Classical properties and semiclassical quantisation of a spherical nuclear potential

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Abstract
The geometrical properties of the classical energy-action surface are studied for a nuclear Woods-Saxon-like spherical potential in connection with the EBK semiclassical method of quantisation. Comparisons are made with other well known cases: the spherical harmonic oscillator and the spherical billiard. The shift of single-particle energies from A=208 to A=16 is calculated by a simple method inspired by the Erhenfest adiabatic invariants. Semiclassical results are then compared with exact Schrodinger energies. It is seen that the most significant features of the single-particle spectrum are explained by local properties of the energy-action surface (curvature, slope) and by their evolution with particle number.