies were carried out. In addition, a fourth set of calculations was based on the configuration interaction Dirac-Fock-Sturm theory. For the 5s 2 5p6s 1 P o 1 state, the final value of B/Q = 703(50) MHz/b differs by 0.4% from the one recently used by Yordanov et al. [Commun. Phys. 3, 107 (2020)] to extract the nuclear quadrupole moments Q for tin isotopes in the range 117−131 Sn from collinear laser spectroscopy measurements. Efforts were made to provide a realistic theoretical uncertainty for the final B/Q value of the 5s 2 5p6s 1 P o 1 state based on statistical principles and on correlation with the electronic contribution to the magnetic dipole hyperfine constant A.

Semi-empirical determination of the nuclear quadrupole moment of $$^{109}$$Sn

“…Therefore, the corrections related to the distortion of inner closed electron shells, referred to Sternheimer shielding (or anti-shielding) factors, are correctly included in the calculations. The value is in excellent concordance with those reported by Yordanov et al (Q( 109 Sn) = 218(7)(15) mb [1] and Papoulia et al Q( 109 Sn) = 219(7)(16) mb [16]. Furthermore, the values of the quadrupole moments for other Sn isotopes, which can be determined from the currently available experimental data and relevant relationships, would be consistent with the values given in Table 1 in Ref.…”

“…[1]. The values of the quadrupole moment obtained in the above-mentioned works are mutually consistent and amount to Q( 109 Sn) = 218(7)(15) mb [1] and Q( 109 Sn) = 219(7)(16) mb [16], respectively. These values are, however, significantly different from the result obtained by Eberz et al [17], which amounted to Q( 109 Sn) = 310(100) mb, and also the re-normalized Eberz's value of 330(110) mb, quoted by Stone in his review work [2].…”

“…Furthermore, the researchers representing leading theoretical groups published together the details of the atomic calculations of the electric field gradient (EFG) values for the 5s 2 5p6s 1,3 P 1 excited states in neutral tin [16], which were previously presented in Ref. [1].…”

“…Since there are no results for quadrupole moments of tin available from measurements on the muonic or pionic atoms and the discrepancy between the recently reported and the formerly accepted value for Q( 109 Sn) is ca. one third of the latter, it is very important to determine the independent quadrupole moment's value using methods other than those presented in the recent works of Yordanow and Papoulia [1,16]. Therefore, we decided to join the research aimed at resolving the above-mentioned discrepancies, using a different method, independent of the value of the electric field gradient.…”

Weak Correlation and Strong Relativistic Effects on the Hyperfine Interaction in Fluorine

“…As observed by Drake [49], it is clear that the culture is changing within the theoretical computational community to make uncertainty quantification (UQ) the usual expectation when theoretical results are presented. The present work is one step in this direction, as a few others in the framework of multiconfiguration variational approaches [50][51][52]. It indeed illustrates how the details of the magnetic dipole hyperfine operators can be explored to point difficult cases in terms of cancellation, either between LS pairs for individual operators, or between the orbital and the spin-dipolar operators, and to asses the reliability of the theoretical hyperfine constants.…”