Nonequilibrium statistical-operator theory of nuclear dissipation

Abstract

The past analyses of the dissipation rate Q ˙ , associated with the motion of nuclear surface, have overlooked the fact that nuclei are nearly incompressible and that consequently the surface motion gives rise to the velocity field u ( r ) inside the nucleus, which leads to heat production in the bulk. To fill this gap we apply the method of nonequilibrium statistical operator by Zubarev to calculate Q ˙ in a finite incompressible Fermi gas with constant over system temperature T and chemical potential μ, but nonuniform u ( r ) . The effects of inter-nucleon collisions are accounted for in terms of the nucleon mean free path λ at the Fermi energy. In addition to the term Q ˙ ( V ) , known from the theory of linear response on deformations of the surface of the mean field potential V ( r ) , new expressions for Q ˙ contain the bulk term Q ˙ ( u ) due to relaxation of the spatial nonuniformities in u ( r ) and the cross correlation term 2 Q ˙ ( V u ) between the bulk and surface modes of dissipation. With the Cassini parametrization of nuclear shapes and Werner–Wheeler approximation for u ( r ) , new friction coefficients are calculated for mass-symmetric fission of 208Pb, 224Th, 248Cf, and 272Ds. The bulk friction is found to be somewhat less than the surface one. The sum of those is sizably reduced by the cross correlation term, appeared to be negative. When λ increases from 20 fm to 50 fm, which corresponds approximately to the change of T from 3.5 MeV to 2 MeV, the total friction coefficients decrease by a factor ≈2.