Helium atom energy from perturbation theory

The Breit interaction is an integral part of the total covariant Coulomb interaction, and is essential for maintaining gauge invariance. In his original application to the helium atom, Breit encountered difficulties which were attributed to unphysical contributions from the negative energy states, and, following analysis by Bethe and Salpeter,136 it was concluded that erroneous results were inevitable if the Breit interaction were to be used other than in first order perturbation theory. 

In the homogeneous metal, there are no real" charge fluctuations, just as in the Helium atom there is no real" dipole moment. Van der Waals attraction between two Helium atoms comes about as the result of the correlated quantum fluctuations of a virtual dipole moment induced in each atom by the other. Similarly, an attractive force comes about from correlated, virtual, charge fluctuations In the two planes. I eliminate H from the Hamiltonian to leading order in W. using the operator generalization of second-order perturbation theory for the energy levels. This yields ... 

This paper reviews progress in the application of atomic isotope shift measurements, together with high precision atomic theory, to the determination of nuclear radii from the nuclear volume effect. The theory involves obtaining essentially exact solutions to the nonrelativistic three- and four-body problems for helium and lithium by variational methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. The results are applied to the calculation of isotope shifts for the short-... 

We must modify perturbation theory to apply it to an energy level that is degenerate in zero order. For example, the two configurations (ls )(2s) and ( s)(2p) of the helium atom correspond to several states that have the same energy in zero order. We assume the same kind of Hamiltonian as in Eq. (G-1) and consider a zero-order energy level with a degeneracy equal to g. We have g zero-order wave functions. We call them the initial zero-order functions. Unfortunately, there is no guarantee that each of these functions would turn smoothly into one of the exact wave functions if A. is increased from 0 to 1. 

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