A model for collective mode damping in nuclei is devised in the frame of a theory of irreversible evolution. The decay width of a fast nuclear vibration, originated in its coupling to the remaining nuclear degrees of freedom, is calculated in a dynamical fashion. To this aim, a set of equations is proposed that describes the simultaneous dynamics of the oscillation or its associated array of bosons and of the interacting fermions that play the role of a heat reservoir. These are, respectively, a quantal master equation and modified kinetic one. The two of them exhibit their mutual coupling in the non-Hermitian terms of their generators of motion. The equations are worked out in detail in (a) the weak-coupling approximation plus (b) the very-close-to-equilibration regime plus (c) the energy-conserving description of intermediate processes. With hypothesis (c) the heat bath can be regarded as lying in a steady state at all times and the master equation is solved for different temperatures and phonon energies. The damping width of the oscillations is thus quantitatively predicted.

[NUCLEAR STRUCTURE Damping width. High-frequency collective modes. Nonstationary fermionic heat reservoir. Coupled dynamics. Quantal master equation. Modified BBGKY hierarchy. Modified kinetic equation. Single-particle lifetime. Temperature-dependent transition rates. Thermal equilibration. Irreversible evolution with effective collision frequency or relaxation time.]

• Received 1 November 1982

DOI:https://doi.org/10.1103/PhysRevC.29.1510