The relativistic J-matrix method in scattering of electrons from model potentials and small atoms

Full text: The J-matrix method is an algebraic method in quantum scattering theory. It is based on the fact that the radial kinetic energy operator is tridiagonal in some suitable bases. Nonrelativistic version of the method was introduced in 1974 by Heller and Yamani and developed by Yamani and Fishman a year after. Relativistic version was introduced in 1998 by P. Horodecki. The main advantage of the method is that it allows to calculate phase shifts for many projectile energies with relatively small computational time. Also, the non-relativistic limit in relativistic calculations is properly achieved. This fact was expected, since the basis sets used in relativistic calculations satisfied the so called kinetic balance condition. Some preliminary applications of relativistic J-matrix method to scattering have been performed for some square-type potentials, using the newly developed Fortran 95 code JMATRIX. These tests proved that the method correctly describes the scattering process. Since these times, the JMATRIX code has been greatly extended and thoroughly tested. In the present work we applied the code (in both non-relativistic and relativistic versions) to calculate some scattering properties of electrons scattered from more complex potentials, i.e. truncated Coulomb, Yukawa and Lenard-Jones potentials and more. In its primary version, the JMATRIX program allowed for applying scattering potentials in analytical forms only. Now the code has been extended, so it allows for applying scattering potential given in any numerical form, i.e. taken from the GRASP92 code. In conclusion, we present the calculated scattering phase shifts and cross sections for many energies of the incident electrons, in cases of the analytical potentials mentioned previously, as well as the numerical potentials of some small atoms. Also, we illustrate the convergence process and describe some limitations of the method. (author)