The van der Waals Interaction of Hydrogen Atoms

The van der Waals interaction energy of two hydrogen atoms at large internuclear distances is discussed by the use of a linear variation function. By including in the variation function, in addition to the unperturbed wave function, 26 terms for the dipole-dipole interaction, 17 for the dipole-quadrupole interaction, and 26 for the quadrupole-quadrupole interaction, the interaction energy is evaluated as $W^{\prime \prime }=-\frac{6.49903e^2}{a_0{\rho }^6}-\frac{124.399e^2}{a_0{\rho }^8}-\frac{1135.21e^2}{a_0{\rho }^{10}}-\cdots ,$ in which $\rho =\frac{R}{a_0}$, with $R$ the internuclear distance. Some properties of the functions $F_{\nu \lambda \mu }(\xi ,\vartheta ,\varphi )$, which are orthogonal for the volume element $\xi d\xi sin\theta d\theta d\varphi$, are discussed, and their usefulness in atomic problems is pointed out.