Modeling the Electromagnetic Structure of Deuteron Using Low Energy Nuclear Theory

Abstract

Deuteron, the simplest possible nucleus consisting of a proton and neutron, is often used as a target in electro-scattering experiments, where a beam of electrons collides with a stationary deuteron sample. To calculate the interaction between the deuteron and electron, it is necessary to have a working model of the deuteron’s nuclear potential and the resulting wave function. In cases where the internal substructure of the nucleons is negligible, such as with elastic scattering, a low energy theory may be used to describe the deuteron. In this regime, the nuclear interaction binding the proton and neutron contains One Pion Exchange potentials (V_OPE), the tensor operator (Š12), and spin/isospin coupling terms. The goal of this project was to calculate the deuteron wave function and physical electromagnetic observables using this low-energy nuclear potential starting from the three-dimensional Schrodinger equation. This was accomplished using both analytical and computational methods. The matrix elements for the spin, isospin, and angular components were derived analytically using Wigner coefficients and angular momentum coupling techniques. The radial component matrix elements were solved computationally using Gaussian-Laguerre quadrature integration and matrix linear algebra. The resulting observables, including the ground-state binding energy (-2.2245 MeV), root mean square radius (1.908 fm), and magnetic moment (0.854 μN), all align with experimental measurements. These results indicate that the interaction potential and low-energy assumptions used are valid and model the deuteron accurately. Electron-deuteron elastic scattering experiments, such as those at Jefferson National Lab, could make use of this model to calculate the theoretical cross-sections to compare to their experimental data. The model could also be extended to experiments outside of Jefferson Lab to compute cross-sections for neutrino-deuteron elastic scattering.