Ab inito calculations of the P-2(1/2)-P-2(3/2) splitting in the thallium atom

The splitting between the P-3(3/2) and the P-2(1/2) terms in the thallium atom has been calculated at the perturbation theory level and by spin-orbit CI calculations, using both the Breit-Pauli asci the no-pair form of the microscopic spin-orbit Hamiltonian. The importance of the spin-other-orbit contribution to the spin-orbit splitting is investigated. and it is also shown that an averaging procedure of the kinematic factors in the expression for the spin-other-orbit integrals in the no-pair spin-orbit Hamiltonian yields highly accurate results. A slightly modified version of a previously proposed mean-field spin-orbit method is shown to have an accuracy of a few wave numbers. Perturbation theory is found to give a term-splitting which is too low by more than 1000 cm(-1), while spin-orbit CI with the no-pair form of the spin-orbit operator with the averaged spin-other-orbit term, and the no-pail mean-field operator, gives results in good agreement with experimental data.