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Introduction Level structure of atomic nuclei, including nuclear level scheme (NLS), nuclear level density (NLD), and radiative strength function (RSF), are all together important quantities, which carry fundamental information on the structure and properties of excited nuclei. For NLS, its completeness plays important roles for the study of not only nuclear reaction and statistical model calculations but also adjustment of the nuclear level density parameters. Ideally, the completeness of NLS can be obtained by studying the spectroscopic data from non-selective reactions. However, in practice, it is almost impossible due to experimental conditions and the complex of gamma spectrum [1]. Therefore, the only way to obtain a complete NLS is to study through various experiments and combine their results together. Most of the NLS data were compiled in the ENSDF library [2] containing about 187,067 datasets for 3,312 atomic nuclei collected from various experiments including beta decay, electron capture, neutron inelastic scattering, compound nuclear reactions induced by ions such as ( 3 He, He’ ), ( , ’), (p, d), (d, t), etc. However, information on the excited states and their corresponding primary and/or secondary transitions of many nuclei in the intermediate energy region, where the thermal neutron capture (n th 3 , ) reaction was mostly employed to extract the data, is still sparse and incomplete. Regarding the NLD and RSF, although they are important quantities for the study in many fields such as low-energy nuclear reactions, astrophysical nucleonsynthesis, nuclear energy production, transmutation of nuclear waste, nuclear reactor design, there is still lacking a lot of experimental data in the literature, in both
vii Contents Declaration of Authorship iii Acknowledgements v List of Figures xi List of Tables xv List of Abbreviations xvii Introduction 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 37 viii Experiment and data analysis 39 2.1 39 Experimental facility and experimental method 2.1.1 2.2 2.3 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 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 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 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 MeV The relative efficiencies of the two detectors Experimental setup for measuring the γ − γ coincidences Experimental system at the neutron beam-port No 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 = 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 Introduction Level structure of atomic nuclei, including nuclear level scheme (NLS), nuclear level density (NLD), and radiative strength function (RSF), are all together important quantities, which carry fundamental information on the structure and properties of excited nuclei For NLS, its completeness plays important roles for the study of not only nuclear reaction and statistical model calculations but also adjustment of the nuclear level density parameters Ideally, the completeness of NLS can be obtained by studying the spectroscopic data from non-selective reactions However, in practice, it is almost impossible due to experimental conditions and the complex of gamma spectrum [1] Therefore, the only way to obtain a complete NLS is to study through various experiments and combine their results together Most of the NLS data were compiled in the ENSDF library [2] containing about 187,067 datasets for 3,312 atomic nuclei collected from various experiments including beta decay, electron capture, neutron inelastic scattering, compound nuclear reactions induced by ions such as (3 He, He’γ), (α, α’), (p, d), (d, t), etc However, information on the excited states and their corresponding primary and/or secondary transitions of many nuclei in the intermediate energy region, where the thermal neutron capture (nth ,γ) reaction was mostly employed to extract the data, is still sparse and incomplete Regarding the NLD and RSF, although they are important quantities for the study in many fields such as low-energy nuclear reactions, astrophysical nucleonsynthesis, nuclear energy production, transmutation of nuclear waste, nuclear reactor design, there is still lacking a lot of experimental data in the literature, in both low- and high-energy regions It has been well-known that the γ − γ coincidence method [3] can be used to study the NLS, NLD and RSF Within this method, the cascade events, which are obtained from the decay of the initial compound state