Pairing and shell effects in the transport coefficients of collective motion

Abstract

The linear response approach to nuclear transport has been extended to pair correlations. The latter are treated within a mean field approximation to a pairing interaction with constant matrix elements $G$. The constraint of particle number conservation has been accounted for on a time dependent average, which leads to modified response functions, both in the pairing degree of freedom as well as in the shape variable. The former is expressed by the gap parameter $\Delta$ and the latter by a $Q$ which specifies the elongation of a fissioning nucleus. The tensors for friction and inertia corresponding to these two collective coordinates are computed along the fission path of $^{224}Th$ for temperatures around $T=1 \mev$ and less. It is seen that dissipation decreases with decreasing temperature and increasing pairing gap and falls well below the values of common "macroscopic models". Both friction and inertia show a sensible dependence on the configurations of the mean field caused both by shell effects as well as by avoided crossings of single-particle levels.