Preamble

Measurement and calculation of transmission neutron spectra from U induced by broad-spectrum neutrons Hui Sun, 1, 2, Xin Zhang, Zhi-Qiang Chen, 1, 2, 3 Rui Han, 1, 2, 3, Bo Yang, Shakhboz Khasanov, Pei-Yan Zhang, Guo-Yu Tian, Bing-Yan Liu, Fu-Dong Shi, Ze-Kun Zhang, Qin Li, and Peng Luo 1, 2, 3 1 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China Gansu Isotope Laboratory, Lanzhou, 730300, China School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China Samarkand State University, Samarkand 140104, Uzbekistan Transmission neutron spectra from a pure U slab sample (dimensions: 100 mm 100 mm 20 mm) bombarded by broad-spectrum neutrons were measured at 0° using the time-of-flight method. The experiment was carried out at the Radioactive Ion Beam Line of the Heavy Ion Research Facility in Lanzhou at the Institute of Modern Physics, Chinese Academy of Sciences. Broad-spectrum neutrons were generated by bombarding a tungsten target with 80.5 MeV/u C ions. Additionally, calculations were performed in GEANT4 with the INCL, BIC and BERT physics models, in combination with the evaluated nuclear data libraries ENDF/B- VIII.0, JEFF-3.3, and JENDL-4.0, and the theoretical results for the transmission neutron spectrum of the were obtained under the same experimental conditions. The results indicate that the GEANT4 calculations can reasonably reproduce the experimental data.

Keywords

Transmission neutron spectra, U, Broad-spectrum neutrons, GEANT4

INTRODUCTION

The Accelerator-Driven System (ADS) is a coupled sys- tem comprising a subcritical reactor and an external proton accelerator[ The system possesses strong transmuta-

tion capabilities, significant neutron economy and reliable 5

safety performance. Not only can it convert spent nuclear fuel into short-lived isotopes, but it also has the potential to both proliferate nuclear fuel and generate electricity in an efficient and sustainable manner[ ]. Therefore, the ADS exhibits favorable energy economics and is an important re- search area within the field of nuclear energy[ advancement of ADS is currently at a critical stage of tech- nological advancement[ ], necessitating substantial support from nuclear data resources[ ]. In the ADS, the sec- ondary neutrons generated by beam-induced spallation reac- tions are characterized by high flux and broad energy spec- trum. These neutrons not only serve as the primary driver for spent fuel transmutation, but the transmitted neutrons also constitute the most critical radiation source term in shielding design. Therefore, investigating neutron transport processes in relevant materials is crucial for the design of core structure, target-core coupling, and radiation shielding. Monte Carlo codes based on established physical models and evaluated nuclear data libraries are fundamental tools for conducting neutron transport simulations. The iterative optimization of subcritical system parameters—including geometric configu- Supported by the National Natural Science Foundation of China (No.U1832205, 12005265 and 12305150) First author, H. Sun, No. 509, Nanchang Road, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu Province, China, R. Han, No. 509, Nanchang Road, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu ration and material selection—using accurate physical mod-

els and evaluated databases is of significant importance for 28

enhancing neutron yield and utilization efficiency, reducing neutron loss, improving neutron flux management in subcriti- cal cores, accurately predicting core temperature distributions under various operational conditions, and achieving optimal radiation protection. 238 U is a critical nuclear material for ADS, and the neu- tron transport nuclear data of U form an important foun- dation for both the ADS and advanced nuclear fuel cycle

systems[ 17 – 20 ]. However, significant discrepancies exist 37

among the evaluated neutron data for U within the energy range below 20 MeV, and such data are notably scarce in the medium and high-energy ranges[ ]. At present, the ex- isting neutron evaluation data for U are difficult to directly apply under the complex conditions of high neutron flux and broad energy spectrum encountered in ADS. Therefore, there is a critical need for detailed and reliable experimental mea-

surements as well as theoretical calculations concerning the 45

relevant nuclear data of the interaction between medium- and high-energy neutrons with U is an extremely criti- cal nuclear material for the Accelerator-Driven System. The content of U in spent nuclear fuel is more than 95 percent, and the proportion of reactions involving spallation neutrons U within the reactor core is high, and these reactions are notably complex. The neutron transport processes in serve as an essential basis for ADS[ ]. After capturing a neutron, U can be transformed into a fissionable nuclide,

