Non-Local Interactions For the Deuteron Using Spherical Bessel Functions

TL;DR

This paper develops analytical wavefunctions for the deuteron using non-local interactions modeled with spherical Bessel functions, providing insights into the deuteron's structure and properties, with promising results for the quadrupole moment.

Contribution

It introduces a novel analytical approach to deuteron wavefunctions with non-local interactions using spherical Bessel functions, simplifying calculations and matching experimental data.

Findings

Wavefunctions are continuous across boundary regions.

Good agreement with experimental quadrupole moment.

Simplified model with equal range parameters b1=b2.

Abstract

Non-local interactions are assumed for the deuteron with form factors $g_C(k)= j_0(b_1k)\,j_0(b_2k)$ for the central part responsible for the S-state and $g_T(k)= j_1(b_1k)\,j_1(b_2k)$ for the tensor part responsible for the D-state, where $b_1$ and $b_2$ are range parameters for the proton and neutron, respectively. The analytically obtained wavefunctions in coordinate space have different forms in three different regions. The inner most region is between $r=0$ and $r=b_2-b_1$ (assuming $b_2>b_1$), followed by a region between $r=b_2-b_1$ and $b_1+b_2$ and finally the region $r>b_1+b_2$. The resulting wavefunctions and their derivatives are found to be continuous at the boundaries. The ensuing calculations are simplified by setting $b_1=b_2=b$. Good agreement is obtained for the quadrupole moment. Neutron-proton scattering calculations will follow in the next communication.