Saturation of nuclear forces in Brueckner theory

The basic equations in the Brueckner theory of nuclear matter are solved for a two-nucleon potential taken as a rectangular well with a rectangular repulsive sphere and the properties of the solutions are investigated for various dimensions of the repulsive sphere. The two-nucleon interaction is considered to be non-vanishing only if the nucleons are in theS-state. Under such assumptions a two nucleon potential always gives saturation, i.e. a minimum of the mean binding energy per nucleon, at a finite nuclear density. It is shown that the nuclear density and the mean binding energy decreases if the height or the width of the repulsive sphere increases. If the repulsive sphere is infinitely high a nucleus can exist as a bound state only if the width of this sphere is sufficiently small. The limit value for the width of the sphere is given. It is shown in the conclusion how the solution of the basic equations will change if the two-nucleon potential does not contain an infinite repulsive sphere, but only a very high one.