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(h6)O(h6) method which can be used to solve the Schrödinger radial equation using a suitable potential V(r)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≠0l≠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 n3S1−n1S0n3S1−n1S0, as well as the n3PJ−n1P1n3PJ−n1P1 energy levels. Finally a simple software implemented in QQ-onia to compute E1 transition rates is presented.

J.L.D.G gratefully acknowledges his Department for financial support, and M.A.S.L. thanks MICINN and Generalitat Valenciana for financial support under grants FPA2005- 01678, FPA2008-02878 and GVPRE/2008/003.