Study Of the characteristics of photonuclear Reaction On 141Pr Induced by 50,60,70 MeV Bremsstrahlung

The experiment of the work reported in this thesis was performed using the 100 MeV electron linac of the Pohang Accelerator Laboratory,POSTECH, Korea.The results were obtained at the Institude of physics, VAST, Hanoi under the guidance of the Assoc.Prof.Pham Duc khue.

- 

-Nguyen Thanh Luan

STUDY OF THE CHARACTERISTICS OF

BY 50-, 60-, 70- MeV BREMSSTRAHLUNG

Submitted in partial fulfillment of the requirements for the degree

of Bachelor of Science in Nuclear Technology

(Advanced Program)

- 

-Nguyen Thanh Luan

STUDY OF THE CHARACTERISTICS OF

BY 50-, 60-, 70- MeV BREMSSTRAHLUNG

Submitted in partial fulfillment of the requirements for the degree

of Bachelor of Science in Nuclear Technology

(Advanced Program)

Supervisor: Assoc Prof Pham Duc Khue

- 

-Nguyễn Thành Luân

NGHIÊN CỨU MỘT SỐ ĐẶC TRƯNG CỦA PHẢN

BỞI CHÙM BỨC XẠ HÃM NĂNG LƯỢNG

và bộ môn Công nghệ hạt nhân nói riêng vì đã dạy dỗ, hướng dẫn và tạo điều kiện tốt nhất cho em trong suốt 4 năm học đại học

Em xin được bày tỏ lòng biết ơn chân thành đến thầy giáo hướng dẫn PGS

TS Phạm Đức Khuê đã tận tình chỉ bảo, giúp đỡ em trong suốt quá trình em học tập, thực tập nghiên cứu và hoàn thành bản khóa luận này Em cũng xin cảm ơn các thầy, các cán bộ của Trung tâm Vật lý hạt nhân, Viện Vật lý đã giúp đỡ và tạo điều kiện cho em trong thời gian thực hiện khóa luận

Em xin được gửi lời cảm ơn đến đề tài nghiên cứu NAFOSTED mã số 103.04- 2015.73, chủ nhiệm là thầy GS.TS Nguyễn Văn Đỗ, đã cung cấp các số liệu thực nghiệm ban đầu để em phân tích số liệu cho bản khóa luận

Cuối cùng, sự động viên, cổ vũ của bạn bè và gia đình là sự giúp đỡ rất lớn

về mặt tinh thần trong suốt quá trình làm khóa luận với em Em muốn gửi lời cảm ơn chân thành đến họ

Sinh viên Nguyễn Thành Luân

TÓM TẮT NỘI DUNG KHÓA LUẬN 1

INTRODUCTION 2

CHAPTER 1: PHOTONUCLEAR REACTIONS 4

1.1 Photonuclear reactions 4

1.2 Nuclear isomer and isomeric ratio 12

1.3 TALYS code 13

1.4 Bremsstrahlung 16

CHAPTER 2: METHODOLOGY AND EXPERIMENT 18

2.1 Methodology 18

2.1.1.Determination of photoreaction yield and isomeric yield ratio 18

2.1.2 Determination of the correction factors 26

2.1.3 Calculation of reaction yield and isomeric yield ratio using TALYS code 27

2.2 Experiment 28

2.2.1 The Bremsstrahlung source 28

2.2.2 The sample irradiation 30

2.2.3 The gamma-ray spectroscopy system 32

2.2.4 The gamma spectrum analysis 36

CHAPTER 3: RESULTS AND DISSCUSSIONS 43

3.1 Isomeric yield ratio of 137mgCe 43

3.2 The 141Pr(γ,xn) 141-xPr reaction 46

CONCLUSIONS 51

REFERENCES 52

TÓM T ẮT NỘI DUNG KHÓA LUẬN

Khóa luận với đề tài “Nghiên cứu một số đặc trưng của các phản ứng quang hạt nhân trên bia 141Pr gây bởi chùm bức xạ hãm 50-, 60-, 70- MeV” trình bày kết quả thí nghiệm nghiên cứu phản ứng quang hạt nhân trên bia Praseodymium (Pr) gây bởi chùm photon hãm năng lượng cao trên máy gia tốc electron tuyến tính 100 MeV tại Trung tâm gia tốc Pohang (PAL), Hàn Quốc Khóa luận tập trung vào việc phân tích số liệu thực nghiệm để nhận diện các hạt nhân sản phẩm, xác định suất lượng các phản ứng sinh nhiều nơtron natPr(γ,xn)141-xPr (x là số nơtron phát ra) và tỉ

