Analysis of the hyperfine structure of the 4s 4p configuration in Ca and the nuclear quadrupole moment of⁴³Ca

Abstract

Hyperfine structure 〈r ⁻³〉 integrals are calculated for the 4s 4p configuration in Ca, including the effects of core polarization. This is done with the use of LS-dependent Hartree-Fock orbitals. The calculated effects describe well the magnetic hyperfine structure for the³ P term. The description of the1 P term is less good, however, due to the effects of the strong correlation between the valence electrons for this term. The intermediate coupling in the lowestsp configurations of Mg, Ca and Sr is analysed considering also the spin-spin interaction. Using theab initio 〈r ⁻³〉 integrals, the determined intermediate coupling and the experimentally known hyperfine constants, second-order hyperfine corrections are calculated and accuratea ^ij- andb ^ij-parameters evaluated for⁴³Ca. This resolves the previously inconsistent results forb ⁰² determined from the³ P ₁ and³ P ₂ b-factors for this isotope. An accurate value forb ⁰² in the³ P term of⁴³Ca isb ⁰²=−13.27(6) MHz. Combined with the calculated 〈r ⁻³〉⁰² integral, this gives a more accurate value for the nuclear quadrupole moment of⁴³Ca than given earlier,Q(⁴³Ca)=−49(5) mb, where the uncertainty comes from the uncertainty estimated for the 〈r ⁻³〉⁰² integral.