The Fractal Geometrical Properties of Nuclei

TL;DR

This paper introduces a fractal geometric approach to nuclear structure, proposing new variables and formulas that better capture the irregular, self-similar features of nuclei, especially cluster and halo types, compared to traditional models.

Contribution

It develops a novel fractal-based model for nuclear structure, including a new potential energy formula and modified binding energy formula incorporating fractal dimensions.

Findings

Calculated fractal dimensions for light nuclei.

Compared fractal mean density radii with liquid drop model results.

Model reflects geometric features of cluster and halo nuclei.

Abstract

We present a new idea to understand the structure of nuclei, which is comparing to the liquid drop model. After discussing the probability that the nuclear system may be a fractal object with the characteristic of self-similarity, the nuclear irregular structure properties and the self-similarity characteristic are considered to be an intrinsic aspects of nuclear structure properties. For the description of nuclear geometric properties, nuclear fractal dimension is an irreplaceable variable similar to the nuclear radius. In order to determine these two variables, a new nuclear potential energy formula which is related to the fractal dimension is put forward and the phenomenological semi-empirical Bethe-Weizsacker binding energy formula is modified using the fractal geometric theory. And one important equation set with two equations is obtained, which is related to the conception that the fractal dimension should be a dynamical parameter in the process of nuclear synthesis. The fractal dimensions of the light nuclei are calculated and their physical meanings are discussed. We have compared the nuclear fractal mean density radii with the radii calculated by the liquid drop model for the light stable and unstable nuclei using rational nuclear fractal structure types. In the present model of fractal nuclear structure there is an obvious feature comparing to the liquid drop model, since the present model can reflect the geometric informations of the nuclear structure, especially for the nuclei with clusters, such as the {\alpha}-cluster nuclei and halo nuclei.