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Nghiên cứu thực nghiệm cấu trúc phổ năng lượng kích thích của các hạt nhân 172Yb và 153Sm trên kênh nơtron của lò phản ứng hạt nhân Đà Lạt (Luận án tiến sĩ)

MINISTRY OF EDUCATION AND
TRAINING

MINISTRY OF SCIENCE AND
TECHNOLOGY

Vietnam Atomic Energy Institute
———————

NGUYỄN NGỌC ANH

EXPERIMENTAL STUDY ON LEVEL STRUCTURE
OF EXCITED 172 Yb AND 153 Sm NUCLEI USING
NEUTRON BEAM FROM DALAT NUCLEAR
RESEARCH REACTOR

DOCTORAL DISSERTATION IN PHYSICS

HÀ NỘI - 2018



MINISTRY OF EDUCATION AND
TRAINING

MINISTRY OF SCIENCE AND
TECHNOLOGY

Vietnam Atomic Energy Institute
———————

NGUYỄN NGỌC ANH

EXPERIMENTAL STUDY ON LEVEL STRUCTURE OF
EXCITED 172 Yb AND 153 Sm NUCLEI USING NEUTRON
BEAM FROM DALAT NUCLEAR RESEARCH REACTOR

DOCTORAL DISSERTATION IN PHYSICS
Subject: Atomic and Nuclear Physics
Code: 9 44 01 06

Supervisors:
1. Dr. Nguyễn Xuân Hải
2. Assoc. Prof. Dr. Phạm Đình Khang

HÀ NỘI - 2018


iii

Declaration of Authorship
I declare that this thesis titled, “Experimental study on level structure of excited
172

Yb and 153 Sm nuclei using neutron beam from Dalat nuclear research reactor”

and the work presented in it are my own under the guidance of my supervisors,
and have not been published by anyone else in any other works or articles. A
part of the results has been published in a peer-review journal and proceeding
of 23rd International Seminar on Interaction of Neutrons with Nuclei held in
Dubna, Russia written in co-authorship with my supervisors and collaborators.
The other part is in preliminary, and we expect to collect more experimental data


before publishing.


v

Acknowledgements
I would like to express my deep gratitude to my supervisors, Dr. Nguyễn Xuân
Hải and Assoc. Prof. Dr. Phạm Đình Khang for their guidance, support and
encouragement during my research work. They provided me not only the motivation and the important knowledge, but also the financial support for my life
from 2013 to 2015 in Đà Lạt.
I would like to thank Dr. A. M. Sukhovoj for his great guidance. He taught me
how to become an honest and effective analyst.
I would like also to thank Assoc. Prof. Dr. Nguyễn Quang Hưng for his interesting conversations and his important suggestions for my research since 2016.
I thank Assoc. Prof. Dr. Nguyễn Mậu Chung, my graduate supervisor for the
valuable fundamental knowledge that he gave me during my graduate studies.
I am grateful to Dalat Nuclear Research Institute and Nuclear Training Center,
Vietnam Atomic Energy Institute for their significant supports to my research.
I also thank my colleagues at Center for Nuclear Physics and Nuclear Electronics,
Training and Education Center, and Reactor Center for their kind help during my
experiment.
I am thankful to Ms. Nguyễn Thúy Hằng and Ms. Nguyễn Thị Diệu Huyền for
their kind assistant during my PhD study.
I also wish to thank Lâm’s photocopy shop, 27 Nguyễn Công Trứ, Đà Lạt, for
financial support to print my dissertation.
Finally, I am deeply indebted to my family for their continuous encouragement
and constant confidence in me.


vii

Contents
Declaration of Authorship

iii

Acknowledgements

v

List of Figures

xi

List of Tables

xv

List of Abbreviations

xvii

Introduction
1

1

Theory

11

1.1

Compound nuclear reaction . . . . . . . . . . . . . . . . . . . . . . .

11

1.1.1

Bohr-independence hypothesis . . . . . . . . . . . . . . . . .

11

1.1.2

Reciprocity theorem . . . . . . . . . . . . . . . . . . . . . . .

13

1.2

Nuclear level scheme . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

1.3

Nuclear level density . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

1.3.1

Fermi-gas model . . . . . . . . . . . . . . . . . . . . . . . . .

18

1.3.1.1

Systematics of the Fermi-gas parameters . . . . . .

21

1.3.1.2

Parity ratio . . . . . . . . . . . . . . . . . . . . . . .

24

1.3.2

Constant temperature model . . . . . . . . . . . . . . . . . .

25

1.3.3

Gilbert-Cameron model . . . . . . . . . . . . . . . . . . . . .

26

1.3.4

Generalized superfluid model . . . . . . . . . . . . . . . . .

27

1.3.5

Microscopic-based models . . . . . . . . . . . . . . . . . . . .

