The Alpha-Particle and Shell Models of the Nucleus

Abstract

It is shown that it is possible to write down α-particle wave functions for the ground states of 8Be, 12C and 16O, which become, when antisymmetrized, identical with shell-model wave functions. The α-particle functions are used to obtain potentials which can then be used to derive wave functions and energies of excited states. Most of the low-lying states of 16O are obtained in this way, qualitative agreement with experiment being found. The shell structure of the 0+ level at 6.06 MeV is analysed, and is found to consist largely of single-particle excitations. The lifetime for pair-production is calculated, and found to be comparable with the experimental value. The validity of the method is discussed, and comparison made with shell-model calculations.