ABSTRACT
As mentioned above, in the case of a Hamiltonian of nucleons moving independently in a central potential well, all states of several nucleons in the same j-orbit are degenerate. Such degeneracy is never observed in actual nuclei and is easily removed if the mutual interaction of the nucleons is added to the Hamiltonian. In order to obtain a rough idea about the order of levels in a two nucleon configuration, let us consider a specific case of mutual interaction. An ordinary interaction whose range is short in comparison with the spatial extension of the single nucleon wave functions may be approximated by a zero range interaction. This is an extreme limit and some care must be taken when using it. In the present context, however, for evaluating matrix elements within a given configuration, a δ(1, 2) = δ(|r 1 − r 2|) potential behaves very regularly. Such a potential has been used since the early days of the shell model. The results reproduce fairly well certain features of nuclear spectra as we shall see in the following.