số suất lượng tạo cặp hạt nhân đồng phân 137m,gCe Phương pháp nghiên cứu dựa trên việc kích hoạt kết hợp với đo phổ gamma Các phép đo phổ được thực hiện nhiều lần với thời gian chiếu khác nhau cũng như thời gian đo khác nhau với khoảng cách phù hợp để có thể ghi nhận được các đồng vị có thời gian sống khác nhau và giảm thiểu sai số thống kê cũng như sai số hình học Phổ gamma được ghi nhận trên hệ phổ kế bán dẫn gecmani siêu tính khiết HPGe có độ phân giải năng lượng cao Việc nhận diện các sản phẩm phản ứng căn cứ vào năng lượng, cường độ của các tia gamma đặc trưng và thời gian bán rã của các đồng vị tạo thành Suất lượng và tỷ số đồng phân được xác định dựa trên số đếm đỉnh phổ gamma Các số liệu hạt nhân được lấy từ các cơ sở dữ liệu hạt nhân quốc tế tin cậy, cập nhật Để tăng độ chính xác của kết quả đo, các hiệu chỉnh sự tự hấp thụ, hiệu ứng trùng phùng tổng, các can nhiễu bức xạ đã được thực hiện Bên cạnh đó, khóa luận còn thực hiện các tính toán suất lượng và tỷ số đồng phân sử dụng chương trình TALYS Kết quả thực nghiệm thu được đối với tỷ số suất lượng đồng phân tương ứng với các chùm bức xạ hãm năng lượng cực đại 50-, 60-, 70-MeV, lần lượt là 0.96 ± 0.17, 1.50 ± 0.23 và 1.75 ± 0.44 Kết quả này tương đối phù hợp với kết quả thu được từ tính TALYS Đối với phản ứng natPr(γ,xn) 141-xPr đã ghi nhận được số nơtron phát ra (x) lên tới 6 và xác định được suất lượng của chúng, đồng thời so sánh suất lượng tương đối với tính TALYS cho thấy có sư phù hợp khá tốt Bên cạnh đó, khóa luận cũng đã xây dựng được hàm giải tích mô tả sự phụ thuộc của suất lượng tương đối vào số neutron phát ra Sai số của kết quả thực nghiệm được đánh giá vào khoảng 15-25% Các kết quả thu được có ý nghĩa trong việc đóng góp các số liệu hạt nhân mới, góp phần làm sáng tỏ hơn cơ chế của các phản ứng quang hạt nhân ở vùng năng lượng cao (E>30 MeV)

The experiment of the work reported in this thesis was performed using the

100 MeV electron linac of the Pohang Accelerator Laboratory, POSTECH, Korea The results were obtained at the Institute of Physics, VAST, Hanoi under the guidance of the Assoc Prof Pham Duc Khue

Due to the lack of information about photonuclear reaction mechanisms with higher incident photon energies of Giant Dipole Resonance, the goal of the experiment is to extend measurements and to study the characteristics of the photonuclear reaction at higher incident photon energies, 𝐸𝐸𝛾𝛾=50-, 60-, 70- MeV on the nature Praseodymium target induced by the Bremsstrahlung

Praseodymium is a rare earth element in lanthanide series It is a soft, silvery, malleable and ductile metal It is valued for its magnetic, electrical, chemical, and optical properties It is too reactive to be found in native form It has many applications in science and technology So far, many authors have studied about the photonuclear reaction on praseodymium, and from 1950s, many studies have been published Nevertheless, most of them involved the photoneutron reaction, in which neutrons are removed Some of them used bremsstrahlung source to study about angular distributions of photoneutron as G.A.Price et al (Phys Rev,1954)[1], or fine structure in the photoneutron spectra as K.G.MCNeill et al (CJP, 1970)[2] or the photoneutron cross-sections for the 141Pr(γ,n) such as T.K.Deague, R.J.J.Stewart (Nucl Phys A,1972)[3] and S.N.Belyaev et al (IZV,1995)[4] Most of these studies are in the Giant Dipole Resonance energy range (E<30 MeV) These show that the measurements with bremsstrahlung are rare and were carried out mainly for simple reactions at low energies, and lack the information about the photonuclear reaction

in which many neutrons are removed and the isomeric ratio of 141Pr(γ,p3n)137m,gCe

From the experimental spectra, after identification and determination of the radioactive nucleus formed via the photonuclear reactions, this thesis particularly interests their reaction yield, and also studies the isomeric yield ratio of

natPr(γ,p3n)137m,gCe; in addition, the results involved natPr(γ,xn)141-xPr reactions with

x from 1 to 6 were also considered The aim of the thesis is to understand the

dependency of reaction yields on both the incident bremsstrahlung energy and the number of neutron removed from the target nuclei To have a broader view, the results obtained from TALYS, a nuclear reaction simulation program, are compared with that of the experiment

