Nuclear and Relativistic Effects in Atomic Spectra

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Abstract
The electronic Hamiltonian for a general atom is obtained as far as terms in 1/c2 and m/MA by reducing a relativistic wave equation with four components for each electron and nucleon to an approximately relativistic form with two components per particle. The presence of non-Hermitian terms in the reduced Hamiltonian is explained. Relativistic corrections to the Coulomb and nuclear interactions and the effect of the intrinsic magnetic moments are treated by first-order perturbation theory. The electronic Hamiltonian is obtained in the centre-of-mass system of the atom. The hyperfine structure interaction is obtained by expressing all electron-nucleon terms as multipole expansions, giving the previously known hyperfine structure expansion with recoil corrections. The exact operator for the nuclear field effect in isotope shift is obtained from the Coulomb interaction. The presence of other corrections depending on nuclear structure is indicated. Terms referring only to s electrons are not considered as the reduction procedure used does not cover the contact approach of particles (cf. Ma 1956). The usual calculation of the normal mass effect in isotope shift is investigated for non-s-electron configurations and is shown to be justified if 0.1% of the spin-orbit interaction and the whole of the other relativistic perturbations are negligible in comparison with the term value.