Coulomb excitation of a damped oscillator and the Brink-Axel mechanism

Multiple Coulomb excitation of collective nuclear modes is examined in the context of an extremely schematic dynamic model consisting of a harmonic os cillator, taken to represent the relevant collective mode, damped by linear coupling to a "bath" consisting also of harmonic oscillators, and forced b y an applied external pulse. The (well-known) exact solution of the model a llows for an estimate cross section which takes into account the joint effe ct of all excitation mechanisms leading to definite excitation energy domai ns, including the Brink-Axel mechanism, which occurs very naturally in this type of model. The semiclassical estimate of cross sections leading to the two-phonon domain shows enhancement with respect to the corresponding valu es obtained in the case of no damping. The magnitude of the enhancement dec reases as the beam energy increases (or, equivalently, as the impact parame ter averaged time width of the external pulse decreases), for model paramet ers chosen to conform to the appropriate nuclear orders of magnitude. [S055 6-2813(99)07505-6].