We present an integral density method for calculating the multifractal dimension spectrum for nucleon distribution in atomic nuclei. This method is then applied to analyze the non-uniformity of density distribution in several typical types of nuclear matter distributions, including the Woods–Saxon distribution, halo structure, and tetrahedral α clustering. The subsequent discussion provides a comprehensive and detailed exploration of the results obtained. The multifractal dimension spectrum shows a remarkable sensitivity to the density distribution, establishing it as a simple and novel tool for studying the distribution of nucleons in nuclear multibody systems.

1.
M.
Hongo
and
D. T.
Son
,
Phys. Rev. Lett.
128
,
212501
(
2022
).
2.
Y.
Ayyad
,
W.
Mittig
,
T.
Tang
et al.,
Phys. Rev. Lett.
129
,
012501
(
2022
).
3.
Z. H.
Yang
,
Y.
Kubota
,
A.
Corsi
et al.,
Phys. Rev. Lett.
126
,
082501
(
2022
).
4.
Y.
Yamaguchi
,
W.
Horiuchi
,
T.
Ichikawa
, and
N.
Itagaki
,
Phys. Rev. C
108
,
L011304
(
2023
).
5.
B.
Mukeru
,
M. B.
Mahatikele
, and
G. J.
Rampho
,
Phys. Rev. C
108
,
064313
(
2023
).
6.
W.-M.
Guo
,
B.-A.
Li
, and
G.-C.
Yong
,
Phys. Rev. C
107
,
064313
(
2023
).
7.
Y. H.
Yang
,
Y. G.
Ma
,
S. M.
Wang
,
B.
Zhou
, and
D. Q.
Fang
,
Phys. Rev. C
108
,
044307
(
2023
).
8.
L.
Zhou
,
S. M.
Wang
,
D. Q.
Fang
, and
Y. G.
Ma
,
Nucl. Sci. Tech.
33
,
105
(
2022
).
9.
S. M.
Wang
and
W.
Nazarewicz
,
Phys. Rev. Lett.
120
,
212502
(
2018
).
10.
C.
Geng
,
Z.-X.
Yang
,
X.-H.
Zeng
, and
Z.-Q.
Feng
,
Nucl. Sci. Tech.
34
,
160
(
2023
).
11.
E.-B.
Huo
,
K.-R.
Li
,
X.-Y.
Qu
,
Y.
Zhang
, and
T.-T.
Sun
,
Nucl. Sci. Tech.
34
,
105
(
2023
).
12.
T. B.
Webb
,
S. M.
Wang
,
K. W.
Brown
et al.,
Phys. Rev. Lett.
122
,
122501
(
2019
).
13.
K. J.
Cook
,
E. C.
Simpson
,
L. T.
Bezzina
,
M.
Dasgupta
,
D. J.
Hinde
, and
K.
Banerjee
,
Phys. Rev. Lett.
122
,
102501
(
2019
).
14.
Y. Y.
Cao
,
J. Y.
Guo
, and
B.
Zhou
,
Nucl. Sci. Tech.
34
,
152
(
2023
).
16.
I.
Tanihata
et al.,
Phys. Rev. Lett.
55
,
2676
(
1985
).
17.
S.
Xu
,
S.
Zhang
,
X.
Jiang
, and
S.
Michael Scott
,
Nucl. Sci. Tech.
34
,
5
(
2023
).
18.
S.
Bagchi
et al.,
Phys. Rev. Lett.
124
,
222504
(
2020
).
19.
20.
S.
Zhang
,
Y. F.
Geng
, and
F. R.
Xu
,
Nucl. Tech.
46
,
080012
(
2023
).
21.
Y.-G.
Ma
and
S.
Zhang
, “Influence of nuclear structure in relativistic heavy-ion collisions,” in Handbook of Nuclear Physics (Springer, Singapore, 2022).
22.
D.-Q.
Fang
,
H.
Hua
,
Y.-G.
Ma
, and
S.-M.
Wang
,
Nucl. Phys. News
33
(
2
),
11
16
(
2023
).
23.
J.
Chen
,
X.
Dong
,
Y.-G.
Ma
, and
Z.
Xu
,
Sci. Bull.
68
,
3252
3260
(
2023
).
24.
C.-W.
Ma
,
Y.-P.
Liu
,
H.-L.
Wei
,
J.
Pu
,
K.-X.
Cheng
, and
Y.-T.
Wang
,
Nucl. Sci. Tech.
33
,
6
(
2022
).
25.
H.-L.
Wei
,
X.
Zhu
, and
C.
Yuan
,
Nucl. Sci. Tech.
33
,
111
(
2022
).
26.
W.
von Oertzen
,
M.
Freer
, and
Y.
Kanada-En’yo
,
Phys. Rep.
432
,
43
(
2006
) and references therein.
27.
W. H.
Ma
,
D.
Patel
,
Y. Y.
Yang
et al.,
Phys. Rev. C
103
,
L061302
(
2021
).
28.
H.
Horiuchi
,
J. Phys. Conf. Ser.
111
,
012054
(
2008
).
29.
W. B.
He
,
Y. G.
Ma
,
X. G.
Cao
,
X. Z.
Cai
, and
G. Q.
Zhang
,
Phys. Rev. Lett.
113
,
032506
(
2014
).
30.
B.
Zhou
,
Y.
Funaki
,
H.
Horiuchi
,
Y.-G.
