Distribution of energy levels for the liquid-drop nuclear model

Abstract

The Bohr liquid-drop model, because of the strong interaction between nuclear particles, has proved suggestive in giving insight into some of the fundamental properties of nuclei, particularly the extremely rapid rise in the density of levels as the excitation energy is increased. Taking for the normal modes of surface (capillary) waves, for which the wave number does not exceed k, the asymptotic expression ρ being the area of the surface, the level separation D(U) is given¹ (ignoring the effect of volume (acoustical) waves) by , , where U is the energy of excitation, A is the mass number and τ' P are each equal to 10 mV. when the nuclear radius R is assumed to be R = r_oA^1/3, r_o = 2.05 × 10^-13 cm. The values (taken from Bethe¹) for U = 10 mV. and for various values of A are given in the following table.