# Finite volume effects on quarkonium dissociation temperature in an impenetrable QGP sphere

## TL;DR

This study investigates how finite volume effects within an impenetrable spherical cavity influence quarkonium dissociation temperatures in a hot QCD medium, revealing that smaller cavities lower dissociation temperatures and affect ground states more.

## Contribution

It introduces the first analysis of quarkonium behavior in a finite spherical cavity with hot medium, deriving boundary conditions and solving the Schrödinger equation numerically.

## Key findings

- Dissociation temperature decreases with smaller cavity radius.
- Finite volume effects are more significant for ground states.
- Lighter constituents and larger quarkonium radius enhance finite volume effects.

## Abstract

The system of a quarkonium confined by an impenetrable spherical cavity filled with a hot quantum chromodynamics (QCD) medium is studied by solving the Schr\"{o}dinger equation. This is the first time this issue has been raised for discussion. The Schr\"{o}dinger equation with an appropriate boundary condition of a quarkonium in an impenetrable cavity filled with a hot medium is derived. The numerical results are obtained with the help of Gaussian Expansion Method. Binding energies and radii of the ground and low-excited states are obtained as a function of the medium temperature and the cavity radius. We find the behaviour of quarkonium in this cavity is different from that in infinite space. Our results show that the quarkonium dissociation temperature decreases as the cavity radius decreases and the finite volume effects on the ground state are more obvious than on the excited states. We also find that the less mass of the constituents and the bigger radius of the quarkonium lead the finite volume effects to become more obvious.