TITLE:
Higher-Order Corrections to Algebraic Derivation of Electric Dipole-Dipole Interaction
AUTHORS:
Haiduke Sarafian
KEYWORDS:
Electric Dipole-Dipole Interaction, Taylor Expansion, Computer Algebra System (CAS), Mathematica
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.11 No.4,
December
8,
2021
ABSTRACT: Nucleons are fermions with intrinsic spins
exhibiting dipole character. Dipole-dipole interaction via their dipole moments
is the key feature quantifying the short-range nucleonics interaction in
two-body physics. For a pair of interacting dipoles, the energy of a pair is
the quantity of interest. The same is true for chemical polar molecules. For
both cases, derivation of energy almost exclusively is carried out vectorially[1]. Although uncommon
the interacting energy can be derived algebraically too. For the latter Taylor,
expansion is applied [2]. The given expression although appears to be correct it is incomplete. In our report, by applying Taylor’s expansion up to the 4th order and utilizing a Computer Algebra System
we formulate the missing terms. Our report highlights
the impact of correcting missing terms by giving two explicit examples.