Structure of Mass-Yield Distributions of 232 Th Photofission Product by Bremsstrahlung at Energy 17.5 MeV

Relevance . One of the most promising areas for studying the fission process is to investigate its features under the action of photon radiation, since the interaction of gamma quanta with the nucleus is completely electromagnetic with well-known characteristics. Information on the yields of 232 Th nuclear photofission products is of particular interest from the standpoint of experimental and theoretical studies. The nucleus of this element is located on the border between pre-actinides and light actinides. Purpose . The purpose of this study is to experimentally investigate the structure of the mass distribution of yields of 232 Th photofission products at a bremsstrahlung energy of 17.5 MeV (energy close to the threshold of the first-chance fission, where experimental data are not available). Methods . 232 Th photofission response was simulated on the electron accelerator of the Institute of Electron Physics NAS of Ukraine – M-30 microtron. The bremsstrahlung spectrum was modelled for the case of electron interaction (E=17.5 MeV) with a tantalum converter (1 mm) using the GEANT4 code 10.7. Yields of 232 Th photofission products were measured by gamma-ray spectrometry. The yields of 232 Th photofission products were modelled using the GEF 2020 / 1.1 and Talys 1.95 codes. Results


Introduction
One of the promising areas of studying the fission process is the investigation of the distribution of the yields of fission products under the action of photons, since the nature of such interaction is well-known (it is completely electromagnetic) [1], and allows obtaining fission nuclei with low excitation energy immediately after their absorption.The use of bremsstrahlung photons formed on electron accelerators allow conducting studies in the low-energy range (where the features of the influence of nuclear structure and dynamics on nuclear fission are clearly manifested [2]) and obtain experimental data on the dependence of the mass and charge distributions of photofission products on the excitation energy of fission nuclei.
Existing estimated experimental data for a wide range of nuclei [3] indicate the presence of a fine structure in the mass distributions of photofission product yields [4].The fine structure is manifested in increased yields of heavy fission products (localised around and near masses 133-134, 138-140, and 143-144) and complementary light yields of fission products [4], which is associated with such an influence of the nuclear structure as the effect of proximity to closed nuclear shells and the odd-even effect [2; 4].
Of particular interest in terms of experimental and theoretical studies is information on the yields of products (post-neutron) of the 232 Th nuclear photofission, which is located on the border between pre-actinides ( 88 At, 89 Ra) and light actinides ( 91 Pa, 92 U) [5; 6].In low-energy fission of isotopes from 221 Th to 230 Th, there is a transition from symmetric to asymmetric fission [7], which is associated with the different probability of development of symmetric and asymmetric fission channels and their influence on the development of mass distributions of fission product yields [2].
Another reason for this interest is the widespread application of the photofission reaction of thorium nuclei [8][9].Information on the yields of thorium isotope fission products under the action of high-energy photons and fast neutrons plays an important role in the development of a new generation of power generating systems, namely: fast neutron reactors (fuel cycle 232 Th -233 U), reactors with accelerators (controlled subcritical systems) [8; 9], as well as for the development of non-destructive methods for isotope analysis of fertile (non-fissionable by thermal neutron) nuclear materials [10].The above-mentioned applications of the Thorium photofission process also require reliable yield information for a wide range of fission products.
Therefore, in terms of obtaining new experimental results and developing new theoretical approaches (models) to describe the of mass distributions of yields of 232 Th nucleus photofission products, as an object of research, is of particular interest.
The purpose of this study is an experimental study of the structure of the mass distribution of yields of 232 Th photofission products at the maximum bremsstrahlung energy of 17.5 MeV and comparison with the simulation results using modern GEF and Talys calculation codes.

