QQ-onia package: a numerical solution to the Schrodinger radial equation for heavy quarkonium

Abstract

This paper presents the basics of the QQ-onia package, a software based upon the Numerov O(h(6)) method which can be used to solve the Schrodinger radial equation using a suitable potential V(r) for the heavy quarkonium system. This package also allows the analysis of relevant properties of those resonances such as the square of the wave functions at the origin, their corresponding derivatives for l not equal 0 states, typical heavy-quark velocities, and mean square radii. Besides, it includes a tool to analyze the spin dependent contributions to the heavy quarkonia spectrum, providing the splitting of n(3)S(1)-n(1)S(0), as well as the n(3)p(J) - n(1)P(1), energy levels. Finally a simple software implemented in QQ-onia to compute E1 transition rates is presented.