Revisiting the charmonium spectra within the non-relativistic framework using the Matrix Numerov method

Charmonium is a composite particle composed of charm and anti-charm quark. Studying spectroscopy on charmonium is one effort to understand the strong interactions. In this study, the mass spectrum of the charmonium is modeled within a non-relativistic framework. As a result, we can use the Schrödinger equation to describe the charmonium system. The results obtained with the non-relativistic framework are reasonable for charmonium because the charm mass is relatively large compared to the quark mass from the first generation. Potential energy for charmonium is composed of phenomenological potential, known as Cornell potential, and terms containing spin-spin interactions. We obtain various charmonium masses by solving the Schrödinger equation using the Matrix Numerov method. The parameters that appear in the potential are adjusted by comparing our calculation of charmonium masses with the data of the charmonium spectra from the particle data group (PDG). When we look at the PDG data, we can see that there are still many charmonia whose quantum numbers are unknown. The results from the model can then predict the quantum number of the charmonia.