A Nuclear Model

Abstract

The problem of a number of bodies which attract each other with forces proportional to the distance can be solved completely in terms of normal vibrations, and the expressions for the frequencies can be written down. From these the quantum mechanical energy levels can be written down directly. This makes a good model for the representation of a nucleus insofar as it can be considered as composed of alpha-particles, protons and neutrons, and can be treated by ordinary quantum mechanics. The assumption of constants of a reasonable order of magnitude makes possible the computation of binding energies which show the observed general trends. The instability of ${\mathrm{Be}}^8$ composed of two alpha-particles is attributed to the high "zero point" energy of the system, although the system of three alpha-particles, ${\mathrm{C}}^{12}$, is stable. The Pauli exclusion principle applied to the neutrons gives a reason for the limited number of observed isotopes.