Theoretical Overview
Detailed analysis of existing experimental data indicates the presence of a fine structure in the mass distributions of asymmetric yields of 232 Th nuclear photofission products for the region of bremsstrahlung photon energies (E γmax ) from 6.5 to 80 MeV, which corresponds to the range of excitation energies (E * ) from ~6 to ~22. 5 MeV [11], where there are possible probabilities of "multi-chance fission" reactions [12][13][14], that is, as emission-free ( 232 Th (γ, f) 232 Thfirst-chance, and fission with pre-emission of one and two neutrons ( 232 Th (γ, nf) 231 Th * -second-chance [6; 7]; 232 Th(γ, 2nf) 230 Th * -third-chance).At high energies (above the threshold of (γ, f) -reactions), competition occurs between fission processes and neutron emission.After neutron evaporation, the excitation energy of the nucleus decreases due to the binding energy and kinetic energy of the released (evaporated) neutron, which affects the final values of product yields and, accordingly, the fine structure of mass distributions [12][13][14].
To estimate the boundaries of the energy region where emission-free photofission occurs and with preliminary neutron emission, calculations are made of the probability dependence of the relative contribution of individual chances (the first -without preliminary neutron emission, the second -with the emission of one neutron, and the third -with the emission of two neutrons) on the excitation energy for the fission of the 232 Th * nucleus using the GEF Code [15;16].The results of the calculations are presented in Figure 1.It is established that the threshold of (γ, nf)-reaction upon 232 Th photofission exceeds ~ 11.5 MeV, which is consistent with the results of modelling the contribution of the reaction cross-sections along the (γ, f) and (γ, nf) channels to the total reaction cross-section of (γ, F) photofission of the 232 Th nucleus as a function of the excitation energy E * , conducted in [17; 18] by the Talys calculation code [19] (Fig. 2).Notably, upon fission with an excitation energy E * >11.5 MeV, a "mixture of fission nuclei" is developed, the components of which are present in all yields of fission products.Existing (or modern) experimental methods do not allow separating the yields of products from simultaneously developed fissile nuclei without and with preliminary neutron emission.Therefore, it is important to investigate the energy region near the first-chance fission threshold, where experimental data are not available (E * >11.2 (E γmax =16) [11] and E * <12.4 (E γmax =20) MeV [20]).Existing experimental data set [21] on product yields for a fission core 232 Th at E * ~ 11.28 MeV (E γmax =17.5 MeV) describes only the shape of the mass distribution curve of the yields, but does not allow drawing a conclusion about its structure due to the limited number of fission products studied.

Materials and Methods
Determination of relative cumulative yields of 232 Th photofission products was performed by semiconductor gammaray spectrometry [22; 23].The studied value during measurements is the counting rate in peaks of total absorption (or peak intensity) of gamma quanta from individual fission products, which depends on its activity, absolute measurement efficiency, self-absorption corrections, and gamma line intensity.

Simulation of the fission target activation process
When conducting experimental studies, 232 Th metal foil was used (in the amount of 5 samples, diameter -12 mm, thickness -2 microns), the mass of which was in the range of 209 ÷ 281 micrograms.The targets were manufactured at the V.G.Khlopin Radium Institute (Saint Petersburg, Russia) in 1981.To accumulate photofission products during activation, 0.1 mm thick aluminum foil collectors were used, which were installed close to the 232 Th fission targets.Irradiation of a fissible assembly (which consisted of 232 Th disks and collector layers) were performed on an electron accelerator of the Institute of Electron Physics of the National Academy of Sciences of Ukraine -an M-30 microtron (electron energy E=17.5 MeV, average beam current ~ 4 µA) [14].The instability of the electron energy during target irradiation did not exceed 0.04 MeV.
To generate bremsstrahlung, a tantalum converter was used (thickness -1 mm), located at a distance of 22 mm from the output window (Ta, thickness -50 microns) of the electron output unit.The fission assembly was installed perpendicular to the beam axis at a distance of 50 mm from the Ta converter.The irradiation time of the fission assembly varied from 30 to 210 minutes.The choice of time parameters (irradiation, cooling, and measurement times) was made considering the half-lives of the studied photofission products and their precursors (the so-called "parent" products) along the isobaric chain.
The GEANT410.7 computing code was used to simulate the spectra of bremsstrahlung photons, residual electrons, and photoneutrons (depending on the energy normalised per electron) [24].The input parameters used in the calculations almost completely reproduced the geometric dimensions (design features) of the electron output unit and the activation schemes of fissile nuclei, which was implemented on an electron accelerator -the M-30 microtron.
The simulation considered the geometric dimensions of the original electron beam: the shape -an ellipse, the dimensions of the semi-axes -11 mm and 3 mm).Calculations were performed for 10 9 (10E9) electrons in the initial beam on two computers with 4-and 12-core Intel(R) Core(TM) processors i7-9750HCPU@2.60GHz and 36 GB and 16 GB RAM.
As a result of the simulation, the total number of photons, residual electrons, and photoneutrons normalised per electron hitting a fission target was calculated: 0,08128 photons (with an energy of 6 MeV, involved in stimulating the photofission reaction -0,01179); -0,01602 electrons and ~10 -5 neutrons.Residual electrons and photoneutrons /10

