The Effect of the Motion of the Nucleus on the Spectra of Li I and Li II

Abstract

The wave equation for a system of $N$ electrons (mass $m$) and one nucleus (mass $M$) is set up and solved approximately. If $W(m)$ are the energy levels for $M=\ensuremath{\infty}$, the energy levels for finite $M$ are $(\frac{\ensuremath{\mu}W(m)}{m})+\ensuremath{\Delta}W$, where $\ensuremath{\mu}=\frac{\mathrm{mM}}{(m+M)}$ and $\ensuremath{\Delta}W$ is calculable.In case $N=2 or 3$, $\ensuremath{\Delta}W$ is zero except for $P$ levels. For these it is given by Eq. (13), which is derived on the assumption that the wave function is a polynomial of hydrogen functions, each with its own effective nuclear charge. The values of the latter previously determined by one of the authors are used in comparing the calculation with Sch\"uler's experimental data on Li II, $\ensuremath{\lambda}5485$ and Li I, $\ensuremath{\lambda}6708$. The agreement is satisfactory and eliminates one objection to Sch\"uler's interpretation of $\ensuremath{\lambda}5485$.