239 Pu (

U + n Pu fissile)[

The recycling of 238 U through the uranium-plutonium cycle 56

plays a significant role in enhancing the disposal capacity for 57

spent nuclear fuel and promoting the efficiency of the nuclear fuel cycle. This is also an important means to achieve the sus- tainable development of nuclear fission energy. In addition, the complex reactions between broad-spectrum neutrons and 238 U will affect the neutron characteristics in the spallation target region.

U target In conclusion, accurate and reliable experimental mea- surements of nuclear data related to broad-spectrum neutron transport in U targets, combined with systematic compar- isons with Monte Carlo simulations based on different phys- ical models and evaluated nuclear data libraries, provides an effective approach for validating the applicability and relia- bility of Monte Carlo codes in ADS design. This work fills a gap in the studies of high-energy neutron transport for the 238 U target. It serves as a critical safeguard for ensuring the safety of ADS design, construction, and subsequent opera- tion and maintenance, as well as an indispensable component of ADS development. Therefore, reliable experimental and calculation studies on the neutron transport process of are required.

In this work, we utilized C + W as the neutron source.

The transmission neutron spectrum is measured by time-of- flight method, by bombarding the U sample target with broad-spectrum neutrons.

Moreover, this study employs GEANT4[ ] to simulate the experimental process in com- bination with the INCL++[ ], BIC[ ] and BERT[ physical models and the ENDF/B-VIII.0[ ], JEFF-3.3[ and JENDL-4.0[ ] evaluation databases.

METHODS

Experimental methodology The experiment was carried out at the Radioactive Ion Beam Line in Lanzhou (RIBLL)[ ], using an 80.5 MeV/u C primary beam. The beam operates in continuous- wave mode, delivered by the Heavy Ion Research Facility in Lanzhou (HIRFL)[ ], located at the Institute of Modern Physics, Chinese Academy of Sciences. perimental device. In this work, the broad-spectrum neutrons generated by this setup served as source neutrons, interacting with a U target sample. The resulting transmission neutron spectrum was then measured. The C ions were accelerated to an energy of 80.5 MeV/u and focused onto a natural tung- sten cylinder target (dimensions: 50 mm 5 mm). The

tungsten target was attached to the exit window, which was made of a 3-mm-thick iron plate at the end of the vacuum chamber. The bombardment of the tungsten target by the beam generates a large number of secondary particles, includ- ing neutrons, gamma rays, protons, deuterons, tritons, and 3 He nuclei. These secondary particles can penetrate through the target medium and the surrounding air, allowing their sig- nals to be detected by the detectors (EJ212 and BC501A). for the transport of broad spectrum neutrons in the U tar- get (dimensions: 100 mm 100 mm 20 mm; thickness

along the neutron penetration direction: d = 20 mm; purity: 112

p = 99.9 %; density: ρ = 18.79 g/cm 3 ). In this experiment, 113

the time-of-flight method was employed to measure the trans- mission neutron spectrum. As shown in the figure, the ex- perimental device is largely consistent with that of the neu- tron source facility (Fig. ). The difference is that the plas- tic scintillation detector (Veto) and the U target are placed on the outer side of the vacuum chamber. The Veto is used to remove the effects of charged particles on the transmis- sion neutron spectrum during data analysis. The beam pickup detector (TP, a plastic scintillator detector) positioned within the vacuum chamber is located 67 cm upstream of the tung-

sten target. During the experiment, the TP served to monitor 124

beam parameters, provide timing information for the beam and count incident particles, while also acting as the stop sig- nal for neutron time-of-flight measurements. Additionally, 12 C ions were fully deposited in the primary target (tung- sten target), with their range calculated using LISE++ being equal to 1.912 mm. In this experiment, the detection system consisted of an EJ212 plastic scintillator detector (Veto) and a BC501A liquid scintillator detector (N1). This system al- lowed effective discrimination between charged and neutral particles. After removing signals due to charged particles,

