# Observation of Ultra Fine Structures in Energy Levels of Prolate Nuclei

## TL;DR

This paper investigates the possibility of observing ultra fine structures in the energy levels of prolate nuclei, drawing parallels to the Zeeman effect in atomic physics, and introduces a modified commutation relation within the X(3) model.

## Contribution

It introduces a deformation in the commutation relations for the X(3) model to predict ultra fine structures in nuclear energy levels.

## Key findings

- Energy level splitting observed in the model.
- Plots illustrating the predicted ultra fine structures.
- Theoretical framework for nuclear energy level splitting.

## Abstract

This article contains a discussion in which we showed that observation of splitting in the energy levels of prolate nuclei, is possible. Similar effects is atomic physics is known as Zeeman effect which is well-known, but in nuclear physics such topic has not been discussed and mentioned if it is possible or is not. In this article, after introducing deformation in commutation relation in three dimensional, these relations has been used in X(3) model. After enough derivation, we evaluate energy spectrum relation for considered system which has splitting. Because of considerations during the derivation, we'd like to call such effect as ultra fine structures in energy levels. At the end some plots have been depicted which illustrate the results.