Quantum theory of dissipation for nuclear collective motion

We present a theory of energy dissipation in heavy ion and fission process. Beginning with the time-independent coupled channels generator coordinate equations, a statistical treatment leads toa quantal equation in the collective coordinates and excitation energy. Assumptions of adiabaticity lead to a momentum coupled Schroedinger-like equation for the statistical wave-function. This equationdescribes, in a statistical manner, quantum mechanical collective motion, including dissipation. Therefore, average inelastic cross sections or fragment excitation energies may be obtained. Of course, phenomenologically known functions such as the nuclear mass parameter or potential energy surface can be simply utilized. The new dissipation function (like all the others) is determined by averages of microscopically calculable quantities. Numerical result for a model calculation exhibiting the structure of the equation are presented.