Many-Body Calculations for the Heavy Atoms

Abstract

Corrections to the Hartree-Fock (HF) theory which arise as a result of electrostatic configuration interaction are calculated for a heavy ion ${\mathrm{Pr}}^{3+}$. The effect of configuration interaction upon the $4f^2$ configuration is represented by effective two-body operators of the form $\Sigma k^{}{a}_k{C}_1^{\mathrm{}\left(k\right)\mathrm{}}{C}_2^{\mathrm{}\left(k\right)\mathrm{}}$. These operators are evaluated using perturbation theory and graphical methods. The effect of the operators of even rank is to depress the values of the Slater $F^k$ integrals below their HF values. The two-body operators of odd rank do not appear within the ordinary HF theory. The Trees parameter $\alpha$ is the coefficient of an operator of this kind. It is found that the corrections to the Slater integrals converge slowly. The contributions to the operators of odd rank converge properly, however, and we obtain the values $\alpha =28\mathrm{}$, $\beta =-616\mathrm{}$, and $\gamma =1611\mathrm{}$. This may be compared with the empirical values $\alpha =24\mathrm{}$, $\beta =-586\mathrm{}$, and $\gamma =728\mathrm{}$. The value of $\gamma$ is determined empirically by the position of a single level, ${}_{}{}^1{}_{}{}^{}S$. It is suggested that the free-ion ${}_{}{}^1{}_{}{}^{}S$ level has not been properly identified.