Linked diagram expansions for the nuclear transition matrix and the normalization of model-space wave functions

Abstract

A unified and relatively simple linked-diagram expansion for performing microscopic calculations of the nuclear transition matrix T fi is derived. We first review a folded-diagram effective interaction theory, based on which, the model-space effective hamiltonian can be calculated from realistic nucleon-nucleon interactions. An important ingredient of this theory is the wave-function decomposition theorem which provides a convenient connection between the true and model-space wave functions. By directly making use of this theorem, a folded-diagram expansion of T fi is readily obtained. Using a partial summation method, the folded diagrams of T fi are then eliminated, leading to a considerably simpler expression for T fi. Our formalism requires that T fi must be calculated in strict consistence with the derivation of the model-space effective hamiltonian H eff. The model-space wave function normalization factor contained in our T fi, may play an important role in “quenching” the calculated nuclear transition matrix. A simple method for evaluating this normalization factor is derived, namely it can be obtained readily from the energy derivative of the respective self-consistent eigenvalue of H eff.