Stability of Pear-Shaped Nuclear Deformations

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Abstract
The possibility of stable pear-shaped deformations of nuclei is treated by a perturbation theory starting from the nucleon wave functions of a spheroidal harmonic-oscillator potential, without spin-orbit coupling. The mixing of states of opposite parity tends to stabilize the deformation, and is opposed by the cohesiveness of nuclear matter that favors a spherical shape. The former is calculated explicitly for a number of cases and the latter is estimated by imposing a constant-volume condition in a simple manner closely analogous to a more familiar treatment of spheroidal deformations. In this approximation the mixing of the states is not quite enough to overcome the competing effect, so it merely "softens" the nucleus and does not stabilize a pear-shaped deformation. The most direct effect of spin-orbit coupling is to bring states of opposite parity closer together, tending to increase the mixing and make pear-shaped nuclei stable.