This thesis consists of the abstract in Vietnamese, the introduction, three chapters, conclusions and references In Chapter 1, the basic knowledge of photonuclear reaction is introduced The methodology and experiment are presented

in Chapter 2 Finally, the results and discussions are given in Chapter 3

CHAPTER 1: PHOTONUCLEAR REACTIONS 1.1 Photonuclear reactions

A photonuclear reaction is described by:

where b may stand for a large variety of particles depending primarily upon the incident photon energy It was first published in 1934 about photoreaction of deuterium bombarded with gamma rays of 208Tl (E = 2.62 MeV) by Chadwick and Goldhaber, and photoneutron reaction of 7Be by Gentner and Szilard and Chalmers With the rapid development of accelerator, the photonuclear reaction is increasingly researched because the reaction in many elements with higher threshold could be studied The general availability of betatrons with high electron energy output in the beginning of the 1940s led to a large amount of studies The first report about the detection of an individual nuclear energy level was published in 1939 and the first message about isomeric photoexcitation dates back to 1941 In the 1950s, systematic work about photonuclear reactions started In the beginning of the 1960s, exact data were established by the development of linac Besides, the photonuclear reaction theory was also developed Until now, a large number of experimental results in the low energy range have shown the appropriateness versus theory However, in higher energy, the photonuclear reaction mechanism is very different and have discussed by many authors.[5]

In order to measure the probability quantitatively that a given nuclear reaction will take place, we use the concept of cross-section, denoted by 𝜎𝜎 In a fundamental way, cross-section is defined as a constant proportional between the number of emitted particles per unit time and the product of the incident particle’s flux per unit area on target with the number of nucleus in target In nuclear physics, the unit of cross-section is a Barn (b), 1 𝑏𝑏 = 10−24 𝑐𝑐𝑐𝑐 A differential cross-section 𝑑𝑑𝜎𝜎/𝑑𝑑Ω, whose unit is barn/steradian, is also used if the number of emitted particles are considered within an element of solid angle 𝑑𝑑Ω in the direction with polar angles (𝜃𝜃, 𝜑𝜑) with respect to the incident beam For the same entrance channel a number of exit channels will be open corresponding to different reaction products at

a given energy As the exit channels are independent, there will not be any quantum

sum of all non-elastic channel cross-sections is called the reaction or absorption cross-section When the elastic cross-section is also added, it become the total cross-section.[6]

An overview of the tendency of photonuclear cross-section according to the increasing of photon energy [5][7][11]:

A general picture of the total photon absorption cross-section is shown in Fig.1.1 in which the interactions that can occur as a function of increasing photon energy are considered

Fig 1.1 Schematic representation of the total cross-section for the absorption of

photons by nuclei [8]

At the lowest energies, there is only Thomson scattering, an important phenomenon in plasma physics It is the elastic scattering of electromagnetic radiation (photon) by a free charged particle, which is non-relativistic, and is also the electric dipole phenomenon The electric field of the incident wave accelerates the charged particle, causing it to emit radiation at the same frequency as the incident wave Its differential cross-section is given by:

𝑑𝑑𝜎𝜎𝑡𝑡𝑑𝑑Ω = 𝐷𝐷2�

1 + 𝑐𝑐𝑐𝑐𝑐𝑐2𝜃𝜃

where D is the scattering amplitude, 𝐷𝐷 = −𝑍𝑍2𝑒𝑒2/𝐴𝐴𝐴𝐴𝑐𝑐2 The cross-section independent of photon frequency, is the important feature

When energy is slightly higher, the photon can disrupt the internal nuclear coordinates and excite nuclear energy levels, of course the incident photon has to have “appropriate energies” The total absorption cross-section, thus sharply rises to

a narrow resonance peak The excited state can decay probability to all lower states, then finally to the ground state Therefore, the total width, Γ𝑘𝑘, of a state at excitation energy, 𝐸𝐸𝑘𝑘, is the sum of the partial widths associated with its decay to all of states below it and the states at higher excitation become progressively wider and wider From the theory of interaction between electromagnetic radiation and nuclei, the expression for the absorption cross-section of one individual nuclear level, with energy of the incident photons is E, is:

� 𝜎𝜎𝑘𝑘(𝐸𝐸)𝑑𝑑𝐸𝐸 = (𝜋𝜋ƛ𝑘𝑘)22𝐼𝐼𝑘𝑘 + 1

It depends on the properties of all the states between the excited state and the ground state On the other hand, it only depends on the photon energy and the ground state radiation width for a level

Above the particle emission threshold, near 8 or 10 MeV for most nuclei, up

to about 30 MeV, the levels broaden much more rapidly until finally they coalesce completely and a very broad resonance maximum is observed in the total photon absorption cross-section This range is called Giant dipole resonance The giant

characterized by a collective vibrational motion of all protons and neutrons within the nucleus It is a large maximum in the cross-section, 3 to 10 MeV in width, located between 13 and 18 MeV for medium and heavy elements and near 20 MeV for the light ones The giant resonance occurs in all nuclei and may be viewed as a general property of nuclear matter It results primarily from the contribution of electric dipole mode The electric giant dipole resonance is generally interpreted as

a collective motion of all protons against all neutrons The energy dependence of the giant resonance absorption cross-section for the medium and heavy nuclei has often been approximated by a Lorentz-shaped resonance line:

