Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method
Abstract
In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for . The mass parameters in the exponentials of the Gaussian base-functions are fixed using the geometric progression recipe of Hiyama-Kamimura. The fitting of the expansion coefficients is linearly and very fast. Application to nucleon-nucleon is given in detail for the recent Extended-soft-core model ESC08c. The NN phase shifts obtained by solving the Lippmann-Schwinger equations agree very well with those obtained in configuration-space solving the Schr\"{o}dinger equations.
Keywords
Cite
@article{arxiv.1409.5593,
title = {Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method},
author = {Th. A. Rijken},
journal= {arXiv preprint arXiv:1409.5593},
year = {2014}
}