NUCLEAR DEFORMATION IN THE SPHEROIDAL SHELL MODEL

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 onehalf, the nondiagonal elements of this Hamiltonian in the harmonic oscillator representation do not vanish, but they were neglected in previous calculations of nuclear deformations by Nilsson and others, in which total shell-model energy at constant volume is minimized. It is shown that in typical cases (without taking spin-orbit coupling into account) 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. (auth)