A thorough singularity analysis of scattering wave functions in the N-body problem is carried out. Operating on the basic Lippmann-Schwinger-Glöckle-Tobocman equations and resorting to a general reversion property for linked-cluster strings of channel resolvents and interactions, we explicitly exhibit the sources of the primary singularities of N-body scattering wave functions. We introduce complete sets of eigenstates of the two-cluster channel Hamiltonians and we arrive at momentum-space representations for two-cluster wave function components, where all the primary singularities appear in separate terms. By means of simple algebraic procedures we show that appropriate sums of the residues at the physical poles lead to the physical transition amplitudes for elastic/rearrangement, partial and total break-up processes.
Singularity analysis of N-body scattering wave functions
CATTAPAN, GIORGIO;
1979
Abstract
A thorough singularity analysis of scattering wave functions in the N-body problem is carried out. Operating on the basic Lippmann-Schwinger-Glöckle-Tobocman equations and resorting to a general reversion property for linked-cluster strings of channel resolvents and interactions, we explicitly exhibit the sources of the primary singularities of N-body scattering wave functions. We introduce complete sets of eigenstates of the two-cluster channel Hamiltonians and we arrive at momentum-space representations for two-cluster wave function components, where all the primary singularities appear in separate terms. By means of simple algebraic procedures we show that appropriate sums of the residues at the physical poles lead to the physical transition amplitudes for elastic/rearrangement, partial and total break-up processes.
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