Landau, Brueckner-Bethe, and Migdal Theories of Fermi Systems

The Landau theory for infinite Fermi systems is discussed, and it is then shown how one can apply the Landau technique of functional differentiation of the energy with respect to quasiparticle occupation numbers to obtain the effective interaction, beginning from the Brueckner-Bethe approximation to the energy. Calculations of this effective interaction by Bäckman from a nucleon-nucleon potential are discussed and criticized. Results of Bäckman's calculation are compared with the parameters in Migdal's effective force, evaluated at the center of the nucleus, the latter parameters having been derived phenomenologically by fitting various nuclear phenomena. There is a large discrepancy between the calculated value of the compressibility of nuclear matter and that obtained phenomenologically. The advantages of introducing a model space in order to improve the accuracy of the calculated results is discussed, and it is pointed out that such an introduction would also be advantageous in recent calculations by Barrett and Kirson of third-order terms in the effective interaction; also, that a model space is effectively introduced in recent calculations with the Midgal theory when it comes to deriving the quadrupole-quadrupole interaction. Calculation of the effective force between two atoms in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is discussed briefly, and it is pointed out that this is a much more ambitious task than in nuclear matter. Calculations carried out within the Brueckner-Bethe formalism are reviewed.