Pseudostate calculation of the Bethe logarithm for H2+

Abstract

The Bethe logarithm is calculated for the hydrogen molecular ion H${{}_{2}}^{+}$ in the states of the rotational quantum number $L=0$ and the vibrational quantum number $v=0--1$ by using the Drake-Goldman method. The precision that is achieved for these two states is a few parts in ${10}^{9}$, which demonstrates the feasibility of the Drake-Goldman method for simple molecular systems. Comparison with the best published results is made.