dc.contributor.author | Jobunga, EO | |
dc.contributor.author | Wandera, CO | |
dc.contributor.author | Okeyo, OS | |
dc.date.accessioned | 2024-02-20T08:22:37Z | |
dc.date.available | 2024-02-20T08:22:37Z | |
dc.date.issued | 2023-06-20 | |
dc.identifier.citation | Jobunga, E. O., Wandera, C. O., & Okeyo, O. S. (2023). Convergence of the Laplace and the alternative multipole expansion approximation series for the Coulomb potential. | en_US |
dc.identifier.other | DOI: https://doi.org/10.21203/rs.3.rs-2971211/v1 | |
dc.identifier.uri | http://ir.tum.ac.ke/handle/123456789/17412 | |
dc.description | DOI: https://doi.org/10.21203/rs.3.rs-2971211/v1 | en_US |
dc.description.abstract | Multipole expansion is a powerful technique used in many-body physics to solve dynamical problems involving correlated interactions between constituent particles. The Laplace multipole expansion series of the Coulomb potential
is well established in literature. We compare its convergence with our recently developed perturbative and analytical
alternative multipole expansion series of the Coulomb potential. In our working, we confirm that the Laplace and the
alternative analytical multipole expansion series are equivalent as expected. In terms of performance, the perturbative
alternative multipole expansion series underapproximate the expected results to some extent while the Laplace and the
analytical alternative multipole expansion series yield results which are relatively accurate but oscillatory in nature even
with a higher number of angular momentum terms employed. As a practical example, we have evaluated the Slater double integrals for two-electron systems using the multipole expansion techniques and a mean field approximation. The
estimated results show that only spherical interactions are dominant while the higher-order interactions are negligible.
Our findings are likely to be useful in the treatment of the Coulomb potential in electronic structure calculations as well
as in celestial mechanics | en_US |
dc.description.sponsorship | TECHNICAL UNIVERSITY OF MOMBASA | en_US |
dc.language.iso | en | en_US |
dc.title | Convergence of the Laplace and the alternative multipole expansion approximation series for the Coulomb potential | en_US |
dc.type | Article | en_US |