Gamma-ray spectrometric studies of 232 Th photofission products
that fell on the fission assembly did not affect the results of the experiment.
The calculated spectrum of bremsstrahlung photons is presented in Figure 3, where the 232 Th (γ, f) reaction cross-section is additionally provided [25], which was used to calculate the average excitation energy of a fissible nucleus [11].Value of the average excitation energies of a fissible 232 Th * nucleus was 11.28 MeV.At the end of the accumulation of fragments, aluminum collectors measured their gamma activity for from 0.25 to 381 hours after the end of irradiation.The duration of individual measurements varied from 0.5 to 6.5 hours.For the research, spectrometric complexes based on semiconductor detectors were used: HPGe (Ortec) and Ge (Li), the volumes of which were 150 and 100 cm 3 with an energy resolution of ~ 2.45 and ~ 3.5 keV for the line 60 Co (1,332.5 keV).When studying the relative cumulative yields of fission products, the final error of the obtained results is primarily affected by the error value of the measured energy efficiency of the detector [13].

Ephoton, MeV
The energy dependence of the peak efficiency of gamma-ray quantum registration was determined using a set of standard certified point sources 22 Na, 57 Co, 60 Co, 109 Cd, 133 Ba, 137 Cs, 151 Eu, 241 Am (produced by D.I. Mendeleev Institute for Metrology, Saint Petersburg, Russia).Additionally, the detectors were calibrated using gamma radiation from the products developed in the 238 U (γ, f) reaction stimulated by bremsstrahlung with an energy of 17.5 MeV, and accumulated in aluminum foil [26], which allowed substantially simplifying the measurement process and consider the real geometry.The value of the statistical measurement error during the calibration procedure did not exceed 4%.
Gamma-ray spectra from photofission products were measured in real time.The dead time of the spectrometer did not exceed 8% during all measurements.During the measurements, the drift of the energy scale, resolution and recording efficiency of the spectrometric complex were constantly monitored using point standard gamma-active sources 57 Co and 60 Co.The drift of these parameters did not exceed 1%.Spectroscopic information was processed using the Winspectrum software package [27].Fission fragments were identified by the energies of their characteristic gamma lines, considering their half-lives and measurement, accumulation, and cooling times.Additionally, the half-lives of their predecessors along isobaric chains were considered.The values of nuclear spectroscopic data of the identified fission products (energies and intensities of gamma lines, half-lives of the formed products and their precursors along the isobaric chain) were taken for calculations from the NNDC nuclear data library (USA) [28].
The statistical error of measurements of the peak intensity of gamma product lines used in the analysis did not exceed 3÷5% for the entire time interval of measurements.Cumulative yields were determined relative to the yields of the 132 Te reference product.
The total error of relative cumulative yields was estimated considering statistical errors of peak intensity of gamma product lines, analysis of time dependencies, spread of values averaged over individual measurements, as well as errors of interpolated efficiency values and nuclear physical constants (energy and intensity of gamma lines, half-lives of products).The total error in determining the relative cumulative yields of fission fragments did not exceed 8÷10%.
From the measured relative cumulative yields of fission fragments Y R and calculated values Z P relative total yields of fission products were determined Y RT (A), and summarised on all mass chains [29]: where Y RT (A) is the total relative cumulative yields of the mass chain A; Y R is the relative cumulative yield of a fragment with an atomic charge Z and a mass number A; Z P is the most probable charge; C is the distribution width parameter (C=0.6 [11]).
To calculate the most probable charges Z P for individual chains of isobar nuclei, the study used the values of the dependence of the yield of prompt neutrons on the mass A of light and heavy fragments ν L.H and average values of the total neutron yield ν tot calculated using semi-empirical formulas [30] and using GEF [16] a = 85; 88; 89; 91; 92; 94; 95; 97; 99; 101, heavy products: a = 131; 132; 133; 134; 135; 138; 139; 140;141; 142; 143; 146) were obtained from the aggregate cumulative yields of fission products using corrections for the charge distribution of fragments.
The results obtained and the analysis of existing data indicate a stable presence of a fine structure of the mass distributions of 232 Th photofission products localised for heavy fragments in the vicinity of masses 133-134, 138-139, and 143-145, for the energy region near the threshold of the first-chance fission (11.2 (E max =16) <E*<12.4(E γmax =20) MeV).The simulations performed using the calculated GEF and Talys1.95codes describe and predict the structure of mass distributions for a fissible 232 Th * nucleus at an average excitation energy of ~ 11.3 MeV.
Structure of mass-yield distributions of 232 Th photofission product by bremsstrahlung…

