Singular Cores in the Three-Body Problem. I. Theory

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Abstract
The three-body formalism for singular cores previously introduced by the author is considered in some detail. A new derivation is presented which clearly demonstrates the uniqueness of this formalism and clarifies its relationship to appropriate boundary conditions on the three-body wave function. It is shown that an auxiliary boundary condition must be imposed to uniquely specify a solution; this leads to an integral equation with a square-integrable kernel. A detailed proof of three-particle unitarity is given for the amplitudes defined by this equation, and explicit formulas are presented for a representative model.