Method of averaging wavefunction corrections in scattering theory

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Abstract
A convergent perturbative method is presented for strong interaction scattering problems. The procedure resembles the method of averaging functional corrections and can be related to a distorted wave perturbation scheme. The method relies on the introduction of a finite linear basis set to approximately describe the wavefunction. This leads to a Lippmann−Schwinger type integral equation with a reduced interaction strength. An iterative solution is obtained similar to the Born series. Improvement of the basis set improves the reliability of the low order terms in the series. The convergence of the series is discussed, and convergence criteria given. The method can also be used to determine the singularities of the T matrix. The wavefunctions associated with these singularities may be used to remove the divergent behavior of the iterative solution to the integral equation. To illustrate the convergence behavior we apply the method to an integral equation with a seperable kernel. The method is applied to several simple examples, and the results are compared to the usual Born series. Significant improvements in accuracy are noted over the Born series as well as an extension of the region of convergence. Comparison with other similar procedures is discussed.