Saturation in heavy quarkonia spectra with energy-dependent confining potential in N-dimensional space

Abstract

We study the energy spectra of Schrödinger Hamiltonian in N-dimensional space with Coulomb plus inverse quadratic term [Formula: see text] and energy-dependent confining potential of the form [Formula: see text]. It is found that the energy spectra exhibit saturation effect, where these spectra are suppressed to finite values at large quantum numbers n and/or [Formula: see text] at any dimensional space N. As a typical application, we obtained a compact mass formula for the spectra of heavy quarkonia ([Formula: see text], [Formula: see text]). It is found that the model is capable of reproducing the mass spectra of these systems with observed saturation governed by a factor [Formula: see text]. The comparison of this work predictions with available experimental data as well as other relevant theoretical works is also presented. The eigenfunctions are expressed in terms of the bi-confluent Heun functions.