| The conventional approach to computing scattering cross sections is to perform a partial-wave decomposition of the scattering amplitude (or T-matrix) and solve the Schrödinger equation for each value of angular momentum up to some cutoff value. The number of partial waves that needs to be computed rapidly increases with energy and number of particles. A direct solution of the momentum-space Lippmann-Schwinger equation, a Fredholm type 2 integral equation, avoids this “partial-wave explosion.” An adaptive Monte Carlo algorithm for the solution of the Fredholm type 2 integral equation is developed. In adaptive Monte Carlo the algorithm during execution teaches itself the minimum-variance distribution from which it should sample. The information-based computational complexity of the Fredholm type 2 integral equation is explored in order to understand the efficiency of this adaptive Monte Carlo algorithm. A genetic algorithm is developed for optimizing the Monte Carlo algorithm's input parameters. Because the output Born (Neumann) series of the algorithm is noisy and often divergent, a maximum entropy method for summing this series is developed. To facilitate coding and software maintenance, object-oriented programming is employed. The approach is tested for elastic scattering of the alpha particle on Yb. |
