II.—The Van der Waals Force between a Proton and a Hydrogen Atom

The calculation of Van der Waals forces has acquired considerable interest recently through the work of Buckingham, Knipp and others (Buckingham, 1937; Knipp, 1939). In these papers the interaction energy between two atoms is expressed as a power series in i/R, where R is the nuclear separation, and the various terms in this series are known as dipole-dipole, dipole-quadrupole, quadrupole-quadrupole, etc… interactions. In most cases only approximate values are obtainable for the coefficients in this series, though for two hydrogen atoms in their ground states, Pauling and Beach (1935) have determined the magnitudes correct to about I in 10 6 . In this paper we discuss the simplest possible problem of this nature, i.e . the force between a bare proton and a normal unexcited hydrogen atom. We shall show that a rigorous determination of the coefficients in the power series can be made.