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

Abstract

In previous work devoted to ab initio calculations of hyperfine structure constants in nitrogen and fluorine atoms, we observed sizeable relativistic effects, a priori unexpected for such light systems, that can even largely dominate over electron correlation. We observed that the atomic wave functions calculated in the Breit-Pauli approximation describe adequately the relevant atomic levels and hyperfine structures, even in cases for which a small relativistic LS-term mixing becomes crucial. In the present work we identify new levels belonging to the spectroscopic terms 2p 4 ( 3 P )3d 2,4 (P, D, F ) of the fluorine atom, for which correlation effects on the hyperfine structures are small, but relativistic LS-term admixtures are decisive to correctly reproduce the experimental values. The Breit-Pauli analysis of the hyperfine matrix elements nails cases with large cancellation, either between LS pairs for individual hyperfine operators, or between the orbital and the spin-dipole contributions. Multiconfiguration Dirac-Hartree-Fock calculations are performed to support the Breit-Pauli analysis. I. INTRODUCTIONThe development of relativistic theories applied to atoms has greatly contributed to improving the agreement between theory and observation. Among the methods accounting for relativity we can cite the multiconfigurational Hartree-Fock (MCHF) approach with Breit-Pauli (BP) corrections [1, 2] and the multiconfigurational Dirac-Hartree-Fock (MCDHF) approach with Breit and QED corrections [3,4]. The methodological developments, combined with the increasing computer resources, allow for accurate calculations of atomic wave functions, which make it possible to study rigorously the balance between electronic correlation and relativistic effects on atomic properties. ATSP2k [5] and GRASP2018 [6] are codes built on, respectively, the MCHF+BP and MCDHF+Breit+QED approaches.Correlation effects are traditionally presented as being dominant in light atoms, on the basis of the Z-dependent perturbation approach of the non-relativistic Hamiltonian [7], while relativistic effects are expected to be more prominent in heavy atoms, due to the large mean velocity of the inner electrons relatively to the speed of light, when increasing the nuclear charge [4,8]. This picture is definitely too simple, as explicitly expressed two decades ago by Desclaux's statement [9]: "It is obvious that correlation and relativistic corrections should be included simultaneously in a coherent scheme." It is nowadays acknowledged that relativity has to be taken into account, even for light atoms [10,11], to obtain accurate predictions of electronic structures.The effects of relativity on the hyperfine interaction in light atoms have been studied in several works [11][12][13][14]. In fully relativistic calculations, as in the MCDHF method, the influence of relativity leads to two effects [15,16]. The first one is a direct effect that results in the contraction of radial orbitals compared to the nonrelativistic ones. The second one, an indirect effect,...