Development of a General and Effective B-spline R-matrix Computer Program for Electron and Photon Collisions with Atoms, Ions, and Molecules

Drake University, Des Moines IA

Investigators

Abstract

Further development of a general and effective program for electron collisions with atoms and ions using a B-spline approach with non-orthogonal orbitals will be undertaken. The approach is based upon an extended version of the R-matrix method, in which non-orthogonal orbitals are extensively used for describing both the target states and the scattering functions. The new approach is essentially free of the three major problems that often arise when the most frequently used suite of R-matrix codes, mostly developed over the past three decades in Belfast and currently used world-wide, is applied to truly complex targets such as heavy noble gases or open-shell transition elements. These problems include i) the difficulties in describing all target states of interest for a given calculation to sufficient accuracy, ii) the likely occurrence of unphysical structures, so-called pseudo-resonances, when an attempt is made to address the former problem, and iii) numerical difficulties due to an ill-conditioned orthogonalization procedure and the need to modify the so called Buttle correction. The excellent numerical properties of a B-spline basis used for the description of the continuum states in the inner region allow for high computational accuracy, while the completeness of the basis will ensure that no Buttle correction to the R-matrix elements is required. With the non-orthogonal orbital technique the target states can be generated from independent calculations, with compact configuration expansions. During the funding period, the following extensions will be undertaken: 1) parallelize the code to allow for the treatment of even more challenging problems; 2) include a sufficient number of pseudo-states to simulate coupling to the ionization continuum, thereby allowing for accurate results to be generated at intermediate energies; 3) use extention 2) above to generate results for ionization processes; 4) generate the target orbitals by the relativistic Hartree-Fock method; 5) treat charged-particle impact and multi-photon single- and double-ionization; 6) treat electron collisions with diatomic molecules.