Calculation of the Quantum Defect for Highly ExcitedSStates of Para- and Orthohelium

Abstract

Experimental term values for the $S$ states of para- and orthohelium for the case when one electron is in the ground state and the other is in a highly excited $S$ state can be represented by the formula $E=-\frac{\mathrm{Rh}}{{(n-{\Delta }_{1,2})}^2}$; ${\Delta }_1$ and ${\Delta }_2$ being the quantum defects for the ortho and para systems, which have the respective numerical values, 0.298 and 0.140. The object of the present paper is to calculate the values of ${\Delta }_1$ and ${\Delta }_2$ by a convenient method quite different from that used by Hylleraas. Neglecting the polarization of the atom core, the results obtained for ${\Delta }_1$ and ${\Delta }_2$ are 0.289 and 0.160, respectively, in contrast to the corresponding values 0.230 and 0.122 obtained by Hylleraas before he corrected for polarization. This difference is due to the more accurate wave functions obtained here and indicates that the effect of polarization is not as great as it would appear from the calculations of Hylleraas.