On the use of the oscillator approximation in nuclear physics

To investigate the connection of the Hartree-Fock and harmonic oscillator results, the paper compares the self-consistent single particle wave functions of spherical nuclei to simple harmonic oscillator ones. The deviation of a given Hartree-Fock Wave function from the harmonic oscillator one of the same indicas n and 1 is measured by the overlap integral of the radial wave functions of the two different approximations. These overlaps were always maximized varying the value of the oscillator constant. The calculations were carried out for spherical nuclei ranging from 16O to 208Pb. The results show that the oscillator model works reasonably well, especially in the case of light nuclei in spite of the fact that since the harmonic oscillator potential tends to infinity with increasing r, the harmonic oscillator single particle wave functions are certainly highly incorrect at large r. (Sz.N.Z.)