Figure 1 .
Dependence of the relative contribution of individual chance upon 232 Th * fission from the excitation energy Source: the data obtained by the authors of this study (squares -1 st ; circles -2 nd ; triangles -3 rd -chance fission)

Figure 3 .
Photon/electron and Talys 1.95 codes [19].The obtained value ν tot (parameter) =2.54 [30], corresponds to the value ν tot (ENDF) =2.41 from the base of estimated nuclear data ENDF [25] within error of ~ 5%, and with values of ν tot (GEF) = 2.75 [16] and ν tot (Talys) =3.03 [19] within of error < 10% and < 20%, respectively.The calculated dependences of neutron yields on the mass of light and heavy fragments ν L.H upon 232 Th photofission were used to find Z P .Relative total yields Y RT (A) of the resulting fission products summed over all mass chains, normalised to a total yield of 200% to calculate the absolute yields of mass chains Y(A).Experimental values of total yields of light and heavy 232 Th photofission products at a maximum bremsstrahlung photon energy of 17.5 MeV are represented in Figure 4 by dark squares (light -a, heavy -b).Circles represent yields of fission products at an energy of 16 MeV [11], triangles -yields fission products at an energy of 20 MeV [20].The presented experimental data are consistent with each other within the experimental errors for the energy region E γmax from 16 to 20 MeV (near the threshold of the first-chance fission).At the same time, the measured values of the yields of fission products in this paper and in [21] within experimental errors are consistent with each other.Figure 4 also presents the yields of fission products for a 232 Th * fission nucleus at an excitation energy of ~ 11.28 MeV, calculated by the GEF code [16] (solid curve and Talys 1.95 code [19] (dashed line), which describe the dependences of product yields on the mass of fragments in general terms and predict their structure.In the resulting mass distribution of yields of 232 Th photofission products, a certain structure is observed (for heavy fragments, the yield of fission products around mass numbers 133-134, 138-139, and 143-145 is increased), which is associated with the influence of asymmetric fission channels on the development of mass distributions, which, in turn, depend on the nuclear structure (the effect of proximity of closed nuclear shells and the odd-even effect) [2; 4; 11; 15].