the remaining spectrum enabled differentiation between neu- 135

tron and gamma signals detected by the liquid scintillator via pulse shape discrimination (PSD), as shown in Fig. . The BC501A liquid scintillator detector primarily consists of a cylindrical liquid scintillator crystal, an optical collection sys- tem, a photomultiplier tube, and a voltage divider. The liquid scintillator crystal inside the BC501A probe has a diameter and length of 12.7 cm each, a maximum emission wavelength of 425 nm, and an emission decay time of approximately 3.2 ns. The EJ212 plastic scintillation detector is a rectangular cuboid with dimensions of 12.7 cm 12.7 cm 5 mm and has a square cross-section facing the incident beam direction.

Its distinguishing characteristic is a very low probability of interaction with neutral particles, while it exhibits high sensi- tivity to charged particles.

B. Electronics and data acquisition 150

data acquisition system employed in the neutron transport ex- periment for U. As shown in the figure, the signal from the beam pickup detector (TP or BM) located in the target cham- ber is divided into four channels. The signal from Channel 1 is fed into a Charge-Integrating Digital Converter (QDC) to record beam energy information. The signal from Channel 2 is processed by a Constant Fraction Discriminator (CFD) and then fed into a Time-to-Digital Converter (TDC) to serve as the stop signal for neutron time-of-flight measurement. The signal from Channel 3 passes through the CFD and enters the

Scaler. The signal from Channel 4 is processed by the CFD

and then directed to a Logic Coincidence Unit (Coin), where 163

it is used in coincidence with the output signal from the neu- tron detector to identify true nuclear reaction events. This coincident signal is subsequently sent to the Scaler and also

serves as the electronics trigger signal (Trigger) for the en- 167

tire experiment. Signals from the plastic scintillator detectors (Veto1 and Veto2) are directly input to the QDC for remov- ing charged particle events during data analysis. The output signal from the liquid scintillator detector (BC501A) is split into three channels as illustrated: The Channel 1 signal is pro- cessed by the CFD and then fed into the TDC to serve as the start time for neutron time-of-flight measurement; The Chan- nel 2 signal is used for fast/slow component discrimination in the QDC; The Channel 3 signal passes through the CFD and

is then input to the coincidence unit for coincidence measure- 177

ment with the BM signal. Monte carlo calculation GEANT4 is a versatile Monte Carlo software toolkit for the calculation of the passage of particles through matter. It is widely used across various fields, including high-energy physics, accelerator physics, astrophysics and space science, medical physics and radiation protection. GEANT4 provides a variety of physical models describing the interaction be- tween particles and nuclei, along with comprehensive lists of

associated models for users to utilize, such as BERT (Bertini 187

intranuclear cascade model), BIC (Binary cascade model), INCL++ (Intranuclear cascade liege). BERT integrates the

Bertini intranuclear cascade model, pre-equilibrium model, 190

fission model, and evaporation model. It is capable of sim- ulating nuclear reactions induced by long-lived hadrons and gamma rays with energies up to 10 GeV. BIC simulates the cascade transport process of primary and secondary particles within the nucleus. It only considers the two-body interac- tions between primary or secondary particles and individual nucleons within the nucleus. INCL++ is applicable for sim- ulating particle bombardment of target nuclei heavier than deuterium within the energy range of 1 MeV/u to 20 GeV/u.

However, its applicability to light and unstable nuclei has not yet been comprehensively validated.

In order to verify the reliability of GEANT4 in the trans- port calculation process, this study employs "Geant4-10.7.4" to simulate the experimental process in combination with the INCL++, BIC and BERT physical models and the ENDF/B- VIII.0, JEFF-3.3 and JENDL-4.0 evaluation databases. The resulting transmission neutron spectra are obtained under the same experimental conditions.

