The Theory and Calculation of Screening Constants

It is shown that if $H$ is the negative energy operator, and $\ensuremath{\varphi}$ any function satisfying the boundary conditions of quantum dynamics and possessing the symmetry properties characteristic of a given spectral series, then $E=\ensuremath{\int}{\ensuremath{\varphi}}^{*}H\ensuremath{\varphi}d\ensuremath{\tau}$ is a lower limit to the term-value of the lowest level of that series. If the integral is evaluated for various $\ensuremath{\varphi}$, the largest value obtained will be the best approximation to this term value. The method is applied to various electronic configurations with satisfactory results. The degree to which $\ensuremath{\varphi}$ approximates the wave function of the state is not determined, but it is shown to be likely that the approximation is not good at large distances from the nucleus.