A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

Abstract

We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the fluctuations are governed by diffusion coefficients D µν . The latter are obtained through a fluctuation dissipation theorem generalized to allow for a treatment of unstable modes. Numerical evaluations of the D µν are presented. We discuss briefly how this picture may be used to describe global motion within a locally harmonic approximation. Relations to other methods are discussed, like "dissipative tunneling", RPA at finite temperature and generalizations of the "Static Path Approximation".

Four-dimensional Langevin approach to low-energy nuclear fission of U236

“…The random force g ij R j (t) is the product of white noise R j (t) and the temperature dependent strength factors g ij . The factors g ij are related to the temperature and friction tensor via the modified Einstein relation [29],…”

“…The parameter ̟ is the local frequency of collective motion [29]. The minimum of T * is given byh̟/2, which corresponds to the zero point energy of oscillators forming the heat bath.…”

Statistical fluctuations for the fission process on its descent from saddle to scission

“…For the computations to be discussed below we chose ω D = 10̟, with the ̟ given by (2). Fortunately, the diffusion coefficients do not depend on ω D too much (see [9]). Changing the latter by a factor of two, our final results would have to be modified by less than 30% which, as we shall see, will not influence much the conclusions we are going to draw below.…”

“…Actually, this T c turns out to be that temperature at which the CΣ eq qq becomes negative. It is of the order of 0.5 MeV or less, depends on the transport coefficients of average motion and decreases with increasing damping, see [9]. On the nuclear scale such values of T can be considered small.…”

“…Prime examples are the evaporation probabilities for light particles [21] and γ-rays (see [17]). Adopting the same normalization as in (7,8) one gets as weighting factor the current j which according to (9) is constant. This implies that for the motion from saddle to scission an average in the coordinate q simply reduces to the algebraic one.…”