DATA ANALYZING PROCEDURE Neutron energy calculation The time-of-flight (TOF) method for measuring neutron energy spectra is based on the principle that neutrons with different energies require different amounts of time to travel

the same distance. It is a measurement technique that calcu- 214

lates neutron energy based on the known flight distance and corresponding travel time, and it is now widely used in neu- tron experiment measurements[ ]. In this experiment, the flight distance is defined as the distance between the center of the target sample and the geometric center of the detector. It should be noted that since the beam pickup detec- tor is positioned at a certain distance upstream from the target, the time difference between the trigger signal and the stop sig- nal cannot be directly used as the neutron time of flight. The actual neutron time of flight is obtained by taking the time difference between the neutron peak and the gamma peak in the TOF spectrum, plus the the flight time of the gamma rays from the target center to the detector center. Fig. displays the time-of-flight spectra of neutrons and gamma rays, with the charged-particle background removed. The neutron en- ergy can then be derived from the TOF spectrum using the following Eq. (

E = ( 1 �

where is the energy of the neutron, is the flight distance from the center of the target to the geometric center of the detector, is the difference of flight times between the prompt gamma ray and the neutron, is the velocity of light in a vacuum, is the rest mass of the neutron.

Energy calibration and neutron-detection efficiency The energy calibration results of the neutron detector di- rectly affect the accuracy and reliability of the transmission neutron spectrum. Therefore, the energy calibration of the detector is of vital importance in neutron transport experi- ments. Based on the principle that the light output of low- energy electrons in the liquid scintillator detector is linearly related to the electron energy, standard gamma-ray sources Co, and Na) were used to calibrate the energy of

the BC501A (N1) detector. The energy calibration results are shown in Fig.

The detection efficiency ( ) is defined as the ratio of the number of detected particles to the number of particles inci- dent on the detector. Due to the limitations imposed by de- tector type, geometric dimensions, energy threshold, the type and energy of the incident particles, as well as the dead time of the data acquisition system, not all neutrons entering the detector can be recorded. To obtain a more accurate neutron transmission spectrum, the neutron detection efficiency must therefore be determined. In this experiment, the SCINFUL- ] simulation program was used to calculate the detection efficiency of the liquid scintillator detector under different detection thresholds. When the neutron energy is be- low 80 MeV, the software employs the SCINFUL model for calculations; for energies above 80 MeV but below 3 GeV, it utilizes the Quantum Molecular Dynamics (QMD) model and the Statistical Decay Model (SDM) for calculations. In previ- ous work, the software has been benchmarked and applied to neutron transport experiments. The result is shown in Fig.

Experimental background Background neutron measurements were conducted to evaluate the background contribution of scattered neutrons in the experimental hall. Fig. shows the experimental setup for measuring scattered background neutrons. A shadow bar made of iron, measuring 15 cm 15 cm in cross-section and 100 cm in length, was placed along the flight path from the target to the liquid scintillator detector. This setup blocked almost all direct neutrons, allowing only the scattered compo- nents to reach the neutron detector. Fig. displays the time- of-flight spectrum of the background neutrons.

Uncertainty and energy resolution The uncertainty of the experimental data consists of sta- tistical and systematic errors. The statistical error was less than 5 % at energies below 20 MeV and increased to 35 % at higher energies end from the neutron counts. The systematic error arises mainly from uncertainties in the detection effi- ciency calculation, being less than 10 % for incident neutron energies in the range of 0.1–80 MeV and approximately 15 % for higher-energy neutrons. The energy resolution can be expressed by the following Eq. (

∆ E E = Υ(Υ + 1)

where is the Lorentz factor, is the flight distance from the center of the target to the geometric center of the detector,

is the flight distance uncertainty, less than 1 cm, the difference in flight times between the prompt gamma ray and the neutron, The time resolution was estimated to be 1.5 ns which is obtained from the Full Width at Half Maxi- mum (FWHM) of the prompt gamma-ray peak, as shown in RESULTS AND DISCUSSION In this experiment, broad-spectrum neutrons emitted from a 5 mm-thick tungsten target bombarded by 80.5 MeV/u ions were measured using the time-of-flight method. Subse- quently, the transmission neutron spectrum at 0° was mea- sured from the interaction of these broad-spectrum neutrons with a U target. Parallel calculations were performed using GEANT4 with the INCL++, BIC and BERT physics models, combined with the ENDF/B-VIII.0, JEFF-3.3 and JENDL- 4.0 evaluated databases. The transmission neutron spectrum under identical experimental conditions was thereby obtained through these calculations. 238 U target with the source neutron spectrum (i.e., the broad- spectrum neutrons generated by C bombardment of the W target).

