Test of the nonrelativistic $c\bar{c}$ potential

TL;DR

This paper tests a nonrelativistic potential model for charmonium, fitting parameters with low-lying states and analyzing the entire spectrum, demonstrating the model's effectiveness in describing charmonium energy levels.

Contribution

It introduces a new parameter set for the nonrelativistic potential model, fitted to S-wave states, and extends analysis to the full fine structure of charmonium.

Findings

The potential model accurately describes charmonium states.

The new parameters fit well with experimental data.

The model effectively accounts for spin-orbit and tensor interactions.

Abstract

We analyze the charmonium states by testing a phenomenological nonrelativistic potential and propose a new set of parameters. This new set of parameters are fixed using only the lowest lying S-wave states of charmonia where the spin-orbit and tensor interactions will not contribute. After fitting the parameters we analyze the whole fine structure of charmonium states taking into account the spin-orbit and tensor interactions too. Calculations showed that the nonrelativistic potential model with the phenomenologically defined parameters is indeed well approximation for describing the charmonium states.