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Direct perturbation theory of magnetic properties and relativistic corrections for the point nuclear and Gaussian nuclear models

2001; American Institute of Physics; Volume: 115; Issue: 16 Linguagem: Inglês

10.1063/1.1405009

1520-9032

Alf Christian Hennum, Wim Klopper, Trygve Helgaker,

Atomic and Molecular Physics

Starting from the Lévy-Leblond equation, which is the four-component nonrelativistic limit of the Dirac equation, a direct perturbation theory of magnetic properties and relativistic corrections is developed and implemented for point-charge and finite nuclei. The perturbed small components are regularized by projecting them onto an auxiliary small-component basis of Gaussian functions. The relevant operators and matrix elements are derived for the point-nuclear and Gaussian nuclear models. It is demonstrated how the usual paramagnetic spin-orbit, Fermi-contact, and spin-dipole integrals of Ramsey’s theory can be evaluated in the same manner as field and field-gradient integrals—that is, as derivatives of potential-energy integrals. A few illustrative calculations are performed.