Nuclear Deformation in the Spheroidal Shell Model

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Abstract
In the usual shell-model procedure, the effective Hamiltonian contains only half the sum of the shell-model potentials of nucleons in order to avoid counting average pairwise interactions twice. Because of the factor one-half, the nondiagonal elements of this Hamiltonian in the harmonic oscillator representation do not vanish, but they have been neglected in previous calculations of nuclear deformations by Nilsson and others, in which one minimizes total shell-model energy at constant volume. It is here shown in typical cases (without taking spin-orbit coupling into account) that the equilibrium deformation is unaltered in second and third order and that the fourth-order modification arising from the nondiagonal elements is very small. The relation of these nondiagonal elements to those of the pairwise interactions is also discussed.