Self-consistency requirement at the Fermi surface in Brueckner theory with a continuous auxiliary potential

We derive the self-consistency requirement at the Fermi surface for the auxiliary potential which appears in the continuous version of Brueckner theory. In contrast with a previous proof which relied on the analytical properties of the nuclear matter mass operator, the present derivation is based on the cancellation of the singularities which appear in diagrams each time one uses a continuous auxiliary potential. Hence it applies to any nuclear matter quantity, in particular to the nuclear matter binding energy which is discussed here