Improved Pauli Hamiltonian for local-potential problems

Abstract

A recently published scheme for obtaining an approximate solution of the Dirac-Hartree-Fock equations for an atom is adapted and applied to the related Dirac-Slater problem. For a given $\mathrm{nl}$, one solves explicitly only for one large component orbital instead of the four determined in the Dirac-Slater calculations. The equation for this single component is closely akin to the Pauli equation. [We find that the Pauli mass-velocity and Darwin operators are accurate to only zeroth (instead of first) order in $\frac{(E\ensuremath{-}V)}{{c}^{2}}$. We present forms which are accurate to first order for cases in which the expansion in $\frac{(E\ensuremath{-}V)}{{c}^{2}}$ is valid.] Atomic calculations for uranium and plutonium demonstrate that this approximate method yields eigenvalues, eigenfunctions, spin-orbit parameters, and excitation energies in close agreement with the Dirac-Slater results. The method can be incorporated into existing nonrelativistic molecular and energy-band computer programs (such as those for the molecular scattered-wave method and the KKR and APW energy-band methods). This would then permit nearly relativistic solutions of the related problems without the complications introduced by the four-component-type solutions. We discuss implementation of the method for the scattered wave and APW methods.