𝜎𝜎𝑘𝑘(𝐸𝐸) = 𝜎𝜎𝑚𝑚 (𝐸𝐸Γ𝑘𝑘)2

(𝐸𝐸𝑘𝑘2− 𝐸𝐸2)2+ (𝐸𝐸Γ𝑘𝑘)2 (1.6) From the theory of the interaction of electromagnetic radiation with nuclei,

an expression for the integrated cross-section of the electric giant dipole absorption

From the Goldhaber-Teller mechanism or that of Steinwedel-Jensen, in Fig 1.2, we can explain the giant dipole resonance and obtain the resonance energy function that depends on the mass number, 𝐴𝐴−1/6 or 𝐴𝐴−1/3 respectively However, with the comparison of the experimental results, this dependence can be described more exactly by the combination of two mechanisms It is:

According to this approximation, the position of the giant dipole resonance on the excitation energy scale varies from 25.5 to 13.5 for the mass number A between 16 and 250 Sometimes, a simpler expression:

𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 78 𝐴𝐴−1/3(𝐴𝐴𝑒𝑒𝑀𝑀) (1.9)

is used for heavy nuclei This picture is much too simple, since the quadrupole oscillations of the nuclear surface can modify this cross-section markedly For light nuclei, the giant resonance is the envelope of a very detailed structure which depends much more on the individual level properties In addition, a fine structure

of the giant dipole resonance was observed, especially for light nuclei, in experiments permitting a high resolution

Fig 1.2 A polarization of nucleus, (a) the Goldhaber-Teller mechanism, (b) the

Steinwedel-Jensen mechanism.[5]

Beyond the giant resonance region (E > 30 MeV), the most important absorption mechanism is through the quasi-deuteron effect or quasi-deuteron disintegration This is also primarily an electric dipole phenomenon that results from the strong two body correlations, a correlated neutron-proton pair bound in a nucleus within framework of this model, in the nuclear ground state The high energy photon, which has low momentum, interacts with a neutron and proton colliding at high velocity and ejects them with the dynamics appropriate to the deuteron photodisintegration Due to the interaction of the high energy photon with only a small number of nucleons, the absorption cross-section is quite low as compared with the giant resonance region The photo-absorption cross-section in a complex nucleus 𝜎𝜎𝑄𝑄𝑄𝑄 is proportional to free deuteron photodisintegration cross-section 𝜎𝜎𝑄𝑄 at the same energy of incident photon It is:

𝜎𝜎𝑄𝑄𝑄𝑄(𝐸𝐸) =𝐿𝐿𝑁𝑁𝑍𝑍𝐴𝐴 𝑒𝑒−𝐷𝐷𝐸𝐸𝜎𝜎𝑄𝑄(𝐸𝐸) (1.10)

where, L is the Levinger factor, NZ/A stands for the number of neutron-proton pairs per unit nuclear volume and the term 𝑒𝑒−𝐷𝐷𝐸𝐸 is a damping factor due to the effect of Pauli blocking on two-particle excitation[9] The validity of this model has been confirmed rather well by several experiments According to the original Levinger formulation, the normalization of the quasi-deuteron wave function inside the nucleus introduces a dependence of the Levinger parameter on the inverse nuclear volume by the expression:

Photon with energies above 140 MeV can produce π-meson, this region is called photomeson The total absorption cross-section rises again beyond the threshold of this process due to photomeson productions

The deexcitation of the nucleus after absorption of a photon

Nuclear reactions induced by electromagnetic radiation can be described, at least for sufficiently low photon energies, in terms of a two-stage process Absorption of a photon leads to an intermediate highly excited state of the nucleus The excitation energy of this, so called compound nucleus, can then be released by emission of photons, neutrons or charged particles.[5]

The excitation energy may be released from the nucleus by elastic scattering (𝛾𝛾, 𝛾𝛾)-reaction, the reemission of a photon with the same energy as the incident photon, or inelastic photon scattering (𝛾𝛾, 𝛾𝛾′)-reaction, emission of the photons with lower energy, or emission of neutrons, protons or composite charged particles if the excitation energy of the nucleus exceeds the particle separation threshold

Photoneutron reactions [5]

If nucleus have the excitation energy higher than the binding energy of a nucleon or a heavier particle (e.g an α-particle), this particle may be emitted from the nucleus instead of electromagnetic radiation In the energy range below the nucleon emission threshold, there are only elastic and inelastic scattering that contribute to the total photon absorption cross-section which exhibits a few isolated absorption lines in this region At higher energy, the excited nuclear state may emit photon or nuclear emission to decay Due to the very short lifetime of levels above the nucleon emission threshold, the absorption lines become increasingly broad At

even higher energy the nuclear level spacing is so small that the excited states partially overlap and the photon absorption leads to collective excitation of all nucleons

