Fractal geometrical properties of nuclei

MA Wei-Hu; WANG Jian-Song; WANG Qi; YANG Lei; YANG Yan-Yun; HUANG Mei-Rong

doi:10.1088/1674-1137/39/10/104101

Chinese Physics C> 2015, Vol. 39> Issue(10) : 104101 DOI: 10.1088/1674-1137/39/10/104101

Fractal geometrical properties of nuclei

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We present a new idea to understand the structure of nuclei and compare it 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 irregular nuclear structure properties and the self-similarity characteristic are considered to be an intrinsic aspect of the nuclear structure properties. For the description of nuclear geometric properties, the 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-Weizsäcker binding energy formula is modified using the fractal geometric theory. One important equation set with two equations is obtained, which is related to the concept that the fractal dimension should be a dynamic parameter in the process of nuclear synthesis. The fractal dimensions of the light nuclei are calculated and their physical meanings are discussed. We compare 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 additional feature compared to the liquid drop model, since the present model can reflect the geometric information of the nuclear structure, especially for nuclei with clusters, such as the α-cluster nuclei and halo nuclei.

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MA Wei-Hu, WANG Jian-Song, WANG Qi, YANG Lei, YANG Yan-Yun and HUANG Mei-Rong. Fractal geometrical properties of nuclei[J]. Chinese Physics C, 2015, 39(10): 104101. doi: 10.1088/1674-1137/39/10/104101

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Received: 2015-02-13
Revised: 1900-01-01

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Fractal geometrical properties of nuclei

Corresponding author: MA Wei-Hu,

Received Date: 2015-02-13

Accepted Date: 1900-01-01

Available Online: 2015-10-10

Abstract: We present a new idea to understand the structure of nuclei and compare it 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 irregular nuclear structure properties and the self-similarity characteristic are considered to be an intrinsic aspect of the nuclear structure properties. For the description of nuclear geometric properties, the 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-Weizsäcker binding energy formula is modified using the fractal geometric theory. One important equation set with two equations is obtained, which is related to the concept that the fractal dimension should be a dynamic parameter in the process of nuclear synthesis. The fractal dimensions of the light nuclei are calculated and their physical meanings are discussed. We compare 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 additional feature compared to the liquid drop model, since the present model can reflect the geometric information of the nuclear structure, especially for nuclei with clusters, such as the α-cluster nuclei and halo nuclei.

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