Damping of collective motion in extended TDHF

In the present work, a formalism suitable to describe low velocity dissipative nuclear collective motion within the framework of the extended TDHF theory in the adiabatic limit is developed. As a first step in such a development, large amplitude slow collective motion described by a single collective variable q(t) and the conjugate variable p(t) is considered. The adiabatic approximation is introduced by assuming the collective velocity is small and, hence, by expanding the phase factor in powers of collective velocity to second order. In the same way expanding the mean field and the collision term in powers of collective velocity and equating the same order term separately, a set of coupled equations is obtained for the collective path rho0 and circumflex Q. In order to make contact with the collective model, the total energy of the system is expressed in terms of the collective variables