The quantum theory of atomic polarization I— Polarization by a uniform field

Abstract Two problems of atomic energy, the energy of polarization of an atom in a plane electrostatic field and the energy of interaction, or van der Waals energy, of two distant atoms, are particularly suited to attack by approximate methods. In each, the disturbing field, whether that of the static field or of the distant atom, is small in comparison with the internal fields acting on the electrons of the atomic system, and so the standard methods by which quantum mechanics deal with small disturbances, namely the perturbation and variation methods, can be and have been successfully applied to these problems. Though the perturbation method, strictly applied, is the more accurate, since it takes into account the possible excited states of the system, its usefulness is restricted to atom s of simple structure, and having relatively simple wave functions. Generally speaking the variation methods, which require a knowledge of the unperturbed state of the system only, are more suitable for larger atom s; ignorance of the excited states is largely compensated for by expressing the perturbed wave functions in term s of parameters, which are then chosen to make the total energy a minimum. As one would expect, the atom s of hydrogen and helium have been studied most fully, the perturbation theory being used by Wang, Eisenschitz and London, and Lennard-Jones, and variation methods by Atanasoff, Hasse, Slater and Kirkwood, Pauling and Beach. Owing to the first order Stark effect, the calculated polarizability of the hydrogen atom cannot be compared with experiment, but the calculated value for helium agrees well in most cases with that observed. The van der Waals energy of two hydrogen atoms given by Pauling and Beach includes accurate values not only of the usual dipole-dipole term, which varies as 1/R6 but also of the dipole-quadripole and quadripole-quadripole terms, varying as 1/Rs, 1/R10 respectively.