Formal Relation among Various Hermitian and non-Hermitian Effective Interactions

Nuclear many-body theory has been intensively studied for many years and reached a high level of understanding, but there still are some unresolved fundamental problems. One of the leading approaches is to introduce an effective interaction and reduce the full many-body problem to a certain model-space problem. There have been many review works concerning the effective interaction theory, for example, Ref. 1. The principle of determining the effective interaction is that it should have the property of decoupling between the model space and the excluded space as discussed by Lee and one of the authors (K.S.). The property of decoupling is necessary for the effective interaction, but it does not give the condition of determining uniquely the effective interaction. Therefore many kinds of the effective interactions are possible. Very recently Holt, Kuo and Brown published a paper to study the various versions of hermitian effective interaction. The purpose of the present paper is to give a general definition of the effective