Partially Connected Faddeev-Weinberg-Rosenberg Equation

In the past few years, many authors have focussed their interest upon the treatment of integral equations for the N-body scattering amplitudes.)-IO) These discussions have revealed that only fully connected kernels can construct solvable equations, so efforts have been devoted to the construction of an equation of this type. Weinberg ) and Rosenberg) have finally succeeded in constructing an N-body integral equation having the desired property. The present paper applies the Faddeev-Weinberg-Rosenberg formalism to the examination of the cluster approximations. The cluster equation is obtained. In this equation, w·e stop the process of connecting the kernels at an intermediate stage. We call this type of equation a partially connected FW -R equation. Since this type of equation is only partially connected, it is in general not solvable. We can introduce approximations into this type of equation, and continue the connecting process until we get the fully connected FW-R equations. In § 2, the partially connected FW -R equation is obtained. In § 3, we discuss the relation between the equation obtained, Eq. (2 · 3), and various existing approximations. In § 4, some concluding remarks are given. Typical example of several~particle systems interacting through the two-body force is found in nuclear system. In particular cluster treatment proves its utility in Be• To take such an example makes the discussion visual.