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 4s4p 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 the 3p term. The description of the 1p 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 lowest sp configurations of Mg, Ca and Sr is analysed considering also the spin-spin interaction. Using the ab initio (r -3) integrals, the determined intermediate coupling and the experimentally known hyperfine constants, second-order hyperfine corrections are calculated and accurate a q-and biLparameters evaluated for 43Ca. This resolves the previously inconsistent results for b ~ determined from the 3P 1 and 3P a b-factors for this isotope. An accurate value for b ~ in the 3p term of 43Ca is b~ -13.27(6) MHz. Combined with the calculated (r-3) ~ integral, this gives a more accurate value for the nuclear quadrupole moment of 43Ca than given earlier, Q(43Ca)=-49(5) mb, where the uncertainty comes from the uncertainty estimated for the (r-3) ~ integral.

Ab-initio calculations of pair-correlation effects on the hyperfine structure of the 4s 4p and 4s 3d configurations of Ca

“…With the resulting description of the valence electrons, the effects of single excitations in the core (core-polarisation effects) induced by the valence electrons have been evaluated. If the valence electrons for the 4s 4p configuration are restricted to be in sp states, results very close to LS-dependent HF plus core-polarisation effects [9] are obtained for the hyperfine parameters. The inclusion of other angular symmetries for the valence electrons had only a small effect on the 3p term, while contributions from pd states had a drastic effect on the 1p term.…”

“…Table 1) a Estimated as the difference between a Dirac-Fock and a Hartree-Fock calculation for the average of the configuration (from Ref. 9) excitations involving a ls electron were included.) These lowest-order valence-core and core-core excitations were then allowed to affect the valence pair including also the effects of using the approximate Brueckner orbitals.…”

“…The other (r -3) parameters are attributed to the 4p electron. Comparisons are made with experimental results extracted from the measured Afactors and with a calculation where LS-dependent Hartree-Fock (LSHF) orbitals were used to evaluate core-polarisation effects [9]. Our total values in the sp-limit are almost identical to the LSHF results for the 1p term, and for the 3p term the LSHF results are only about 3 ~o larger.…”

“…Since the nuclear magnetic dipole moment of 43Ca is known from direct measurements [8], the magnetic hyperfine structure can be used to test the theoretical calculations. In an earlier paper [9] the hyperfine integrals in the 4s4p configuration were evaluated using LS-dependent Hartree-Fock orbitals and including core-polarisation effects. Reasonable results were achieved for the 3p term while the experimental result for the 1p term could not be reproduced.…”

Isotope shift of182Hg and an update of nuclear moments and charge radii in the isotope range181Hg-206Hg

“…Using these values and 3bp~/=B(3p2)=399.150(2)MHz which is equal to -812(7) MHz for 2~ [105]. Using the effective operator parametrization of the (s, p)-hfs interaction given in [106], one easily verifies that also the core-polarization terms cancel in (B 5). The sum reduces to S= lag a + 3/5 3ai~2 =2 2 3aP 1 q-3/5 3ap 2 .…”