29

1.4

Radiative strength function . . . . . . . . . . . . . . . . . . . . . . .

33

1.5

Conclusion of chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . .

37


viii
2

Experiment and data analysis

39

2.1

39

Experimental facility and experimental method . . . . . . . . . . . .
2.1.1

2.2

2.3
3

Dalat Nuclear Research Reactor and the neutron beam-port
No.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

2.1.2

The γ − γ coincidence method . . . . . . . . . . . . . . . . .

41

2.1.3

γ − γ coincidence spectrometer . . . . . . . . . . . . . . . . .

44

2.1.3.1

Electronic setup and operation principle . . . . . .

44

2.1.3.2

Main properties . . . . . . . . . . . . . . . . . . . .

46

2.1.4

Experimental setup and target information . . . . . . . . . .

49

2.1.5

Sources of “systematic” errors in γ − γ coincidence method

51

Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

2.2.1

Pre-analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

2.2.2

Two-step cascade spectra . . . . . . . . . . . . . . . . . . . .

61

2.2.3

Determination of gamma cascade intensity . . . . . . . . . .

65

2.2.4

Construction of nuclear level scheme . . . . . . . . . . . . .

66

2.2.5

Determination of gamma cascade intensity distributions . .

67

2.2.6

Extraction of nuclear level density and radiative strength
function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

2.2.6.1

Basic ideas and underlying assumption . . . . . . .

69

2.2.6.2

Determination of the functional form of the γ-rays
transmission coefficient . . . . . . . . . . . . . . . .

72

2.2.6.3

Determination of nuclear level density . . . . . . .

76

2.2.6.4

Determination of radiative strength function

. . .

78

Conclusion of chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . .

79

Results and discussion
3.1

Nuclear level scheme of 172 Yb and 153 Sm

81
. . . . . . . . . . . . . . .

81

3.1.1

172

Yb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

3.1.2

153

Sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

3.2

Gamma cascade intensity distributions of 172 Yb . . . . . . . . . . . .

97

3.3

Nuclear level density and radiative strength function of 172 Yb . . . 105


ix

3.4

3.3.1

Comparison with other experimental data . . . . . . . . . . 108

3.3.2

Comparison with theoretical models . . . . . . . . . . . . . . 111
3.3.2.1

Nuclear level density . . . . . . . . . . . . . . . . . 111

3.3.2.2

Radiative strength function . . . . . . . . . . . . . . 111

Conclusion of chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . 114

Summary and outlook

115

List of publications

117

References

118


xi

List of Figures
1.1

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16

β − -decay with
from 60
Nuclear level scheme of 60
27 Co33
28 Ni32
T1/2 =1925.8 days extracted from ENSDF library. . . . . . . . . . . . .
The horizontal cross-section view of the DNRR. . . . . . . . . . . .
The detail structure of the neutron beam-port No. 3. . . . . . . . .
Two-step gamma cascades corresponding to the decays from a
compound state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The γ − γ coincidence electronics. . . . . . . . . . . . . . . . . . . . .
The TAC amplitude spectrum measured with 60 Co. . . . . . . . . .
The channel-energy relationship of the two detectors. Data of the
detector B has an offset of 1000 on y-axis. . . . . . . . . . . . . . . .
The energy resolution of the two detectors in the energy range from
0.5 MeV to 8 MeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The relative efficiencies of the two detectors. . . . . . . . . . . . . .
Experimental setup for measuring the γ − γ coincidences. . . . . .
Experimental system at the neutron beam-port No. 3 of the DNRR.
An illustration for a three-step cascade. . . . . . . . . . . . . . . . .
Illustration of the cross talk effect. BS: Compton backscattered photon; Ann: annihilation photon. . . . . . . . . . . . . . . . . . . . . .
Data analysis procedure. . . . . . . . . . . . . . . . . . . . . . . . . .
The discrepancy between two datasets. Dataset A is collected from
detector A and dataset B is collected from detector B. . . . . . . . .
Dataset B is corrected according to dataset A. . . . . . . . . . . . . .
Summation spectrum for 171 Yb(n,2γ) reaction. E1 +E2 is sum of energies measured from two detectors. Energies (in keV) of the final
levels in the cascades are pointed near the peaks of the full absorption energy. The notations SE and DE correspond to the single- and
double-escape peaks, respectively. . . . . . . . . . . . . . . . . . . .

