The proton-neutron resonance states by solving Schrodinger equation

TL;DR

This paper models proton-neutron interactions using the Schrödinger equation with a Yukawa potential, identifying two resonance states that could inform future experimental research.

Contribution

It introduces a method to calculate proton-neutron resonance states by solving the Schrödinger equation with a Yukawa potential, fixing parameters based on deuteron binding energy.

Findings

Identified two proton-neutron resonance states at complex energies 1905-i13 MeV and 2150-i342 MeV.

Provided a theoretical framework for understanding proton-neutron interactions and resonance phenomena.

Suggested potential experimental investigations based on the calculated resonance states.

Abstract

The proton-neutron interaction is investigated by solving the Schrodinger equation, where a Yukawa type of potential with one pion exchanging between the proton and the neutron is assumed. Since the deutron is the unique bound state of the proton-neutron system, the coupling constant is fixed according to the binding energy of the deutron. The scattering process of the proton and the neutron is studied when the outgoing wave condition is taken into account, and two proton-neutron resonance states are obtained by solving the Schrodinger equation, which lie at $1905-i13$MeV and $2150-i342$MeV on the complex energy plane, respectively. It is no doubt that the calculation results would give some hints on the experimental research on the proton-neutron interaction in future.