Higher-Order Corrections to Algebraic Derivation of Electric Dipole-Dipole Interaction

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.