(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP

(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP(Luận án tiến sĩ) Nghiên cứu tham số hoá tiết diện quang phân hạch của 238U và mô phỏng tối ưu sử dụng Geant4 phục vụ cho thiết kế hệ thiết bị IGISOL tại dự án ELI NP

MINISTRY OF EDUCATION VIETNAM ACADEMY AND TRAINING OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY LÊ TUẤN ANH STUDY ON PARAMETRIZATION OF PHOTOFISSION CROSS-SECTION OF 238U AND OPTIMIZATION SIMULATION USING GEANT4 FOR DESIGN OF THE IGISOL FACILITY AT ELI-NP PROJECT Major: Atomic and nuclear physics Code: 9440106 SUMMARY OF DOCTORAL THESIS Hanoi - 2021 Cơng trình hồn thành tại: Học viện Khoa học Công nghệ Viện Hàn lâm Khoa học Công nghệ Việt Nam Người hướng dẫn khoa học 1: TS Phan Việt Cương Người hướng dẫn khoa học 2: GS TS Dimiter L Balabanski Phản biện 1: Phản biện 2: Phản biện 3: Luận án bảo vệ trước Hội đồng chấm luận án tiến sĩ, họp Học viện Khoa học Công nghệ Viện Hàn lâm Khoa học Công nghệ Việt Nam vào hồi … …’, ngày … tháng … năm 2021 Có thể tìm hiểu luận án tại: - Thư viện Học viện Khoa học Công nghệ - Thư viện Quốc gia Việt Nam INTRODUCTION The motivation of the thesis The Extreme Light Infrastructure- Nuclear Physics (ELI-NP) is expected to be the most advanced research facility in the world in the field of photonuclear physics, and a new interdisciplinary research field that brings together, for the first time, high-power lasers and nuclear physics ELI-NP will offer a highly-polarized tunable mono-energetic γ beam in the range from 200 keV to 19.5 MeV The ELI-NP gamma beam is also suitable for the production of the radioactive ion beam (RIB) through photofission of Uranium An IGISOL facility will be constructed to extract the photofission fragments to form RIBs at ELI-NP To support this idea, an accurate calculation for production cross-section of photofission fragments is crucial Therefore, it is necessary to develop a reliable tool for this job This empirical parametrization will be useful for photofission facilities worldwide, and ELI-NP is one of them Moreover, It is important to series of prerequisite calculations and simulations to lead to the conceptual design for the particular case of the CSC at ELI-NP IGISOL facility The aim of the thesis The works in this thesis aim to fulfill two goals: i) the first one is to develop a reliable empirical parametrization for the calculation of photofission cross-section over a wide energy range below 30MeV ii) The second one is to implement a Geant4-based code and carry out a series of simulations to optimize the design of CSC at ELI-NP Main research content of thesis • General overview of the ELI-NP project, photofission process, methods for production of radioactive ion beam, Geant4 simulation toolkit and its application fields • Construct the empirical parametrization for total cross-section, mass yield and isobaric charge distribution of 238U photofission • Prediction of neutron-rich nuclei yield • Implement the photofission process into Geant4 Within this thesis, a Geant4-based code was developed for the simulation of photofission, inverse Compton backscattering processes, as well as the electromagnetic processes of particles (ions,gamma, electrons) with matter This code, then, was be used for optimizing the design of cryogenics stopping cell for IGISOL facility at ELI-NP Chapter 1.OVERVIEW 1.1.The Extreme Light Infrastructure Nuclear Physics facility The Extreme Light Infrastructure (ELI) is a Research Infrastructure of Pan-European interest ELI will be a multi-sited Research Infrastructure with complementary facilities located in the Czech Republic, Hungary, and Romania for the investigation of light-matter interactions at the highest intensities and shortest time scales ELI-NP facility in Romania, which is one of the three pillars of the ELI, will develop a scientific program using two beams of 10 PW laser and a Compton back-scattering (CBS) high-brilliance and intense low-energy gamma beam The ELI- NP project consists of two main experimental areas: the ELI-NP High-Power Laser System (HPLS) and Gamma Beam System (GBS) Fig 1.1 expresses the sketch of ELI-NP machines and experimental areas 1.1.1.Gamma Beam System A highly-polarized (≥ 95%) tunable γ beams of spectral density of 104 photons/(s.eV ) in the range from 200 keV to 19.5 MeV with a bandwidth of ≥ 0.3% will be produced by ELI-NP GBS These γ beams will be produced through laser Compton backscattering (CBS) off an accelerated electron beam delivered by a linear accelerator The Compton backscattering (also called inverse Compton scattering) is considered as ”photon accelerator” Fig 1.2 shows the geometry of the CBS between a laser photon EL energy, incident at angle θL respect to the electron beam direction, and a relativistic electron with energy Ee Fig 1.3 presents two types of beams that will be delivered at ELI-NP The broad gamma beam displayed with blue dots has the energy range 10 − 18.5 MeV It was obtained by using Ee = 720M eV and collimating the beam below 0.7 mrad with a lead collimator The red dots in Fig 1.3 presents the pencil beam with the narrow energy range around 12.9 MeV The pencil beam was obtained by setting Ee = 600M eV and collimating the beam below 0.09 mrad Bases on such kinds of gamma beams, ELI-NP GBS will provide the following experiments such as The Nuclear Resonance Fluorescence (NRF), Experiments above the Neutron Separation Threshold, and Photofission experiments and the production of RIB 1.2.Methods for production of RIB To address which method is suitable for producing RIB at ELI-NP, the details of each method will be discussed as following 1.2.1.The ISOL technique In the ISOL technique, the radioactive ion beams are produced via light-ion-induced spallation or fission of a thick actinide target The fission reactions can be induced by thermal neutrons, fast neutrons, protons or photons This method requires a high intensity of the primary beam and a thick hot target The great advantage of the thick targets is a large number of target atoms available for the production of the ions Even for such exotic nuclei with extremely low production cross-sections can still be obtained However, short-lived isotopes cannot be obtained because of the time required for diffusion and effusion Another disadvantage with ISOL production is that it is difficult to achieve high beam purity due to the many isobars of different elements produced simultaneously in the target Furthermore, refractory elements are in general difficult to produce due to the high temperatures required to make them volatile, see figure 1.6 1.2.2.The in-flight method The lower drawing in Fig 1.5 expresses the scheme of In-Flight technique In this method, the fragmentation or fission of intense heavy-ion beams in a thin target made of Figure 1.1: Sketch of the ELI-NP machines and experimental areas HPLS High Power Laser System; OPCPA: Optical Parametric Chirped Pulse Amplification; XPW: Cross Polarised Wave system; LBTS: Laser Beam Transport System; GBS Gamma Beam System; DPSSL: Diode Pumped Solid State Laser; E1-E8 Experimental areas Figure 1.2: Geometry of the inverse Compton scattering of a laser photon on a relativistic electron light elements such as carbon and beryllium was used for the production of RIB The thin target allows the fragments to release from the target surface still at very high velocity and forward momentum which is exploited for mass separation and study or further reactions An advantage of this method, which is opposite to ISOL technique, is that the production of the RIBs is independent of the chemical properties of the element Moreover, isotopes with very short half-lives and even isomers are available as RIBs On the contrary, the optical properties of the RIBs are poor due to the kinetic energy spread and their divergence that results from the production process Since the intensities of the heavy-ion beams are generally lower than that of the light-ion beams used for the ISOL method, the yields of some exotic fragments may also be somewhat lower 1.2.3.Ion guide isotope separation online technique Figure 1.7 illustrates the principle of IGISOL method based on the very beginning design The idea of this technique is that the nuclear reaction products which release from the target into gas will be slowed down and thermalized in the gas cell to 1+ charge state The buffer gas Figure 1.3: The simulated results for energy-angle correlation for two gamma beams: a broad beam up to 18.5 MeV collimated below 0.7 mrad (blue) and a pencil beam up to 12.9 MeV collimated below 0.09 mrad (red) The pencil beam is enclosed in a dashed red box for visibility Figure 1.4: The energy spectra of the broad beam between 10–18.5 MeV (blue squares) and of the pencil beam at 12.9 MeV ( red circles) from Fig 1.3 is typically helium, argon could be used in some special cases In some senses, the IGIGOL is similar to ISOL, except for the target part Instead of using a thick target, in this approach, one or several thin targets are used The release ions are swept by the gas flow out of the cell and injected through a pumped electrode system into the isotope separator The thickness of the target is limited to the range of the recoil ion in the target to obtain the highest release efficiency The range, for instance, is of the order of mg/cm2 for fusion-evaporation residues and 15 mg/cm2 for fission fragments 1.2.4.Method for production of RIB at ELI-NP At ELI-NP the RIB will be created through the photofission process, namely, the incident particle will be gamma Therefore, as mentioned in subsection 1.2.2, the In-flight method is not suitable The ISOL method seems to be usable for the incident particle of gamma However, at ELI-NP, the RIB will be dedicated to studying the exotic neutron-rich isotopes in the Zr-Mo-Rh region which is the refractory elements As shown in Fig 1.6, Zr-Mo-Rh region has a very high boiling and melting point Hence, they can not be diffused to the target surface by heating As a consequence, the ISOL method is not the candidate for the production of RIB at ELI-NP Meanwhile, by using thin targets, the IGISOL method can be used for the production of RIB in the refractory region Therefore, at ELI-NP an IGISOL facility will be constructed Figure 1.5: Scheme of ISOL and In-Flight techniques 1.3.The future ELI-NP IGISOL Figure 1.8 presents the layout of the proposed Gamma Beam System located within the accelerator hall The length of the hall is approximately 90m There will be two foreseen interaction points: one at E=300 MeV of electron energy and one at E=720 MeV of electron energy respectively identified as Low and High energy Interaction Points The gamma beam used for photofission to produce RIB at the IGISOL facility will come from the latter one At ELI-NP, the RIB will be produced in the photofission of 238 U targets induced by the CBS gamma beam Main components of ELI-NP IGISOL include CSC and the collimator which are installed along the beamline The 238 U targets will be placed inside CSC filled with Helium gas The fission fragments will be extracted and delivered to measurement stations through the radio frequency quadrupole (RFQ), the analyzing magnet and the MR-TOF-MS in directions depicted by red dashed arrows The CSC, the Pb collimator and RFQ will be located on a common platform, which can be placed in and out of the γ beam Note that, the gamma beam for photofission in CSC will be fed by the high-energy interaction point There are two possible locations where CSC can be mounted The first one is 7m far away from the high-energy interaction point, while the other one is at 40 m from the high-energy interaction point A series of simulations have to be done to answer what are the optimal number, tilting angle, thickness, dimensions and spacing of the uranium targets to obtain the highest intensity of RIB Within this thesis, the Geant4 simulation toolkit is used for this task 1.4.Introduction of Geant4 toolkit Geant4 which is based on the Monte-Carlo method is a toolkit dedicated to simulating the passage of particles (heavy ions, light ions, γ, e, ) through matter It has been used in applications in particle physics, nuclear physics, accelerator design, space engineering and medical physics Geant4 is chosen because it provides users with many models for simulating the transportation of particles in matter In our case, the simulation of photofission fragments traveling in targets and gas will help optimize the design of CSC However, the photofission process is not available in Geant4 Therefore, a new Geant4 process has to be implemented for handling photofission To so, the study of photofission, especially its cross-section, is necessary Figure 1.6: Boiling and melting point of elements Figure 1.7: The principle of IGISOL method 1.5.Photofission process In 1939, Bohr and Wheeler introduced a theory to explain the mechanism of the nuclear fission process The theory showed that fission should occur when a heavy nucleus, which locates well beyond the minimum of the packing faction curve, is given sufficient excitation energy to lead to the division of the nucleus The excitation energy can be provided via either particle capture (n,p,e ) or gamma absorption Photofission process is defined as the process in which a nucleus undergoes nuclear fission and splits into two or more fragments after absorbing a gamma-ray The reaction is first observed in 1940 by Haxby et al by irradiating uranium and thorium with high intensity γ-rays of 6.3 MeV from fluorine Since then, photofission reactions, and in particular low energy photofission reactions, have been widely investigated These photofission studies are very important not only for understanding the photofission mechanism but also for exploring nuclear structure effects Recently, there has been growing interest in photofission, because it provides one of the most powerful methods for producing neutron-rich exotic nuclei close to the r-process path For instance, photofission of uranium targets has been or will be used at the ALTO facility at Figure 1.8: Gamma source schemetic layout There will be two foreseen interaction points: one at E=300 MeV of electron energy and one at E=720 MeV of electron energy respectively identified as Low and High energy Interaction Points IPN Orsay, the DRIBs at JINR, the ARIEL facility at TRIUMF, the ANURIB at VECC, and the IGISOL facility at ELI-NP For producing neutron-rich nuclei, designing nuclear physics experiments, and many other applications, an accurate calculation for production cross-sections of photofission fragments is crucial Calculations for these cross-sections in 238 U photofission at low energies over the whole giant dipole resonance (GDR) region are of specific interest for estimating the production yields of neutron-rich fragments and optimizing nuclear physics experiments at the above mentioned facilities General fission models, e.g., GEF and FIPRODY , have been developed for predicting the manifold fission observables in various fission systems, however, their predictive power for production yields of 238 U photofission fragments is not validated Since calculations by these statistical fission models can be very time consuming, a fast and accurate empirical parametrization for production cross-sections of fragments produced by 238 U photofission at low energies is particularly useful Recently, an empirical parametrization , based on the mass yields measured at the average photon energy of 13.7 MeV , has been proposed to calculate production cross-sections of fragments produced by photofission of 238 U at 13.7 MeV However, this parametrization cannot be used to describe the mass yields at other energies below 30 MeV, especially for the fission modes with a strong energy dependence such as the symmetric mode, according to the mass yields measured at different excitation energies Thus, there is a need to develop a reliable empirical parametrization for the above mentioned applications 13 Figure 2.3: Difference between the most probable charge Zprob from experimental data measured by Donzaud et al., Frenne et al., as well as Pomme et al and (Zs − 3.8) proposed by Bhowmick Figure 2.4: Elemental yields Y (Z) = ments Y (A, Z) measured in two 238 U photofission experi- compared with the mass yields calculated by this parametrization As shown in Fig 2.5, the calculated and measured mass yields are in good agreement for both experiments Based on these comparisons, the average excitation energies in the calculations using this parametrization are estimated to be 18 ± 0.9 and 16.5 ± 0.8 MeV for two experiments 2.3.Prediction of neutron-rich nuclei yield As an example, Fig 2.9 shows the calculated cross sections of neutron-rich fragments produced by photofission of 238 U using 14 MeV photons The calculated results demonstrate clearly that the 238 U photofission is particularly suitable for producing many neutron-rich exotic nuclei with 31 ≤ Z ≤ 62 and 80 ≤ A ≤ 160 For many neutron-rich nuclei on or close to the r-process path, a production cross section of the order of about mb can be achieved by using 238 U photofission at low energies For instance, it is interesting to notice that production cross sections of 80–82 Ge and 85–87 Se around the closed shell N = 50 are about 0.17 and 1.1 mb, respectively, while production cross sections of 132 Sn and 134 Te around the closed shell N = 82 are roughly 0.66 and 6.4 mb,respectively The above cross sections calculated with proposed parametrization can be applied to 14 Figure 2.5: Comparison between the mass yields measured in two experiments at GSI via the virtual photon induced fission of 238U and those calculated by the parametrization in this work Figure 2.9: Cross sections of fragments produced by photofission of 238 U using 14 MeV photons, calculated by the developed parametrization The dotted lines illustrate the position of the rprocess path The proton and neutron closed shells are indicated with the black solid lines estimate the production rates of neutron-rich nuclei produced by 238 U photofission and optimize nuclear physics experiments As an example, production rates of 132 Sn and 134 Te in 238 U targets with a total thickness of 251 àm are about ì 104 and × 105 ions/s, respectively, according to calculations by the proposed parametrization for the IGISOL facility at ELI-NP In this calculation, the total intensity of the gamma beam (with a broad energy distribution between 10 and 18.5 MeV) is conservatively estimated to be × 1010 γ/s at the γ production point, while 238 U target is placed around m after this γ production point 2.4.Chapter conclusion The work in this Chapter has fulfilled the first goal of the thesis An empirical parametrization for the calculation of photofission cross-section over a wide energy range below 30 MeV has been established This parametrization consists of the total photofission cross-section, the mass yield, and the isobaric charge distribution A good agreement can be observed between the parametrization and experimental data available in literatures 15 Chapter 3.OPTIMIZING THE DESIGN OF CRYOGENIC STOPPING CELL FOR IGISOL FACILITY AT ELI-NP In this work, a Geant4-based code was implemented for simulation of physics processes occurring in the CSC filled with He gas, and was used for optimizing the design of CSC at ELI-NP IGISOL 3.1.The structure of the implemented Geant4 code Users have to write their own C++ code based on Geant4 for the specific problem Our developed code aim to simulation the generation of the gamma gamma beams through CBS (see in 1.1.1), simulate the photofission process, and handle the transportation of ions, electrons, gammas in the matter Fig 3.1 shows the structure of the Geant4-based code developed within this thesis The simulation results are stored in ROOT file (TFile object) to be later analyzed by ROOT framework The Physics-Lists part plays a very important role in the simulations The available Geant4’s physics-lists contain all the models for physics processes for γ, ions, electrons, except for photofission 3.2.Implementation of photofission process into Geant4 Because the photofission process is not available in Geant4, one of the crucial task of our study is its implementation The implementation of a new process into Geant4 includes two modules: The first one involves the calculation of reaction cross-section Our empirical parameterization, which is presented in the previous Chapter, is used for the calculation of cross-section The second module controls the final state distribution of outgoing particles and residuals Figures 3.2 and 3.3 show the features of photofission fragments created with our Geant4-based implementation These results were produced by exposing 39 238 U foils with a thickness of 3um to a γ-ray with and the broad 10 − 18.5 MeV energy spectrum 3.3.Ionic effective charge In Geant4, the Ziegler-Manoyan q-parameterization is implemented under the class G4ionEffectiveCharge This class is included by default in the G4ionIonisation process In order to understate the impact of ionic effective charge, two new parameterizations has been added into Geant4 in our study The first parameterization implemented is Shima et al qparameterization which is tailored for low energy ions The another parameterization that we included in Geant4 implementation is developed by Schiwietz and Grande Figure 3.1: The structure of the implemented Geant4 code 16 Figure 3.2: Kinetic energy versus atomic mass A of photofission fragments produced with our implementation Figure 3.3: Kinetic energy versus emitted angle θ of photofission fragments produced with our implementation 3.4.Target geometry optimization The beam spot size A at distance D is determined as: A = 2Dθmax = 4D EL /Eth − EL /Eγmax (3.1) where EL = 2.4 eV is the laser photon energy The beam transversal distributions at D = m with red triangles and at D = 40 m with blue circles, for a beam with Emax = 18.5 MeV and a threshold energy Eth = 12 MeV, are shown in Fig 3.4 In this work, the bulk target is sliced into many thin foils of thickness t These foils have to be tilted at an angle a with respect to the γ beam axis z for two reasons: (i) the foils should not face each other to avoid a large fraction of the released fragments from hitting neighboring foils and (ii) tilting a foil increases the beam path through it t/sin(a), without increasing its thickness Such a stacked foil target, with the transversal size A and total thickness T, has the total length Lt and the number of foils N given by: A (N − 1) tan (a) T N = sin(a) t Lt = (3.2) (3.3) (3.4) 17 Figure 3.4: Gamma beam transversal distribution at distance D = m from the beam origin and Eth = 12 MeV (red triangles), at D = 40 m and Eth = 12 MeV (blue circles) and at D = 40 m and Eth = MeV (black squares) The maximum beam energy is Eγ max = 18.5 MeV The corresponding dashed lines show the beam spot sizes A calculated with Eq (3.1) Figure 3.5: View of the yz-plane of the target geometry inside the gas cell The gamma beam propagates along the z axis and the DC field drifts ions along the x axis Figure 3.6: The dependence on the 238 U foil thickness t of the photofission rate Nf with black circles and of the fragment release rate Nr with colored squares The two colors of the squares correspond to different q-parameterizations: Schiwietz-Grande in red and Ziegler-Manoyan in blue 18 Figure 3.7: The dependence of PB on the backing foil thickness The total thickness is calculated as: T (t, A, a) = t Lt + Acos(a) sin(a) (3.5) The photofission fragment release rate Nr (t, B, A, a) is expressed as: Nr (t, B, A, a) = Nf (3.6) t B where Nr (t, A, a) is the photofission rate, t is the the fragment release efficiency for the foil target, and B is the the fragment release efficiency for the backing layer The aim is to find the parameter set (t;B; A; a;) that maximizes the fragment release rate 3.4.1.Optimize the thinkness of foil targets The increase of the photofission rate Nf with the foil thickness is shown in Fig 3.6 with black circles for Lt =1m, A =6mm and a=10o , hence a number N = 30 of foils If A; a and Lt are fixed, an increase of t implies a proportional increase in Nf However, since the release efficiency t decreases with the foil thickness, their product, the fragment release rate Nr , increases quickly and saturates after a certain foil thickness This is demonstrated in Fig 3.6 with red squares for the Schiwietz-Grande q-parameterization and with blue squares for the Ziegler-Manoyan q-parameterization Saturation is reached in the first case for t > 1µm and in the second case for t > 2µm It is the level of the saturation rate that depends on the other target geometry parameters, but not the shape of Nr (t) Hence, the optimal foil thickness is t ≈ 2µm 3.4.2.The thinkness of backing layers The backing is the thin layers of graphite covering the optimize the backing thickness, the quantity PB (%) is used: PB = 238 U foil for supporting To Number of ions lost in the backing layers % Number of ion released from the 238 U foils (3.7) Fig 3.7 shows the dependence of the loss fraction PB on backing thickness for both Schiwietz-Grande and Ziegler-Manoyan q-parameterizations If PB = 5% marked by dash line is the acceptable value, then the optimal number for backing thickness can be in the range 0.4 − 0.9µm 19 3.4.3.The dependence of the photofission fragment release rate on foil transverse size A, the foil tilting angle a, and the inter-foil distance The target transversal size A is shown on the upper x axes in Fig 3.8 in black for D = m and blue for D = 40 m This maximum rate is obtained by setting A at the two locations to 0.7 cm and 3.9 cm, respectively The fragment release rate has a weak dependence on the foil tilting angle a For example, the distributions in Fig 3.8 decrease by 2% and increase by 5%, respectively, when a is varied by 10o Figure 3.8: Dependence of the fragment release rate Nr on the γ beam threshold energy Eth at D=7m with black circles, on the left y axis, and at D=40m with blue squares, on the right y axis The maximum γ energy is Emax = 18.5 MeV The corresponding foil transverse sizes A, at D=7m with black and at D=40m with blue, are shown on the upper x axes There is however another quantity that has a significant impact at large tilting angles, namely the fraction floss of released fragments that are lost because they hit neighboring foils It increases fast at large a: from 1% at 5o , to 3.5% at 15o , to 24% at 45o This loss can be recovered by using increasingly larger inter-foil distances s, which was kept null so far For a = 45o , it can be brought back below 5% by using s > cm However, this means removing more than half of the foils to keep the same CSC length Lt and losing also more than half of the fragment release rate Therefore, increasing s to decrease floss does not lead to optimal rates The above 3.5% efficiency loss is considered acceptable, and fixing s = and a = 15o is the optimal choice 3.4.4.Remarks for target geometry From the results obtained as described above, some conclusions can be derived for taget geometry optimization The CSC at m from the HIP with a target length of 1m should be made of 39 foils tilted at 15o , with the size 0.7 × 2.7cm2 and a thickness of 2µm It would have a total thickness of 304µm, a mass of 0.28g, and would release photofission fragments at a rate of ∼ 1.9 × 106 ions/s Alternatively, the CSC at 40m from the HIP with a target length of 2m should be made of 15 foils tilted at 15o , with the size 3.9 × 15cm2 and the thickness of 20 Table 3.1: Results for target geometry Lt is the total length of target stack N is the number of 238 U foils D is the distance between location of CSC and the ELI-NP high-energy interaction point Symbol t is the thickness of each 238 U foil, while a stands for the tilting angle (see in Fig 3.5) D=7m D=40m Lt (m) N 39 15 t foil size (cmìcm) (àm) 0.7ì2.7 3.9ì15 2 a Release rate (ions/s) 15o 15o 1.9 × 106 0.85 × 106 Figure 3.9: The (Z,A) distributions of fission fragment at the time created inside target foils µm It would have a total thickness of 114 µm, a mass of 3.3 g, and would release photofission fragments at a rate of ∼ 0.85 × 106 ions/s These values are obtained for a γbeam below 17 MeV, which corresponds to a 690 MeV electron beam As discussed, each of the parameters (t; A; a) can be safely varied in some interval with small losses in the rate of released fragments 3.5.The stopping length of photofission fragments in He gas 3.5.1.The characteristics of release photofission fragments from backing layers Fig 3.9 presents the (Z,A) distributions of fission fragment at the time created inside foils After being created, these fragments travels insides Uranium foils, and backing layers before entering into gas Becasue of ionisation process, some fragents will loose their kinetic energy and stop in the foils Fig 3.10 presents the (Z,A) distributions of released fragments The Ziegler-Manoyan q-parameterization creates (Z,A) distribution consisting of two humps with a small difference in the heights In case of using Schiwietz-Grande q-parameterization, this difference is clear The fragments with (Z > 45, A > 120) would stop more in the targets and backing layers 21 (a) Ziegler-Manoyan (b) Schiwietz-Grande Figure 3.10: The (Z,A) distribution of release fragments from backing layers into He gas: a) Ziegler-Manoyan, and b) Schiwietz-Grande q-parameterizations 3.5.2.Ion stopping in the gas cell Choosing the width of CSC Our study uses the three sets of pressures and temperatures of the He gas listed in Table 3.2 as (A), (B) and (C), in increasing order of the density The fragment stopping length distributions, for each of the above parameter sets, are shown in Fig 3.13: (A) with blue triangles, (B) with red circles and (C) with black squares If the maximum stopping length, Lmax , is defined as the length at which 95% of the fragments have stopped, the values shown in the fifth row of Table 3.2 are obtained In all cases, the following relationship holds: ρ.Lmax = 2.33mg/cm2 (3.8) The spatial distribution of the ionization processes induced in the gas at 0.206 mg/cm3 by the photofission fragments is shown in Fig 3.14 A small cylindrical asymmetry can be seen in the xy view in the upper panel It is due to the foil geometry, which is rotated around the x 22 Figure 3.11: Kinetic energy KE distribution of photofission fragments at their release from the target foils into the gas cell with the Ziegler-Manoyan q-parameterization (black circles), the Schiwietz-Grande q-parameterization (red squares) and the Shima et al q-parameterization (blue triangles) Figure 3.12: Stopping length L of the released photofission fragments in He gas at 0.206 mg/cm3 density with the Ziegler-Manoyan q-parameterization (black circles), the Schiwietz-Grande qparameterization (red squares) and the Shima et al q-parameterization (blue triangles) Table 3.2: Gas density dependence of the following parameters: maximum stopping length Lmax , mean charge density rate < Q >, He+ mobility in He gas, photofission fragments (pf) mobility in He gas Our study uses the three sets of pressures and temperatures of the He gas listed in this Table as (A), (B) and (C) (A) ρ[mg/cm3 ] 0.053 P [mbar] 100 T [K] 90 Lmax [cm] 43.7 Q [ions/cm3 /s] 2.6ì107 à(He+ )[cm2 /(V.s)] 56.0 µ(pf )[cm2 /(V.s)] 65.9 (B) (C) 0.120 200 80 19.4 6.0×107 24.9 29.3 0.206 300 70 11.3 14.2×107 14.5 17.1 23 axis, such that its plane remains parallel to the DC field lines, shown with black lines In the xz view of the ionization processes in the lower panel, the gamma beam propagation through the gas cell is shown with a black line Figure 3.13: Stopping length for various densities of the He gas: ρA = 0.053mg/cm3 (blue triangles), ρB = 0.120mg/cm3 (red circles) and ρC = 0.206mg/cm3 (black squares) The width of the CSC is set slightly above d ≈ 2Lmax 3.6.The extraction of photofission fragments out of CSC After the stopping process, the stopped fragments are transported by the DC as well as RF fields to the extraction nozzle positioned at the center of the RF carpet, namely, the innermost ring electrode (see Fig 3.15) The DC and RF fields in the gas cell have been optimized by simulations using the SIMION software SIMION is a software package used to calculate electric fields and the trajectories of charged particles in those fields The final position and velocity of stopped fragments in the stopping process are from Geant4 simulations in Subsections 3.5 and are used as inputs for SIMION simulations According to many SIMION simulations, an extraction efficiency of about 50% and a short extraction time (average time around 15 ms) can be reached for photofission fragments after the DC and RF fields have been optimized Thus, the total rate of fragments extracted from the gas cell is around 5×105 ions/s Final rates, for instance, of 132 Sn and 134 T e extracted from the gas cell are about × 103 and × 104 ions/s, respectively Figure 3.15 shows the preliminary design for the gas cell of the planned IGISOL facility at ELI-NP As shown in Fig 3.15, the fragment extraction is performed in the perpendicular direction with respect to the gamma beam, which leads to a very short extraction path and time This perpendicular extraction method is particularly useful for the investigation of very exotic and short-lived nuclei Typical trajectories of two fragments in the gas cell are shown with the black solid arrows in Fig 3.15 3.7.Chapter conclusion The work in Chapter has fulfilled the second goal of the thesis A Geant4-based code has been implemented The highlight of the implementation is the construction of a process for simulating the photofission with Geant4 An extensive set of simulations, which were done with this code, has established the optimization of CSC’s parameters, as well as those of the target configuration inside The optimal target geometries at two locations of the CSC have been deduced, offering the maximum release rates in the range of 106 to 107 photofission fragments per second for the γ beams at ELI-NP 24 Figure 3.14: Vertices of ionization processes induced by the released fragments in the CSC at 0.206 mg/cm3 in the xy plane (upper panel) and in the xz plane (lower panel) The arrows show the DC field in the xy plane and the γ beam in the xz plane The anode is at x ≈ −12 cm The cathode is on the wall with the exit nozzle, at x ≈ +12 cm, along which the RF carpet field acts The RF carpet is shown with hashed brown boxes Figure 3.15: Schematic drawing of the gas cell for the proposed IGISOL facility at ELI-NP The RF carpet is composed of a stack of concentric ring electrodes The direction of the gamma beam is indicated with the dotted arrow Examples of trajectories of two photofission fragments in the gas cell are shown by the solid arrows 25 Conclusion In this work, an empirical parametrization is proposed for accurately calculating production cross-sections (yields) of neutron-rich fragments produced by photofission of 238 U over a wide energy range This parametrization consists of the total photofission cross-section, the mass yield, and the isobaric charge distribution The formulas for the total photofission crosssection can reproduce the experimental data over a wide energy range (below about 30 MeV) The mass yield distribution is based on the multimodal fission model, while an energy dependence is introduced according to the mass yield distributions measured at different energies Furthermore, a correction term is included for the most probable charge number to reproduce measured isobaric charge distributions Parameters used in this parametrization have been obtained by comparing with many experimental data This empirical parametrization will be useful for producing neutron-rich nuclei, designing nuclear physics experiments and many other applications not only at ELI-NP but also at other photofission facilities worldwide A Geant4-based simulation code was implemented for optimizing the conceptual design of ELI-NP CSC A new Geant4 process, which is based on the proposed empirical parametrization, was added to simulate the photofission process Other processes corresponding to gamma, electron, positron and ions are also included in the simulation To understate the impact of ionic effective charge, two new q-parameterizations has been added into the implementation This Geant4-based code will be used for helping to design the future experiment set-up at ELI-NP Using this implemented Geant4-based code, the optimal target geometries at two locations of the CSC have been established, providing the maximum release rates in the range of 106 to 107 photofission fragments per second for the γ beams at ELI-NP The CSC at m from the HIP with a target length of 1m should be made of 39 foils tilted at 15o , with the size 0.7 ì 2.7cm2 and a thickness of 2àm It would have a total thickness of 304µm, a mass of 0.28g Alternatively, the CSC at 40m from the HIP with a target length of 2m should be made of 15 foils tilted at 15o , with the size 3.9 × 15cm2 and the thickness of µm It would have a total thickness of 114 µm, a mass of 3.3 g These values are obtained for a γbeam below 17 MeV, which corresponds to a 690 MeV electron beam As discussed, each of the parameters (t; A; a - see in 3.5 for interpretation of these parameters) can be safely varied in some interval with small losses in the rate of released fragments These fragments are stopped in a CSC at 300 mbar and 70 K with the dimensions of 24 × 24cm2 in the plane transversal to the γ beam More generally, the CSC dimensions on both transversal directions need to be 4.66/ρ centimeters, with the density ρ in mg/cm3 The operational regime of the CSC for IGISOL facility at ELI-NP depends on the actual values of several parameters related to the γ beam, the He gas and the electric field properties This work provides guidance for the impact of future decisions and technical solutions on the ELI-NP CSC operation 26 New findings of the thesis • A reliable empirical parametrization for calculating production cross-sections (yields) of neutron-rich fragments from photofission process is proposed It will be used not only at ELI-NP but also at other photofission facilities for estimating the yield of neutron-rich nuclei, designing experiment setup and many other applications • A Geant4-based code has been implemented The highlight of the implementation is the construction of a process for simulating the photofission with Geant4 • An extensive set of simulations, which were done with this code, has established the optimization of CSC’s parameters, as well as those of the target configuration inside The optimal target geometries at two locations of the CSC have been deduced, providing the maximum release rates in the range of 106 to 107 photofission fragments per second for the gamma beams at ELI-NP 27 Publications Publications: P Constantin, D.L Balabanski, L.T Anh, P.V Cuong, B Mei, Design of the gas cell for IGISOL at ELI-NP, Nucl Instr and Meth B 397 (2017) 1-10 B Mei, D.L Balabanski, P Constantin, L.T Anh, P.V Cuong, Empirical parametrization for production cross sections of neutron-rich nuclei by photofission of 238 U at low energies, Phys Rev 96 (2017) 064610 B Mei, D.L Balabanski, P Constantin, L.T Anh, P.V Cuong, Production of neutron-rich nuclei approaching r-process by gamma-induced fission of 238 U at ELI-NP, EPJ Web of Conferences 178, 04009 (2018) Conferences: L.T Anh, Geant4 Simulation of the Exotic Nuclei Production in a Gas Cell, The International Symposium on Physics of Unstable Nuclei 2017 (ISPUN17), Halong City, Vietnam, September 25 – 30, 2017 ... Luận án bảo vệ trước Hội đồng chấm luận án tiến sĩ, họp Học viện Khoa học Công nghệ Viện Hàn lâm Khoa học Công nghệ Việt Nam vào hồi … …’, ngày … tháng … năm 2021 Có thể tìm hiểu luận án tại: ... gamma beam The ELI- NP project consists of two main experimental areas: the ELI- NP High-Power Laser System (HPLS) and Gamma Beam System (GBS) Fig 1.1 expresses the sketch of ELI- NP machines and... the production of RIB at ELI- NP Meanwhile, by using thin targets, the IGISOL method can be used for the production of RIB in the refractory region Therefore, at ELI- NP an IGISOL facility will be