Application of Perturbation Methods to the Theory of Nuclear Matter

A generalized perturbation theory is developed in such a way that it can be applied to a many-body problem with strong forces between the particles. The Brueckner expression for the energy is shown to be the first-order term in a particular case of this expansion. Some of the higher-order terms in the expansion are studied, and the importance of self-consistency in the energy denominator of Brueckner's equation and of the use of the exclusion principle in intermediate states is assessed. A possible simplification of the methods used is suggested, which involves solving the Brueckner equation for the hard core, and using normal perturbation theory for the attractive part of the potential. The methods developed are used to analyze some details of previously published calculations.

The lack of equality between the Fermi energy and the binding energy in the nuclear matter calculations shows that there must be a rearrangement energy. A simple formula for the rearrangement energy is derived, and its importance for single-particle excited states, such as occur in the optical model, is shown. The relation between the rearrangement energy and the departure of the system from a degenerate Fermi-gas state is shown. The effect of the rearrangement energy on the ground-state energy is indirect, but it is as important as the self-consistency condition. The rearrangement energy seems to come mainly from the hard core, and simple numerical estimates of the rearrangement energy from a hard core potential show that it is somewhat less than 16 Mev at the Fermi surface. The ground-state energy is reduced by perhaps 1 Mev. There seems to be a discrepancy between the calculated and observed energy dependence of the real part of the optical model potential.