Binding Energies and Dissociation Temperatures of Heavy Quarkonia at Finite Temperature and Chemical Potential in theN-Dimensional Space

T A Abdel-Karim,E M Khokha,M Abu-Shady

doi:10.1155/2018/7356843

T A Abdel-Karim, E M Khokha + Show 1 more

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https://doi.org/10.1155/2018/7356843

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Abstract

TheN-dimensional radial Schrödinger equation has been solved using the analytical exact iteration method (AEIM), in which the Cornell potential is generalized to finite temperature and chemical potential. The energy eigenvalues have been calculated in theN-dimensional space for any state. The present results have been applied for studying quarkonium properties such as charmonium and bottomonium masses at finite temperature and quark chemical potential. The binding energies and the mass spectra of heavy quarkonia are studied in theN-dimensional space. The dissociation temperatures for different states of heavy quarkonia are calculated in the three-dimensional space. The influence of dimensionality number (N) has been discussed on the dissociation temperatures. In addition, the energy eigenvalues are only valid for nonzero temperature at any value of quark chemical potential. A comparison is studied with other recent works. We conclude that the AEIM succeeds in predicting the heavy quarkonium at finite temperature and quark chemical potential in comparison with recent works.

Highlights

The solution of the radial Schrodinger equation with spherically symmetric potentials has vital applications in different fields of physics such as atoms, molecules, hadronic spectroscopy, and high energy physics
The aim of this work is to find the analytic solution of the N-dimensional radial Schrodinger equation with generalized Cornell potential at finite temperature and chemical potential using the analytical exact iteration method (AEIM) to obtain the energy eigenvalues, where the energy eigenvalues are only valid for nonzero temperature for any value of quark chemical potential
We have employed the analytical exact iteration method (AEIM) for determining the analytic solution of the N-dimensional radial Schrodinger equation, in which the Cornell potential is generalized at finite temperature and quark chemical potential

Summary

Introduction

The solution of the radial Schrodinger equation with spherically symmetric potentials has vital applications in different fields of physics such as atoms, molecules, hadronic spectroscopy, and high energy physics. Most of the theoretical studies have been developed to study the solutions of radial Schrodinger equation in the higher dimensions. These studies are general and one can directly obtain the results in the lower dimensions [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. The N-dimensional radial Schrodinger equation has been solved for different types of spherical symmetric potentials as Coulomb potential [15], pseudo-harmonic potential [20], Mie-type potential [21], energy-dependent potential [11], Kratzer potential [22], and Cornell potential type [13, 23] that consists of the Coulomb term and the linear term, anharmonic potential [14], the Cornell potential with harmonic oscillator potential [12], and the extended Cornell potential [19]

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