In the figure, the blue solid squares represent the U target with the source neutron spectrum source neutron spectrum.

The red solid circles show the transmission neutron spectrum at 0° after the source neutrons transported through the U target. The results indicate that the 20 mm-thick U target affects neutrons across the en- tire studied energy range, with a more pronounced influence observed for neutrons below 50 MeV. and GEANT4 calculation results for the transmission neu- tron spectrum of the U target at the 0° direction. solid black dots represent the experimental results obtained in this study, while lines in other colors (red, green, and blue) correspond to different physics models (INCL++, BIC, and BERT). The solid lines, dashed lines, and dash-dotted lines respectively represent different evaluated databases (ENDF/B-VIII.0, JEFF-3.3, and JENDL-4.0). It can be ob- served in Fig. that the GEANT4 simulation results agree well with the experimental data.

Since GEANT4 utilizes

U target at 0° U target at 0° (below 20 MeV) evaluated databases for calculation calculations in the energy range below 20 MeV, a separate comparison between experi- mental measurements and calculation results for the transmis- sion neutron spectrum below 20 MeV is presented in Fig. to highlight differences among the databases. imental values. As is shown in the figure, within the 20-70 MeV energy range, the results from all three models agree well with the experimental data, with a discrepancy not ex- ceeding 15%. Above 70 MeV, the errors in the calculation results of all three models increase, with a clear underes- timation of the experimental data.

Overall, for the trans- port of broad-spectrum neutrons in U, GEANT4 combined with the three aforementioned physics models yields reason- ably good agreement with experimental data in the energy range above 20 MeV. Nevertheless, the description deterio- rates in the higher energy region, indicating that the high- energy models still require further optimization.A combined analysis of Fig. reveals that: below 20 MeV, the differences in results obtained by invoking different evalu- ated databases (ENDF/B-VIII.0, JEFF-3.3 and JENDL-4.0) are very small for the same physical model. This is because the evaluated databases are well-established and show little variation in this energy region. However, below 10 MeV, a

significant discrepancy emerges between the theoretical cal- 354

culations and the experimental data. All the calculation re- sults collectively overestimate the experimental data. sides, the BERT model yields higher results than INCL++ and BIC in this low-energy range (below 10 MeV). Above 10 MeV, the results from all three models show good agreement.

CONCLUSIONS

The experiment described in this paper was carried out at the Radioactive Ion Beam Line in Lanzhou (RIBLL). The time-of-flight (TOF) method was employed to measure the transmission neutron spectrum at 0° generated by the inter- action of the broad-spectrum neutrons (high-energy white- light neutrons) with a U target. Additionally, calculations were performed using GEANT4 combined with the INCL++, BIC, and BERT physics models, as well as the evaluated nu- clear data libraries ENDF/B-VIII.0, JEFF-3.3, and JENDL-

4.0. Under same experimental conditions, the theoretical re-

sults for the leaked neutron spectrum were obtained.

The results indicate that the calculations using the three physical models combined with different evaluated nuclear data libraries all accurately reproduced the experimental data.

However, slight overestimations were observed below 10 MeV when these models were paired with different data li- braries. Overall, GEANT4 demonstrates reliable calculations for the transport process of high-energy neutrons in U tar- gets.

This work fills a gap in the studies of high-energy neu- tron transport for the U target. The reliable transport ex- perimental data provide valuable reference information for

the design and construction of ADS projects. Additionally, the study examines the reliability of the evaluated databases and theoretical models in the GEANT4 program, and con- tributes to model improvement and the refinement of evalu-

ated databases, which is of significant importance. 387

Acknowledgements The authors would like to express sin- cere thanks to the staffs of the Heavy Ion Research Facility in Lanzhou for their excellent operation of the accelerator and assistance during the irradiation.

Author contributions All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Hui Sun, Xin Zhang and Rui Yee-Rendon, Overview projects world.

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