Toroidal and spherical bubble nuclei

Abstract

Attention is fixed on nuclei with new types of topology proposed by Wheeler many years ago. Only the most important types of instability arising from collective deformations are considered in conjunction with only the simplest new topologies, those of a torus and a bubble. In the liquid-drop model, a toroidal nucleus with a fissility parameter x ≳ 1.0 is stable against symmetry-preserving breathing deformations due to the balance between Coulomb repulsion and surface tension. However, at the breathing deformation minimum, the nucleus is unstable against sausage deformations which make the torus thicker in one section and thinner in another. Simple vorticity does not help to stabilize such a nucleus against sausage deformations. A spherical liquid-drop bubble nucleus is stable against breathing deformation for x ≳ 2.1, in which case it is nonetheless unstable against one type of spheroidal deformation or another. Attention is turned to the independent particle model, where one finds shells in both the toroidal and the bubble nuclei in their breathing deformation degrees of freedom. The presence of these shells allows some “doubly-magic” toroidal and bubble nuclei to gain additional stability against breathing deformations, whose deformation energy surfaces are studied with Strutinsky's theory of renormalization. Approximate shell-model calculations reveal further that a shell in the breathing deformation of a toroidal nucleus is also a shell in its sausage deformation. Insofar as liquid-drop-type instability in the sausage deformation degree of freedom can be effectively counterbalanced by the stabilizing tendencies due to shells, which is thus suggested but is yet to be worked out in detail, there are doubly magic toroidal nuclei stable against collective deformations. The situation is similar but more definite for the bubble nuclei. There are doubly magic spherical bubble nuclei stable against collective vibrations. Stability against spheroidal deformations is not of major concern there mainly because a spherical bubble nucleus with x < 1.0 is stable against spherical deformations even in the liquid-drop model. Furthermore, additional stability may be gained as a shell in the breathing deformation is also a shell in the spheroidal deformation degrees of freedom.