Survival probability for the Yamaguchi potential

Different decay behaviours of the survival probability are examined. Technically, the survival probability of an arbitrary state psi is determined by the psi matrix element of the resolvent of the full Hamiltonian. The analytical properties of this matrix element can be analyzed in terms of the properties of the kernel of the Lippmann-Schwinger equation. For the Yamaguchi potential and several initial states, all functions are explicitly calculated. This approach allows the decomposition of the survival amplitude into a sum of decaying exponential terms and w-functions associated with the pole positions of the resolvent matrix element in the complex momentum plane. Novel decay behaviours are found for the decay of states associated with the resolvent poles and the decay of a state which is dominated by the form of the wave function rather than by the resolvent poles. Certain anomalous short time decay behaviour is also exemplified. (C) 1996 Academic Press, Inc.