Wave Functions for the Excited States of Neutral Helium

Abstract

Wave functions have been found for the excited states of neutral helium for the $^{1}S$, $^{3}S$, $^{1}P$, $^{3}P$, $^{1}D$, and $^{3}D$ series up through terms for which the principal quantum number of the running electron is 9 for the $S$ series and 8 for the others. The wave functions are obtained from the minimum principle by a configuration-interaction procedure. At the final stage of the calculation, the wave functions are found by the solution of a secular equation of order 9\ifmmode\times\else\texttimes\fi{}9 or less. If one excludes the energy of the $1^{1}S$ term, the average agreement between computed and observed energies for the 42 remaining terms is better than 1 part in 300 000. The energies gotten for the more highly excited states appear to be more than an order of magnitude, better than any which have been previously obtained. The values of the parameters in the various wave functions are made available.