Quantum Gravity Corrections to the Mean Field Theory of Nucleons

TL;DR

This paper investigates quantum gravity-induced modifications to the mean field potential of nucleons by deforming the Schrödinger equation with a minimal length, analyzing their effects on energy levels and wave functions.

Contribution

It introduces a novel approach to incorporate quantum gravity effects into nuclear mean field theory via a deformed Schrödinger equation with minimal length.

Findings

Derived corrections to energy eigenvalues of nucleons

Constructed wave functions under quantum gravity corrections

Analyzed modifications to the Woods-Saxon potential

Abstract

In this paper, we analyze the correction to the mean field theory potential for a system of nucleons. It will be argued that these corrections can be obtained by deforming the Schr\"{o}dinger's equation describing a system of nucleons by a minimal length in the background geometry of space-time. This is because such a minimal length occurs due to quantum gravitational effects, and modifies the low energy quantum mechanical systems. In fact, as the mean field potential for the nucleons is represented by the Woods-Saxon potential, we will explicitly analyze such corrections to this potential. We will obtain the corrections to the energy eigenvalues of the deformed Schr\"{o}dinger's equation for the Woods-Saxon potential. We will also construct the wave function for the deformed Schr\"{o}dinger's equation.