G-Matrix Equation in the Resonating-Group Method

TheG-matrix equation is most straightforwardly formulated in the resonatinggroup method if the quark-exchange kernel is directly used as the driving term for the infinite sum of all the ladder diagrams. The inherent energydependence involved in the exchange term of the normalization kernel plays the essential role to define the off-shell T -matrix uniquely when the complete Pauli-forbidden state exists. We analyze this using a simple solvable model with no quark-quark interaction, and calculating the most general T -matrix in the formulation developed by Noyes and Kowalski. This formulation gives a certain condition for the existence of the solution in the Lippmann-Schwinger resonating-group method. A new procedure to deal with the corrections for the reduced masses and the internal-energy terms in the ΛN -ΣN coupled-channel resonating-group equation is proposed. ∗e-mail: [email protected]