A Mathematical Method for Dealing with the Nucleon Eigenvalue Problem in Finite Nuclei II: Shell-Model Solutions of the Homogeneous Fredholm's Equation

Nucleon eigenvalues in finite nuclei are evaluated by means of a variation-iteration method applied to the homogeneous Fredholm's equation in momentum space. The shell model potential deduced in preceding papers is used; its remarkable feature is that, except for the spin-orbit coupling constant, no other parameters are left free for phenomenological fits. The method relies on the fact that the value of the shell model potential at r=0 is known. The validity of the potential and the reliability of the method are extensively tested assuming40Ca as a paradigm. It has been proved that the eigenvalues calculated with the potential, and with its lowest approximation expressed by a quartic potential, differ by less than few percent. Finally, a simple approximate procedure for calculating nucleon eigenvalues is outlined using the Bohr-like description of the shell model and the concept of equivalent harmonicoscillator potential, discussed in part I of this paper.