TIME-DEPENDENT OPTICAL POTENTIALS - NON-MARKOVIAN AND DOORWAY APPROACHES

We propose new approximations to the time-dependent optical potential coupling that part of the Hilbert space in which standard truncated close coupling equations are solved (P space) and the complementary Q space. We define a dynamical basis in P space allowing for a transparent separation of P-Q and Q-Q coupling from P-P coupling, thus ensuring that we account for the latter exactly within any approximate scheme. Studying the time structure of the evolution operator in Q space, we are led to propose a non-Markovian scheme going beyond the instantaneous approximation. Alternatively, a topological study of the coupling between P and Q space leads to a doorway space approximation consisting in a dynamical extension of the P space by that pan of the Q space to which it is directly coupled.