Lower Bounds on Phase Shifts for Three-Body Systems:n−dQuartet Scattering

Abstract

The Faddeev equations are used to provide a variational-bound formulation of the three-body scattering problem. The present method has the distinct advantage that the Feshbach projection operators, which enter into previous formulations and which are generally difficult to construct, do not appear. The method requires the calculation of a variational approximation to the exact effective potential for the scattering of a particle by a bound two-body system. A reaction matrix is determined by using this effective potential as input to a two-body Lippmann-Schwinger equation which is easily solved numerically. The eigenphase shifts thus obtained provide lower bounds on the true eigenphases for energies below the three-body breakup threshold. To test its practicability, the method is applied to the problem of neutron-deuteron scattering in the quartet state. The results are in agreement with previous calculations and with experiment.