In the giant dipole resonance region, the distribution of elastic and inelastic scattering and emission of a single neutron, (𝛾𝛾, 1𝑛𝑛)-reactions, from the excited nucleus on the total cross-section is more important than emission of nucleons or a charged particle because of the coulomb barrier, so that the giant resonance structure is clearly pronounced in the (𝛾𝛾, 1𝑛𝑛)-cross-section The(𝛾𝛾, 1𝑛𝑛)-cross-section include (𝛾𝛾, 𝑛𝑛)-cross-section and (𝛾𝛾, 𝑛𝑛𝑛𝑛)-cross-section Therefore, for medium and heavy nuclei, this partial cross section is nearly identical with the (𝛾𝛾, 𝑛𝑛)-cross-section because proton emission is severely hindered by the coulomb barrier The total photoneutron cross-section of medium and heavy nuclei nearly equals the photon absorption cross-section However, for low atomic number the emission of charged particles especially protons – significantly contributes to the total reaction cross-section, but this partial cross-section is not included in the total photoneutron cross-section

Sometimes higher order reactions such as (𝛾𝛾, 2𝑛𝑛) or even (𝛾𝛾, 3𝑛𝑛) or even more neutrons emitted must be used if (𝛾𝛾, 𝑛𝑛)-reactions cannot be produced suitable radionuclides for analysis The threshold energies for (𝛾𝛾, 2𝑛𝑛)-reactions, however, are nearly twice those of (𝛾𝛾, 𝑛𝑛)–reactions and the peak cross-sections are considerably lower

Reaction with emission of charged particles

The emission of charged particles from an excited nuclei is hindered by nuclear forces and by the Coulomb barrier Therefore, the photonuclear cross-section for charged reaction products very slowly rises above the threshold and then strongly increases as the photon energy exceeds the coulomb barrier Since the height of the coulomb barrier rises with increasing atomic number, the effective threshold also increases in contrast to the (𝛾𝛾, 𝑛𝑛)- threshold Due to the high effective threshold and the low cross-section it is difficult to observe (𝛾𝛾,charged particle)–reactions for heavy nuclei These reactions are important only in the case of light and medium elements except very few heavier elements for analysis[5][6]

Photospallation reaction

Photospallation reaction is photonuclear reaction emitting many nucleons It can occur in energy range above 40 MeV In high energy, photospallation reaction (𝛾𝛾, 𝑥𝑥𝑛𝑛𝑥𝑥𝑛𝑛) is a competitive entrance channel that is more dominant in different reactions, in which x is the number of neutrons and y is the number of emitted proton (x≥1, y≥1)

Its mechanism is explained based on the intranuclear cascade model of Serber This model includes two stages In the first stage, the incident particles collide with the individual nucleons in the target nuclei The reabsorption of pion, the scattering of recoil nucleons makes a cascade of nucleon and pion inside nuclei The nucleus can emit the single nucleons or group of them In next stage, the residual nucleus still has enough energy, the deexcitation can release through two competitive channels, fission and particle evaporation In general, the emission of particle by evaporation has more probability and lasts when the excitation energy reduces until particles no longer emitted The distribution of photospallation reaction yield was analyzed on the basis of semi-empirical formula of Rudstam

Yield of photonuclear reactions

Yield is defined as the number of photonuclear reaction or radioactive nuclei was created in one second on a target nuclei induced by bremsstrahlung It is represented by the following expression:

the flux density of the activating photons, there is immediately to obtain the effective cross-section of the reaction.[5]

1.2 Nuclear isomer and isomeric ratio

An isomer is nuclide that is capable of existing in excited state for sufficiently long time to be observed, called metastable state Its half-live maybe range from 1 s to 8 months or even more Metastable isomers can be produced through nuclear fusion or nuclear reactions.[6]

The nuclear isomer was first discovered in 1921 by Hahn, but the nature of this phenomenon was revealed a part with the experiment by I Kurchatov, B Kurchatove, Mysovskii and Rusinov in 1935 The isomer has been investigated quite extensively at present. [11]

The condition for the existence of isomer is the presence of an energy level near the ground state, differing strongly from the latter in its angular momentum It was mentioned above that gamma transitions between such levels must be severely hindered and hence the corresponding lifetimes may be of the order of several hours, days or even years The depending on the multipolarity of the gamma transition, the lifetime of the excited state may vary over a wide interval It means that these levels play the role of metastable states of the isomer nuclei [11]

There are two ways in which the excitation can be removed from a metastable nuclear state First, the nucleus goes over from the metastable state to the ground state by gamma decay, called an isomeric transition, after this, beta decay may occur from the ground state Second, it is beta decay that decay directly from metastable

