Nuclear level spacings

T. D. Newton's shell-dependent level spacing formula depends upon the densities of single-particle orbits near the Fermi level in the nucleon gas. It has been found that these densities can be computed by taking appropriate averages of the second differences between adjacent atomic masses, using the writer's semiempirical mass formula from which electrostatic and pairing energy terms have been omitted. With this procedure, observed nuclear level spacings have been fitted with a root mean square error factor of 1.74. This fit shows that the level spacings are proportional to (2J + 1)−1 to a good approximation. Since the average density of single-particle orbits depends on the nuclear excitation energy, and since its computation takes a long time even with an electronic computer, an approximation formula with five coefficients has been fitted to the computed orbit densities for each Z and N in the ranges and . These coefficients are tabulated.