A Mathematical Method for Dealing with the Nucleon Eigenvalue Problem in Finite Nuclei I: The Shell-Model ``Equivalent" Harmonic-Oscillator Potential

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 throughout. The consistency of the numerical results turns 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.