Confined States of a Positronium in a Spherical Quantum Dot

TL;DR

This paper investigates the energy states of a positronium confined within a spherical quantum dot across different size-quantization regimes, providing analytical and numerical solutions for each case.

Contribution

It offers a comprehensive theoretical analysis of positronium confined in quantum dots, deriving analytical expressions in strong and weak regimes and numerical results in the intermediate regime.

Findings

Analytical wave functions and energies in strong SQ regime

Analytical energies and binding energies in weak SQ regime

Numerical and variational results in intermediate SQ regime

Abstract

Confined states of an electron-positron pair in the spherical quantum dot (QD) are theoretically investigated in three size-quantization (SQ) regimes: strong, weak and intermediate. In the strong SQ regime, analytical expressions for the wave functions (WFs) and energy of the pair are obtained. In the weak SQ regime, the positronium energy and binding energy are analytically calculated. To calculate the positronium energy in the intermediate SQ regime, variational and numerical methods are used. It is shown that, in the corresponding limits, the results obtained by variational method agree with those obtained in the strong and weak SQ regimes.