A note on the calculation of the spacing of energy levels in a heavy nucleus

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Abstract
It is known as a result of various experiments on slow neutrons (1) that a heavy nucleus possesses an enormous number of energy levels which are very closely spaced if the nucleus is highly excited. Strong theoretical reasons for the existence of this great number of levels were given by Bohr (2) and since then various attempts have been made to calculate the number of energy levels of a heavy nucleus. In the first of these, due to Bethe(3), it was assumed that the interaction between the nucleons was small so that the nucleus could be treated as a gas. The alternative assumption, that we may consider the interaction to be large in comparison with the kinetic energy of the nucleons, was proposed by Bohr and Kalckar(4). In the present note we assume as our model a nucleus consisting of neutrons and protons independent of one another; we then have a neutron-gas in equilibrium with a proton-gas, Fermi-Dirac statistics being applied to both.