to the different final states, are separated into different Two-Step-Cascade (TSC) spectra Particularly, only correlated gamma transitions are detected, therefore the number of γ-rays contributed to the TSC spectra is less than that presented in a normal prompt gamma spectrum, leading to the significant reduction of the overlapping γ-rays as well as improving the detecting ability of this method In addition, different from the normal gamma spectra, the TSC spectra obtained using the γ − γ coincidence method, after applying the background subtraction algorithm, have almost no Compton background Therefore, the detection limit of the coincidence method is much improved in comparison with the normal gamma spectra analysis method Beside that, the state from which a secondary gamma transition is decayed can be determined in the coincidence method if one of the two γ-rays in the cascade is a known primary transition Based on these above advantages, the γ − γ coincidence method is appropriate for the determination of excited states with low spin in the energy region from 0.5 MeV to Bn − 0.5 MeV (Here, Bn is the neutron binding energy) Furthermore, the γ − γ coincidence method can also be used to determine the gamma cascade intensity distributions, which are related to the NLD and RSF [see e.g Eq (2.1)] Therefore, it is possible to determine the experimental NLD and RSF based on this method Nuclear level scheme of 172Yb and 153Sm 172 Yb and 153 Sm are two deformed and rare earth nuclei Their NLS are absolutely necessary for either confirming or enhancing the predictive powers of the nuclear models for heavy nuclei The adopted nuclear levels and gamma transitions of 172 Yb and 153 Sm are given in Ref [4] and Ref [5], respectively A summary of important investigations on the NLS of these two nuclei is presented as follows For 172 Yb NLS of 172 Yb has been thoroughly studied in different methods such as beta decay of 172 Tm [6], electron capture decay of low-lying states in 172,174 172 Lu [7], neutron inelastic scattering for Yb [8], (n, n’γ) reactions using fast neutrons from reac- tors [9], 170 Er(α,2n)172 Yb reaction for high-spin states [10], 171 Yb(n,γ) reaction for low-spin states [11, 12] Additional methods, which are also able to provide the level scheme of 172 Yb based on the compound nuclear reactions induced by light ions, include [16], 173 172 Yb(3 He,3 He’γ) [13], (d,t) [17], 173 172 Yb(α,α’) [14], Yb(3 He,γ), (3 He,αγ) [17, 18], 170 173 Yb(p,d) [15], 171 Yb(d,p) Yb(t,p) [19], and elastic and inelastic proton scatterings [20, 21] Furthermore, lifetimes of a number of levels have been also determined via the 172 Yb(γ, γ’) reactions using the nuclear reso- nance fluorescence [22] and Coulomb excitation [23, 24] methods Through these experiments, the low-lying discrete level scheme of 172 Yb in the low-energy re- gion (E < 2.4 MeV) has been well understood [4] In this low-energy region, energies of the levels were determined with the accuracy of ten to hundred eV, whereas spins and parities were also identified for a majority of levels However, information on the excited states and their corresponding primary transitions in the intermediate energy region (2.4 MeV < E < MeV), where the thermal neutron capture reactions (nth ,γ) were mostly employed to extract the data, is sparse and incomplete In particular, based on the neutron capture reaction with both thermal and 117 List of publications Nguyen Ngoc Anh, Nguyen Xuan Hai, Pham Dinh Khang, Nguyen Quang Hung, Ho Huu Thang, Updated level scheme of 172 Yb from 171 Yb(nth ,γ) reaction studied via gamma–gamma coincidence spectrometer, Nucl Phys A 964 (2017) 55–68 Nguyen Ngoc Anh, Nguyen Xuan Hai, Pham Dinh Khang, Ho Huu Thang, A.M Sukhovoj, L.V Mitsyna, Parameters of cascade gamma decay of 153 Sm compound-states, in proceeding of 23rd International Seminar on Interaction of Neutrons with Nuclei, Dubna, 2015, pp 241–250 Nguyen Ngoc Anh, Nguyen Xuan Hai, Pham Dinh Khang, Ho Huu Thang, First results in the study of level scheme for 172 Yb based on gamma-gamma coincidence spectrometer, Nucl Sci Technol (2016), VINATOM, 6, 26–31 N.A Nguyen, X H Nguyen D K Pham, D C Vu, A M Sukhovoj, L V Mitsyna, Thresholds for the Break of Nucleon Cooper Pairs and Special Features of the Decay of the 172Yb Nucleus in the Reaction 171 Yb(nth ,2γ), to be published on Physics of Atomic Nuclei 119 References [1] T Belgya, O Bersillon, R Capote, T Fukahori, G Zhigang, S Goriely, M Herman, A V 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