Transport coefficients for shape degrees in terms of Cassini ovaloids

Previous computations of the potential landscape with the shapes parametrized in terms of Cassini ovaloids are extended to collective dynamics at finite excitations. Taking fission as the most demanding example of large scale collective motion, transport coefficients are evaluated along a fission path. We concentrate on those for average motion, namely, stiffness $C$, friction $\gamma$, and inertia $M$. Their expressions are formulated within a locally harmonic approximation and with the help of linear response theory. Different approximations are examined and comparisons are made with both previous studies, which involved different descriptions of single-particle dynamics, and macroscopic models. Special attention is paid to an appropriate definition of the deformation of the nuclear density and its relation to that of the single-particle potential. For temperatures above 3 MeV the inertia agrees with that of irrotational flow to less than a factor of 2, but shows larger deviations below, in particular in its dependence on the shape. Also, friction exhibits large fluctuations along the fission path for small excitations. They get smoothed out above 3–4 MeV where $\gamma$ attains values in the range of the wall formula. For $T>~2$ MeV the inverse relaxation time $\beta =\gamma /M$ turns out to be rather insensitive to the shape and increases with $T$.