Quantum Gravity Corrections to the Mean Field Theory of Nucleons

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 Schrödinger'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 Schrödinger's equation for the Woods-Saxon potential. We will also construct the wave function for the deformed Schrödinger's equation.

Accepted in The European Physical Journal C, in press

References in corpus (24)

• Quantum Gravity at a Lifshitz Point
• Double Field Theory
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• No Existence of Black Holes at LHC Due to Minimal Length in Quantum Gravity
• Fusion-fission reactions with modified Woods-Saxon potential
• Generalized uncertainty principles and quantum field theory
• Asymptotic Safety, Emergence and Minimal Length
• The Most General Form of Deformation of the Heisenberg Algebra from the Generalized Uncertainty Principle
• Incorporation of Generalized Uncertainty Principle into Lifshitz Field Theories
• Quantum Black Hole and the Modified Uncertainty Principle
• A new bound on polymer quantization via an opto-mechanical setup
• Quantum time scales in alpha tunneling
• Reply to "Comment on 'Universality of Quantum Gravity Corrections' "
• Do the Modified Uncertainty Principle and Polymer Quantization predict same physics?
• Effects of GUP in Quantum Cosmological Perfect Fluid Models
• Polymer Quantization of a Self-Gravitating Thin Shell
• Effects of the Modified Uncertainty Principle on the Inflation Parameters
• Effect of nuclear magnetization distribution within the Woods-Saxon model: Hyperfine splitting in neutral Tl
• The bound state solutions of the $D$-dimensional Schrödinger equation for the Woods-Saxon potential
• Shape and shell-structure of lighter (N<90) neutron-rich nuclei based on phenomenological Woods-Saxon potential