Ma
,
G.
Röpke
,
P.
Schuck
,
A.
Tohsaki
, and
T.
Yamada
,
Nat. Commun.
14
,
8206
(
2023
).
32.
W.-H.
Ma
,
J.-S.
Wang
,
Q.
Wang
,
S.
Mukherjee
,
L.
Yang
,
Y.-Y.
Yang
, and
M.-R.
Huang
,
Chin. Phys. C
39
,
104101
(
2015
).
33.
A.
Ozawa
, “Matter radii and density distributions,” in
Handbook of Nuclear Physics
, edited by I. Tanihata, H. Toki, and T. Kajino (Springer, Singapore, 2022).
34.
M. Q.
Ding
,
D. Q.
Fang
, and
Y. G.
Ma
, “Neutron skin thickness and its effects in heavy-ion collisions,”
Nucl. Sci. Tech.
arXiv:2409.07059 (to be published) (2024).
36.
K.
Falconer
and
F.
Geometry
,
Mathematical Foundations and Application
, 2nd ed. (
John Wiley and Sons, Ltd
,
2003
).
37.
A.
Chhabra
and
R.
Jensen
,
Phys. Rev. Lett.
62
,
1327
1330
(
1989
).
38.
H. G. E.
Hentschel
and
I.
Procaccia
,
Physica
8
,
435
(
1983
).
39.
K.
Rafsanjani Amin
,
R.
Nagarajan
,
R.
Pandit
, and
A.
Bid
,
Phys. Rev. Lett.
129
,
186802
(
2022
).
40.
K.
Rafsanjani Amin
,
S.
Sankar Ray
,
N.
Pal
,
R.
Pandit
, and
A.
Bid
,
Commun. Phys.
1
,
1
(
2018
).
41.
A.
Rodriguez
,
L. J.
Vasquez
, and
R. A.
Römer
,
Phys. Rev. Lett.
102
,
106406
(2009).
42.
S.
Tan
and
R.
Ni
,
Phys. Rev. Lett.
128
,
114502
(2022).
43.
D.
Gella
,
I.
Zuriguel
, and
J.
Ortin
,
Phys. Rev. Lett.
123
,
218004
(
2019
).
44.
P.
Perlekar
,
R.
Benzi
,
D. R.
Nelson
, and
F.
Toschi
,
Phys. Rev. Lett.
105
,
144501
(
2010
).
45.
N.
Ahmad
,
T.
Ahmada
, and
O.
Singh
,
Eur. Phys. J. Plus
137
,
653
(
2022
).
46.
L.
Zhao
,
W.
Li
,
C.
Yang
,
J.
Han
,
Z.
Su
, and
Y.
Zou
,
PLoS One
12
(1),
e0170467
(
2017
).
47.
Y. G.
Ma
,
Eur. Phys. J. A
30
,
227
242
(
2006
).
48.
M. I.
Abdulhamid
et al.
(The STAR Collaboration)
,
Phys. Lett. B
845
,
138165
(
2023
).
49.
G.
Brandi
and
T.
Di Matteo
,
Int. Rev. Fin. Analysis
84
,
102324
(
2022
).
50.
Y.-W.
Zhou
,
J.-L.
Liu
,
Z.-G.
Yu
,
Z.-Q.
Zhao
, and
V.
Anh
,
Physica A
416
,
21
32
(
2014
).
51.
M.
Wqtorek
et al.,
Biomed. Signal Process. Control.
91
,
105916
(
2024
).
53.
B. I.
Henry
,
P. R.
Hof
,
P.
Rothnie
, and
S. L.
Wearne
,
Emergent Nature: Patterns, Growth and Scaling in the Sciences
(
World Scientific
,
2002
), pp.
65
75
.
54.
T.
Vicsek
,
F.
Family
, and
P.
Meakin
,
Europhys. Lett.
12
,
217
222
(
1990
).
55.
C.-H.
Lam
,
Phys. Rev. E
52
,
2841
2847
(
1995
).
56.
F.
Jestczemski
and
M.
Sernetz
,
Physica A
223
,
275
282
(
1996
).
57.
T.
Tél
,
Á.
Fülöp
, and
T.
Vicsek
,
Physica A
159
,
155
166
(
1989
).
58.
L. C.
Chamon
,
B. V.
Carlson
,
L. R.
Gasques
et al.,
Phys. Rev. C
66
,
014610
(
2002
).
59.
T.
Moriguchi
,
A.
Ozawa
,
S.
Ishimoto
et al.,
Phys. Rev. C
88
,
024610
(
2013
).
60.
J.
Dudek
,
A.
Gozdz
,
N.
Schunck
, and
M.
Miskiewicz
,
Phys. Rev. Lett.
88
,
252502
(
2002
).
61.
R.
Bijker
and
F.
Iachello
,
Phys. Rev. Lett.
112
,
152501
(
2014
).
62.
Y.-A.
Li
,
S.
Zhang
, and
Y.-G.
Ma
,
Phys. Rev. C
102
,
054907
(
2020
).
63.
C.
Ding
,
L.-G.
Pang
,
S.
Zhang
, and
Y.-G.
Ma
,
Chin. Phys. C
47
,
024105
(
2023
).
64.
Y.-G.
Ma
and
S.
Zhang
,
Sci. Sin.-Phys. Mech. Astron.
54
,
292004
(
2024
).
65.
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