ON THE SPHERICAL OSCILLATOR NUCLEUS

The degree of consistency of an oscillator model of a nucleus is examined by means of a type of Hartree–Fock calculation based on a simple form of internucleon potential valid at low energies. An effective mass equal to 0.757 times the mass of a free nucleon is used. The oscillator wave functions are found to be not far from self-consistent and the oscillator frequency derived is physically reasonable, but the bound on the binding energy is not good. It is also shown that the oscillator wave functions are a good approximation for the state functions of particles bound in a finite potential well having the shape of a cutoff oscillator so that the Hartree–Fock calculation can be used to prescribe a shell model potential.