Isomer may also be exhibited in the form of several half-lives for the spontaneous fission of the nucleus Metastable states may also be observed for beta-stable nuclei In this case, this state is de-excited through emission of gamma and conversion electrons Thus, in all cases, the essence of isomer lies in the existence

of an excited state of the nucleus with a measurable life-time

On account of the comparatively long lifetime, this state in fact exhibits the properties of a new isomeric nucleus with altered values of mass, spin, parity, isospin, lifetime and so on (but with the same values of Z and A).[11]

About hundred long-lived isomers are known to exist A statistical analysis

of their distribution according to the number of nucleons contained in them leads to the following interesting regularities Nucleus with odd mass number have the largest number of isomeric states These isomeric states are encountered quite frequently in odd-odd nuclei, while they are very rare in even-even nuclei Isomeric nuclei with odd A is distributed in accordance with the number of protons or neutrons contained in them It can be explained within the frame-work of the shell model of nucleus

Some isomers have been considered in some quarters as weapon because they can be induced to emit very strong gamma radiation and other are used in medical and industrial applications.[24]

The isomeric yield ratios were determined based on the activities of the spin state and that of low-spin state Therefore, it can be determined by[16-18]:

high-𝐼𝐼𝑅𝑅 = 𝜎𝜎ℎ𝑖𝑖𝑖𝑖ℎ−𝑟𝑟𝑡𝑡𝑚𝑚𝑖𝑖𝑟𝑟

With the incident beam is bremsstrahlung, the continuous spectrum, the yield ratio is used instead of cross-section ratio to obtain an average value of the isomeric ratio, which is assumed to be nearly constant

The measurement of the isomeric ratio can be related to the spin dependence

of the nuclear level density and give more information about the nuclear reaction mechanism and also about nuclear mechanism

1.3 TALYS code

TALYS is a computer code system created at NRG Patten, the Netherlands and CEA Bruyères-le-Chaatel, France for the analysis and prediction of nuclear reactions The objective is to provide a complete and accurate simulation of nuclear reactions in the 1 keV - 200 MeV energy range that involve neutrons, photons, protons, deuterons, tritons and particles (3He and alpha) for a target nuclides of mass 12 and heavier, through an optimal combination of reliable nuclear models, flexibility and user-friendliness “First completeness, then quality” is the principle

to develop TALYS.[10]

TALYS has two main purposes It can be used for analysis of basic scientific experiments or to generate nuclear data for applications First, it is a nuclear physics

tool that can be used for the analysis of nuclear reaction experiments The interplay between experiment and theory give insight in the fundamental interaction and precise measurement enable to constrain TALYS’s models In return, when the resulting nuclear models are believed to have sufficient predictive power, they can give an indication of the reliability of measurements Second, it is also a nuclear data tool The nuclear data libraries that are constructed with these calculated and experimental results provide essential information for existing and new nuclear technologies It has important application when it is used in order to generate data involve such as conventional and innovative nuclear power reactors (GEN-IV), transmutation of radioactive waste, fusion reactors, accelerator application, homeland security, medical isotope production, radiotherapy, single-event upsets in microprocessors, oil-well logging, geophysics and astrophysics.[10]

Specific features of the TALYS package[10] are mentioned as:

• In general, an exact implementation of many of the latest nuclear models for direct, compound, pre-equilibrium and fission reactions

• A continuous, smooth description of reaction mechanisms over a wide energy range (0.001-200 MeV) and mass number range (12-339)

• Completely integrated optical model and coupled-channels calculations

• Incorporation of recent optical model parameterizations for many nuclei, both phenomenological (optionally including dispersion relations) and microscopical

• Total and partial cross-section, energy spectra, angular distributions, double-differential spectra and recoils

• Discrete and continuum photo production cross-sections

• Excitation functions for residual nuclide production, including isomeric cross-sections

• An exact modeling of exclusive channel cross-sections, spectra, and recoils

• Automatic reference to nuclear structure parameters as masses, discrete levels, resonances, level density parameters, deformation parameters, fission barrier and gamma-ray parameters, generally from the IAEA Reference Input Parameter Library

• Various width fluctuation models for binary compound reactions and, at higher energies, multiple Hauser-Feshbach emission until all reaction channels are closed

• Various phenomenological and microscopic level density models

• Various fission models to predict cross-section and fission fragment and product yields, and neutron multiplicities

• Models for pre-equilibrium reactions, and multiple pre-equilibrium reactions up to any order

• Generation of parameters for the unresolved resonance range

• Reconstruction of resonance range into pointwise cross-section using tabulated resonance parameters

• Astrophysical reaction rates using Maxwellian averaging

• Medical isotope production yields as a function of accelerator energy and beam current

• Option to start with an excitation energy distribution instead of a projectile-target combination, helpful for coupling TALYS with intranuclear cascade codes of fission fragment studies

