A New Effective Potential for Deuteron

TL;DR

This paper analytically calculates the static properties of the deuteron using supersymmetric quantum mechanics, deriving a new effective potential fitted to experimental data and providing explicit wave functions and state contributions.

Contribution

It introduces a novel effective potential for the deuteron derived via supersymmetric quantum mechanics, with parameters fitted to experimental data and analytical wave functions.

Findings

Derived a new effective potential for the deuteron.

Obtained analytical expressions for the deuteron wave function.

Identified linear proportionality between saddle point radius and wave function maximum.

Abstract

We calculate for the first time the static properties of the deuteron, within the framework of supersymmetric quantum mechanics, analytically. A new effective potential and its partner are derived from a superpotential so that all parameters are fitted by the experimental data. An analytical expression is obtained for the deuteron wave function and contributions of the orthogonal $^{13}S_{1}$ and $^{13}D_{1}$ states are determined, explicitly. Compared to one pion exchange, the superpotential produces an electrostatic as well as two pion exchange terms for the potential. The saddle point radius of the potential and the maximum of the wave function are linearly proportional.