Calculations of three-body scattering amplitudes

We develop and study two techniques for the calculation of threebody scattering amplitudes. The first is a variational principle based on the Faddeev equations. In form it resembles a Schwinger principle. The wave functions that are varied are products of the two-body potentials and the normal three-body wave function. This results in a very simple asymptotic behavior, even for energies above the breakup threshold. Numeric results are presented for s-wave calculations using separable potentials for elastic, rearrangement and breakup scattering. The convergence is rapid and the technique seems very successful. Accuracies on the order of several parts per million are easily achieved. The specific forms of the equations for problems involving two or three identical bosons are also presented and the breakup calculations for these cases are presented as Dalitz plots. The second technique is based on the analytic structure in the total energy of the three-body T-matrix. The T-matrix is computed for energies less than the physically allowed energies and the results of these calculations are then numerically analytically continued to the physical region. Because the wave function has very simple asymptotic behavior beneath threshold, these calculations are easy to do. Calculations have again been done for separable potentials so the results can be compared with the results from the first technique. We conclude that this is a reliable technique for scattering beneath the breakup threshold and that useful results are achieved for positive total energies, if there is not too much breakup scattering. The technique is then applied to a local s-wave calculation using Yukawa potentials. A Kohn type variational principle is used to find the beneath threshold T-matrices. The final results show good convergence and with the above mentioned lUnitation, this appears to be a good technique for local calculations.U of I OnlyThesi