Helium atom perturbation method application

There are many problems of wave mechanics which cannot be conveniently treated either by direct solution of the wave equation or by the use of perturbation theory. The helium atom, discussed in the next chapter, is such a system. No direct method of solving the wave equation has been found for this atom, and the application of perturbation theory is unsatisfactory because the first approximation is not accurate enough while the labor of calculating the higher approximations is extremely great. 

We find, then, that a systematic application of the theory of perturbations does not lead to a satisfactory model of the normal helium atom. It might be supposed that the failure of our method was due to the fact that we are dealing here with the normal state, where several electrons move in equivalent orbits, and that a better result would be anticipated in the case of the excited states, where the main characteristics of the spectra are reproduced by the quantum theory in the form used here. We shall now show that this again is not the case. 

The Perturbation Method and Its Application to the Ground State of the Helium Atom... 

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-... 

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