Studies of the nuclear inertia in fission and heavy-ion reactions

Abstract

On the basis of the non-self-consistent cranking model we study some aspects of the nuclear inertia of interest in fission and heavy-ion reactions. First, we consider in the adiabatic limit the inertia for a doubly closed-shell nucleus in a deformed spheroidal harmonic-oscillator single-particle potential plus a small perturbation. When expressed in terms of a coordinate that describes the deformation of the nuclear matter distribution, the inertia for small oscillations about a spherical shape is exactly equal to the incompressible, irrotational value. For large distortions it deviates from the incompressible, irrotational value by up to about ±1 % away from level crossings. Second, in order to study the dependence of the inertia upon a level crossing, we consider in detail two levels of the above system. This is done both in the adiabatic limit and for large collective velocities. At level crossings the adiabatic inertia relative to the deformation of the matter distribution diverges as 1/| ΔV|, where | ΔV| is the magnitude of the perturbation. However, for large collective velocities the contribution to the inertia from a level crossing is less than 4| ΔV| r 2 m, where r m is the collective velocity of the matter distribution. Although we have not considered the effect of large velocities on the remaining levels of the many-body system or the effect of a statistical ensemble of states, some of our results suggest that for high excitation energies and moderately large collective velocities the nuclear inertia approaches approximately the irrotational value.