Distinguishable-Electron Method for Electronic Structure Calculations. III. Contact Spin Densities - TheS2andP2States of Atomic Li

The distinguishable electron method is used to compute the spin density at the nucleus of a lithium atom in its lowest ${}_{}{}^2{}_{}{}^{}S$ and ${}_{}{}^2{}_{}{}^{}P$ states. For the initial approximation, we take an open-shell product of Slater-type orbitals with optimized exponents. The required perturbation functions are determined entirely by the exact solution of a single one-electron differential equation. A final mixing of spin states, which significantly affects the spin density, can be carried out perturbatively due to the weak correlation interaction. Our final results are comparable in accuracy with those determined by Brueckner-Goldstone perturbation theory, but do not involve the calculation of correlated wave functions.