15
40
40
42
45
47
48
48
49
50
51
52
54
57
58
59

60


xii
2.17 Summation spectrum for 152 Sm(n,2γ) reaction. E1 + E2 is sum of
energies measured from two detectors. Energies (in keV) of the
final levels in the cascades are pointed near the peaks of the full
absorption energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.18 Explanation of the input variables used in the procedure of obtaining the TSC spectra given in Fig. 2.19. . . . . . . . . . . . . . . . . .
2.19 Detail procedure for obtaining the TSC spectra. . . . . . . . . . . . .
2.20 a. experimental TSC spectrum; b. simulated TSC spectrum, c. unresolved TSC spectrum with noise line, d. unresolved TSC spectrum without noise line corresponding to the decays from the compound state to the ground state of 172 Yb. . . . . . . . . . . . . . . . .
2.21 Procedure of extracting the NLD and RSF. . . . . . . . . . . . . . . .
2.22 Illustration of the shifting procedure for 172 Yb nucleus with Em =
3.625 MeV, Em = 3.875 MeV and Efmax = 1.198 MeV. The superposed energy range is between the two vertical arrows. The
curve (1) simulates the standard dataset (circle), while the curve
(2) models the to-be-shifted dataset (triangle). The k factor is the
ratio between the area under the curve (1) and that under the
curve (2). The two curves have the form of an exponential function C0 exp(C1 E), whose parameters (C0 , C1 ) are obtained via the
fitting to the corresponding datasets. . . . . . . . . . . . . . . . . .
2.23 The final dataset describes the functional form of γ-rays transmission coefficient of 172 Yb nucleus in the energy region from 0.5 to
7.5 MeV. The line is the average values over an 250 keV energy
interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.24 Comparison of the γ-rays transmission coefficients of 172 Yb nucleus obtained by different starting excitation-energy bins. Histogram with black color is the average of the γ-rays transmission
coefficients obtained by all the starting excitation-energy bins from
2.125 MeV to 5.375 MeV. The corresponding uncertainties are given
by upper and lower lines. . . . . . . . . . . . . . . . . . . . . . . . .
3.1
3.2

TSC spectrum corresponding to the ground state of 172 Yb. . . . . .
TSC spectrum corresponding to the final level with the energy Ef =
78.8 keV of 172 Yb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60
62
64

68
71

73

75

76
88
89


xiii
3.3

3.4
3.5
3.6
3.7
3.8
3.9

3.10

3.11

3.12
3.13

Experimental level scheme of 172 Yb obtained within the gamma
cascades from compound state to six distinct low-lying discrete
levels with spin from 0¯
h to 2¯h. Explanation of the figure is given in
text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
TSC spectrum corresponding to the final levels with energies Ef =
0 and 7.8 keV of 153 Sm. . . . . . . . . . . . . . . . . . . . . . . . . . .
TSC spectrum corresponding to the final level with the energy Ef
= 35.8 keV of 153 Sm. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NLS of 153 Sm obtained within this present work. Explanation of
the figure is the same as in Fig. 3.3. . . . . . . . . . . . . . . . . . . .
The gamma cascade intensity distributions of 172 Yb obtained
within the present work. . . . . . . . . . . . . . . . . . . . . . . . .
The extracted NLD and RSF of 172 Yb obtained within the present
work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between the experimental gamma cascade intensity
distributions and the calculated one obtained from the extracted
NLD and RSF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between the NLD obtained within the present work
and the other experimental data. Explanation for this figure is
given in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between the RSF obtained within the present work
and the other experimental data. Explanation of this figure is given
in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between the NLD obtained within the present work
and a few common theoretical models. . . . . . . . . . . . . . . . . .
Comparison between RSF obtained within this work and few theoretical models. See explanation of the figure in text. . . . . . . . .

91
95
95
96
98
106

107

109

110
112
113


xv

List of Tables
2.1
2.2

Selected parameters of the electric modules. . . . . . . . . . . . . . .
Parameters of the relative efficiency functions. . . . . . . . . . . . .

3.1

Primary and secondary gamma-ray energies and absolute intensities obtained from the 171 Yb(nth , γ) reaction. The experimental
values are compared with the ENSDF data. . . . . . . . . . . . . . .
Primary and secondary gamma-ray energies and absolute intensities obtained from the 152 Sm(nth , γ) reaction. The experimental
values are compared with the ENSDF data. . . . . . . . . . . . . . .
The gamma cascade intensity distribution of 172 Yb and the contribution of the resolved cascades. . . . . . . . . . . . . . . . . . . . . .

3.2

3.3

46
49

81

93
99


xvii

List of Abbreviations
NLS
NLD
RSF
CTM
BSFG
GSM
ENSDF
HFBCS
DNRI
DNRR
KMF
TSC

Nuclear Level Scheme
Nuclear Level Density
Radiative Strength Function
Constant Temperature Model
Back-Shifted Fermi Gas
Generalized Superfluid Model
Evaluated Nuclear Structure Data File
Hartree-Fork plus Bardeen-Cooper-Schrieffer
Dalat Nuclear Research Institute
Dalat Nuclear Research Reactor
Kadmenskij Markushev Furman model
Two- Step Cascade


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