• Use of systematics if an adequate theory for a particular reaction mechanism is not yet available or implemented, or simply as a predictive alternative for more physical nuclear models

• Automatic generation of nuclear data in ENDF-6 format (not included in the free release)

• A transparent source program

• Input/output communication that is easy to use and understand

• An extensive user manual

• A large collection of sample cases

With TALYS, a complete set of cross-sections can already be obtained with minimal effort, through a four-line input file of the type:

In which, “projectile”, “element”, “mass” and “energy” are keywords This code means that this is photonuclear reaction (g=gamma) with nature praseodymium (Pr and 141) induced by photon energy of 50 MeV There are more than 340 keywords that can be specified in TALYS for user’s purpose The input can be simple or as complex as user want

1.4 Bremsstrahlung

When electron through matter, it loses energy in two ways: ionization and radiation or Bremsstrahlung The electrons undergo radiative collision mainly with the electrostatic field of the nucleus When Bremsstrahlung is usually produced by stopping an electron beam from an accelerator in a heavy metal disc, a certain portion of the electron energy is converted into photons, the rest is dissipated in the converter as heat The photon energy spectrum extends from low energy to the maximum value equal to the particle energy, with the low energy to the preferably emitted The total average energy loss per path length 𝑑𝑑𝑥𝑥 integrated over all frequencies is given by:

−(𝑑𝑑𝐸𝐸)������𝑟𝑟𝑚𝑚𝑟𝑟 =4𝑍𝑍(𝑍𝑍 + 1)137 𝑁𝑁𝐸𝐸𝑟𝑟𝑟𝑟2𝑙𝑙𝑛𝑛𝑍𝑍1831/3𝑑𝑑𝑥𝑥 (1.14) where N is the number of nuclei per 𝑐𝑐𝑐𝑐3, E is the energy of electron and 𝑟𝑟𝑟𝑟 =

𝑒𝑒2/𝑐𝑐𝑐𝑐2 is the classical electron radius.[6]

Quantum mechanical calculations yield the result that the energy of bremsstrahlung photon ranges from zero up to a maximum value which equals to the energy of the incident electrons, and the contribution of low energy photons to the total bremsstrahlung intensity is indeed much higher than that of high energy photon near the maximum energy The spectrum of bremsstrahlung also depends on the photon emission angle with respect to the direction of the incident electrons The intensity rapidly decreases for all photon energies due to the increasing angle

In addition, the spectrum becomes more soft because the decrease with emission angle is more pronounced for high energy photons than for low ones[5] The spectrum of bremsstrahlung is shown in Fig 1.3

The conversion efficiency between electron beam power and the radiated power, as bremsstrahlung photons, depends on the electron energy and the material

that the bremsstrahlung efficiency reaches maximum because the thickness dependent of photon flux that is produced and that is out are slightly contrast The optimum converter thickness corresponds approximately to half the electron range The bremsstrahlung converter can be used to produce a neutron source A fraction

of the bremsstrahlung photons produced in the converter interacts with the converter material by photonuclear reactions Since the (𝛾𝛾, 𝑥𝑥𝑛𝑛) reactions have a reactively high effective cross-section the bremsstrahlung converter is always a neutron source with a considerable intensity The number of photoneutron reactions induced by the bremsstrahlung increase with the rising of layer thickness.[5]

The bremsstrahlung beam that irradiation sample maybe contains the transmitted electrons and neutron They can damage the sample and make unexpected entrance channels Therefore, there are shielding materials surrounded the converter and to avoid damage from electron, a cleaning magnet is used

Fig 1.3 The angular and energy distribution of the bremsstrahlung emission per

incident electron (with energy E) made from W and UCx with the thickness d [12]

CHAPTER 2: METHODOLOGY AND EXPERIMENT

2.1 Methodology

2.1.1.Determination of photoreaction yield and isomeric yield ratio

As the yield’s definition, its express is given by (1.12):

𝑌𝑌 = � 𝜑𝜑(𝐸𝐸)𝜎𝜎(𝐸𝐸)𝑑𝑑𝐸𝐸

𝐸𝐸 𝑚𝑚𝑚𝑚𝑚𝑚

(2.1)

In which, 𝐸𝐸𝑡𝑡ℎ is the energy threshold of reaction, 𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 is the maximum energy

of incident photon, 𝜑𝜑(𝐸𝐸) is the flux of incident photon and 𝜎𝜎(𝐸𝐸) is the cross-section

of photonuclear reaction It means that yield has relative with cross-section and is useful for photonuclear reaction induced by bremsstrahlung It also shows that with particular reaction, reaction yield is nearly constant[16]

As definition of isomeric yield ratio (IR), it can calculate by (1.13):

Fig 2.1 The irradiation model of isomeric pair

Fig 2.2 The time dependent of activity with irradiation time (ti), waiting time

(tw) and counting time (tc)

