A modification of the projection operator method for resonances

摘要

The Projection Operator Method as applied to the study of resonances is first briefly reviewed. Its shortcomings, in the context of reactions that involve forbidden states are mentioned. The forbidden states arise due to the requirement of antisymmetrization imposed by the Pauli exclusion principle, on the many body wave function. A modification that takes into account the forbidden states is suggested. The modified formalism is applied to the alpha-alpha scattering involving realistic interactions. In place of the usual practice of using oscillator wave functions, bound states are extracted from the scattering potential and are used in obtaining the results. The calculated resonance energies, widths and phase shifts, show excellent agreement with experiment. Since forbidden states should be present in almost any nucleus-nucleus interaction the procedure has a wide range of applicability. It is concluded that the modifications are necessary, if agreement with experiment is to be established. [References: 21]