Parametrized Slater Modified Hartree-Fock Method Applied to Actinide Ions

A Slater modified Hartree-Fock calculation is applied to several actinide ions. The coefficient of the Slater free electron exchange potential is treated as a parameter which is evaluated by matching a calculated $4f$ orbital of ${\mathrm{Pr}}^{+3\mathrm{}}$ to a Hartree-Fock $4f$ orbital. The parameter is then used in the calculation of orbitals for ${\mathrm{Th}}^{+2\mathrm{}}$, ${\mathrm{U}}^{+4\mathrm{}}$, ${\mathrm{Np}}^{+4\mathrm{}}$, and the trivalent ions from ${\mathrm{Pa}}^{+3\mathrm{}}$ to ${\mathrm{Cf}}^{+3\mathrm{}}$. The valence orbitals are used to calculate the matrix elements $〈r^2〉$, $〈r^4〉$, $〈r^6〉$, $〈r^{-3\mathrm{}}〉$, $\zeta$, $F^2$, $F^4$, and $F^6$ which are presented in tabular form.