In the irradiation, there are two processes that take place simultaneously: the formation of radionuclides from reaction and the decay of radionuclides The formation of isomeric pair in irradiation process can be expressed by the following equations[16-18]:

𝑑𝑑𝑁𝑁𝑚𝑚

𝑑𝑑𝑁𝑁𝑖𝑖𝑑𝑑𝑑𝑑 = 𝑌𝑌𝑖𝑖− 𝜆𝜆𝑖𝑖𝑁𝑁𝑖𝑖+ 𝑃𝑃𝑚𝑚𝑖𝑖𝜆𝜆𝑚𝑚𝑁𝑁𝑚𝑚 (2.4) where: Ni, Yi, λi and Pmg are respectively the number of nuclei for i state, the yield, the decay constant and the branching ratio for the decay of the isomeric states to the ground state, with i = m, g (m = metastable state and g = ground state)

With the initial conditions: 𝑁𝑁𝑚𝑚(𝑡𝑡=0) = 𝑁𝑁𝑖𝑖(𝑡𝑡=0) = 0

Solve these equations, we obtained:

After irradiation with 𝑑𝑑𝑖𝑖𝑟𝑟, we waited with 𝑑𝑑𝑙𝑙 In this time, 184mgRe followed the radioactive decay law as following equations:

𝑑𝑑𝑁𝑁𝑚𝑚

𝑑𝑑𝑁𝑁𝑖𝑖𝑑𝑑𝑑𝑑 = −𝜆𝜆𝑖𝑖𝑁𝑁𝑖𝑖+ 𝑃𝑃𝑚𝑚𝜆𝜆𝑚𝑚𝑁𝑁𝑚𝑚

𝑆𝑆𝑖𝑖𝑓𝑓𝑖𝑖

where: 𝐼𝐼𝑖𝑖, 𝜀𝜀𝑖𝑖, 𝑓𝑓𝑖𝑖 are respectively the intensity of the measured gamma-ray, the detection peak efficiency for the gamma-ray of interest and the related correction factor in the experiment

That take place simultaneously: the formation of radionuclides from reaction and the decay of radionuclides The formation of isomeric pair in irradiation process can be expressed by the following equations:

𝑑𝑑𝑁𝑁𝑚𝑚

where: Ni, Yi, λi and Pmg are respectively the number of nuclei for i state, the yield, the decay constant and the branching ratio for the decay of the isomeric states to ground state, with i = m, g

With the initial conditions: 𝑁𝑁𝑚𝑚(𝑡𝑡=0) = 𝑁𝑁𝑖𝑖(𝑡𝑡=0) = 0

Solve these equations, we obtained:

𝐴𝐴𝑘𝑘 =1−𝑟𝑟𝜆𝜆−𝜆𝜆𝑘𝑘𝑡𝑡𝑖𝑖

𝑘𝑘 , 𝐵𝐵𝑘𝑘 = 𝑒𝑒−𝜆𝜆𝑘𝑘𝑡𝑡𝑤𝑤, 𝐶𝐶𝑘𝑘 = 1 − 𝑒𝑒−𝜆𝜆𝑘𝑘𝑡𝑡𝑐𝑐 (k = m,g) However, using gamma spectrum analysis software, we determined the photo-peak areas 𝑆𝑆𝑖𝑖 for the detected gamma-ray It is related to 𝐶𝐶𝑖𝑖 according to the following expression:

𝑆𝑆𝑖𝑖𝑓𝑓𝑖𝑖

where: 𝐼𝐼𝑖𝑖, 𝜀𝜀𝑖𝑖, 𝑓𝑓𝑖𝑖 are respectively the intensity of the measured gamma-ray, the detection peak efficiency for the gamma-ray of interest and the related correction factor in the experiment

However, sometimes, the distribution of other isotope created from another reaction channels can be dominant in the activity of isomeric pair It can make error,

so it needs to be considered In this work, the model in Fig 2.3 is mentioned

Fig 2.3 the distribution of two isotopes on the other

In the irradiation, the process can be expressed by:

(2.25)

With the initial conditions: 𝑁𝑁1(𝑑𝑑 = 0) = 𝑁𝑁2(𝑑𝑑 = 0) = 𝑁𝑁3(𝑑𝑑 = 0) = 0, its

𝑁𝑁1(𝑑𝑑 = 0) = 𝑁𝑁1−𝑟𝑟𝑒𝑒𝑟𝑟; 𝑁𝑁2(𝑑𝑑 = 0) = 𝑁𝑁2−𝑟𝑟𝑒𝑒𝑟𝑟; 𝑁𝑁3(𝑑𝑑 = 0) = 𝑁𝑁3−𝑟𝑟𝑒𝑒𝑟𝑟

we solve and obtain:

𝐶𝐶𝑖𝑖 = 1 − 𝑒𝑒−𝜆𝜆𝑖𝑖𝑡𝑡𝑐𝑐The radiation emitted from source is: