(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

STUDY ON PARAMETRIZATION OF PHOTOFISSION CROSS-SECTION OF 238 U AND OPTIMIZATION SIMULATION USING GEANT4 FOR DESIGN OF THE IGISOL FACILITY

Công trình được hoàn thành tại: Học viện Khoa học và Công nghệ -

Viện Hàn lâm Khoa học và 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

Có thể tìm hiểu luận án tại:

- Thư viện Học viện Khoa học và Công nghệ

- Thư viện Quốc gia Việt Nam

for photofission facilities worldwide, and ELI-NP is one of them Moreover, It is important to

do series of prerequisite calculations and simulations to lead to the conceptual design for theparticular case of the CSC at ELI-NP IGISOL facility

2 The aim of the thesis

The works in this thesis aim to fulfill two goals: i) the first one is to develop a reliableempirical parametrization for the calculation of photofission cross-section over a wide energyrange below 30MeV ii) The second one is to implement a Geant4-based code and carry out aseries of simulations to optimize the design of CSC at ELI-NP

3 Main research content of thesis

• General overview of the ELI-NP project, photofission process, methods for production ofradioactive ion beam, Geant4 simulation toolkit and its application fields

• Construct the empirical parametrization for total cross-section, mass yield and isobariccharge distribution of 238U photofission

• Prediction of neutron-rich nuclei yield

• Implement the photofission process into Geant4 Within this thesis, a Geant4-basedcode was developed for the simulation of photofission, inverse Compton backscatteringprocesses, 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 stoppingcell for IGISOL facility at ELI-NP

Chapter 1.OVERVIEW1.1.The Extreme Light Infrastructure Nuclear Physics facility

The Extreme Light Infrastructure (ELI) is a Research Infrastructure of Pan-Europeaninterest 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 mainexperimental 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

in the range from 200 keV to 19.5 MeV with a bandwidth of ≥ 0.3% will be produced byELI-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 showsthe geometry of the CBS between a laser photon EL energy, incident at angle θL respect to theelectron 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 gammabeam displayed with blue dots has the energy range 10 − 18.5 MeV It was obtained by using

in Fig 1.3 presents the pencil beam with the narrow energy range around 12.9 MeV The pencil

Bases on such kinds of gamma beams, ELI-NP GBS will provide the following iments such as The Nuclear Resonance Fluorescence (NRF), Experiments above the NeutronSeparation Threshold, and Photofission experiments and the production of RIB

exper-1.2.Methods for production of RIB

To address which method is suitable for producing RIB at ELI-NP, the details of eachmethod will be discussed as following

1.2.1.The ISOL technique

In the ISOL technique, the radioactive ion beams are produced via light-ion-inducedspallation or fission of a thick actinide target The fission reactions can be induced by thermalneutrons, fast neutrons, protons or photons This method requires a high intensity of theprimary beam and a thick hot target The great advantage of the thick targets is a large num-ber of target atoms available for the production of the ions Even for such exotic nuclei withextremely low production cross-sections can still be obtained However, short-lived isotopescannot be obtained because of the time required for diffusion and effusion Another disadvant-age with ISOL production is that it is difficult to achieve high beam purity due to the manyisobars of different elements produced simultaneously in the target Furthermore, refractoryelements are in general difficult to produce due to the high temperatures required to make themvolatile, 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 thismethod, 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 LaserSystem; OPCPA: Optical Parametric Chirped Pulse Amplification; XPW: Cross Polarised Wavesystem; LBTS: Laser Beam Transport System; GBS Gamma Beam System; DPSSL: DiodePumped Solid State Laser; E1-E8 Experimental areas.

Figure 1.2: Geometry of the inverse Compton scattering of a laser photon on a relativisticelectron

light elements such as carbon and beryllium was used for the production of RIB The thintarget allows the fragments to release from the target surface still at very high velocity andforward momentum which is exploited for mass separation and study or further reactions Anadvantage of this method, which is opposite to ISOL technique, is that the production of theRIBs is independent of the chemical properties of the element Moreover, isotopes with veryshort 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 fromthe production process Since the intensities of the heavy-ion beams are generally lower thanthat of the light-ion beams used for the ISOL method, the yields of some exotic fragments mayalso 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 targetinto 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 broadbeam up to 18.5 MeV collimated below 0.7 mrad (blue) and a pencil beam up to 12.9 MeVcollimated 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 ofthe 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 issimilar 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 celland 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 toobtain the highest release efficiency The range, for instance, is of the order of 1 mg/cm2 forfusion-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 incidentparticle will be gamma Therefore, as mentioned in subsection 1.2.2, the In-flight method is notsuitable The ISOL method seems to be usable for the incident particle of gamma However, atELI-NP, the RIB will be dedicated to studying the exotic neutron-rich isotopes in the Zr-Mo-Rhregion which is the refractory elements As shown in Fig 1.6, Zr-Mo-Rh region has a very highboiling 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 withinthe accelerator hall The length of the hall is approximately 90m There will be two foreseeninteraction points: one at E=300 MeV of electron energy and one at E=720 MeV of electronenergy respectively identified as Low and High energy Interaction Points The gamma beamused for photofission to produce RIB at the IGISOL facility will come from the latter one

the CBS gamma beam Main components of ELI-NP IGISOL include CSC and the collimatorwhich are installed along the beamline The 238U targets will be placed inside CSC filled withHelium gas The fission fragments will be extracted and delivered to measurement stationsthrough 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 belocated 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-energyinteraction 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 thehigh-energy interaction point

A series of simulations have to be done to answer what are the optimal number, ing angle, thickness, dimensions and spacing of the uranium targets to obtain the highestintensity of RIB Within this thesis, the Geant4 simulation toolkit is used for this task

tilt-1.4.Introduction of Geant4 toolkit

Geant4 which is based on the Monte-Carlo method is a toolkit dedicated to simulatingthe 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 andmedical physics

Geant4 is chosen because it provides users with many models for simulating the portation of particles in matter In our case, the simulation of photofission fragments traveling

trans-in targets and gas will help optimize the design of CSC However, the photofission process isnot available in Geant4 Therefore, a new Geant4 process has to be implemented for handlingphotofission To do 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 method1.5.Photofission process

In 1939, Bohr and Wheeler introduced a theory to explain the mechanism of the nuclearfission process The theory showed that fission should occur when a heavy nucleus, whichlocates well beyond the minimum of the packing faction curve, is given sufficient excitation

either particle capture (n,p,e ) or gamma absorption Photofission process is defined as theprocess in which a nucleus undergoes nuclear fission and splits into two or more fragmentsafter absorbing a gamma-ray The reaction is first observed in 1940 by Haxby et al byirradiating uranium and thorium with high intensity γ-rays of 6.3 MeV from fluorine Sincethen, photofission reactions, and in particular low energy photofission reactions, have beenwidely investigated These photofission studies are very important not only for understandingthe photofission mechanism but also for exploring nuclear structure effects

Recently, there has been growing interest in photofission, because it provides one of themost 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 respectivelyidentified as Low and High energy Interaction Points.

by these statistical fission models can be very time consuming, a fast and accurate empirical

low energies is particularly useful Recently, an empirical parametrization , based on the massyields measured at the average photon energy of 13.7 MeV , has been proposed to calculateproduction cross-sections of fragments produced by photofission of 238 U at 13.7 MeV How-ever, this parametrization cannot be used to describe the mass yields at other energies below 30MeV, especially for the fission modes with a strong energy dependence such as the symmetricmode, according to the mass yields measured at different excitation energies Thus, there is aneed to develop a reliable empirical parametrization for the above mentioned applications

σ(A, Z) = σf(Eγ) Y (A, Z)/100 (2.1)

σf(Eγ) is the photofission cross section at an incident photon energy Eγ and Y(A,Z) representsthe independent yield per 100 photofission events In the following, details of different terms

in Eq 2.1 will be discussed separately

2.1.1.Parametrization for total Cross-section

In the present work, the energy range is increased and 238U photofission cross sectionsbetween 5.93 and 30 MeV (above the fission barrier) are parametrized by the sum of two Lorentzfunctions:

2.1.2.Parametrization for photofission mass yield

Based on the multimodal fission model, the mass distribution of photofission fragmentscan be written as a sum of contributions from three different fission modes, namely, one sym-metric mode (SM) and two asymmetric modes (ASMI and ASMII) Therefore the total yield

of photofission fragments with a given mass number A (per 100 photofission events) can be

Figure 2.1: The 238U photofission cross sections measured by Caldwell et al., Ries et al., andCsige et al., as a function incident photon energy The relative uncertainty is less than 20% formost of the measured data The full line indicates calculations by the parametrization used inthis work based on Eqs (2.2) and (2.3), whereas the dotted line represents a fit of Eq (2.2) tothe measured photofission cross sections

Table 2.1: The values of constants used in the empirical parametrization for 238U photofissiontotal cross-section

described by the sum of five Gaussian functions:



(2.4)The amplitude of the symmetric mode is parametrized as:

end-point energies 12, 19.5, 29.1, and, 70 MeV The corresponding average photon energies are (a)9.6, (b) 11.9, (c) 13.7, and (d) 17.2 MeV The full lines indicate fits by Eq (2.4) The sym-metric mode (SM) (dash-dotted lines) as well as the asymmetric modes ASMI (dashed lines)and ASMII (dotted lines) are also shown.

The parameterized values are shown in Table 2.2

2.1.3.Parametrization for isobaric charge distributions

After the mass yield has been determined, one can calculate the independent yield of thephotofission fragment with the given A and Z (per 100 photofission events) with the following

where the isobaric charge distribution of photofission products with a given mass A is

fragments with a given mass A, while Cp indicates the width of the charge distribution for theisobaric chain The mass yield Y(A) is calculated by Eq (2.4)

number Nprob = 82, which is due to the strong impact of the closed neutron shell 82

be derived from the liquid drop model mass formula:

2/3)/(2x)]

The width parameter Cp in Eq (2.8) is found to be almost constant, Cp = 0.85

The values of various constants used in the above equations are listed in Table 2.3.2.2.Validation of the empirical parametrization

238U photofission experiments at different average excitation energies with the calculations byour parametrization is shown The calculated elemental yields are in excellent agreement withthe two experimental data within the uncertainties

To continue the validation of our work, the mass yields measured in inverse ics at two different projectile energies via the virtual photon induced fission of 238U are also