Test of three-body separable pole expansions at negative and positive energies

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Abstract
We compare the performance of separable pole expansions for the three-body amplitude in reproducing three-body data at both negative and positive energies. In addition to the generalized unitary pole expansion and the energy dependent pole expansion, we present results for two new expansions. As benchmarks for our calculations, we use the three-boson results of Aaron, Amado, and Yam. At negative energies, we give off-shell scattering amplitudes and investigate how well the expansions are capable of generating the second bound state of the three-boson problem, if the first is put explicitly into the expansions. At positive energies, we calculate phase shifts and inelasticities. We find that the convergence properties of the expansions investigated change rather markedly above the three-particle breakup threshold and only one of the four expansions is capable of reproducing the data in this energy region. In general, the results get better the more energy dependence is explicitly contained in the expansion functions. The relevance of these findings for four-body calculations, which employ separable three-body input, is discussed briefly.