A mathematical method for dealing with the nucleon eigenvalue problem in finite nuclei: Pt. 1

The role played by the isotropic harmonic oscillator in the shell model is extensively investigated. A Bohr-like model of the shell model is outlined with the purpose of providing a logical justification of the concept of harmonic-oscillator potential equivalent to the true shell model one as far as the calculation of nuclear energy levels is concerned. The potential equivalence defined according to different criteria, is used throghout. The consistency of the numerical results turn out to be excellent. Their critical analysis has suggested a calculational method of nucleon energy levels in finite nuclei which will be discussed in a forthcoming paper