Test of gamma-ray strength functions in nuclear reaction model calculations

Photon strength functions and nuclear level densities: invaluable input for nucleosynthesis

The pivotal role of nuclear physics in nucleosynthesis processes is being investigated, in particular the intricate influence of photon strength functions (PSFs) and nuclear level densities (NLDs) on shaping the outcomes of the i-, r- and p-processes. Exploring diverse NLD and PSF model combinations uncovers large uncertainties for (p,[Formula: see text]), (n,[Formula: see text]) and ([Formula: see text],[Formula: see text]) rates across many regions of the nuclear chart. These lead to potentially significant abundance variations of the nucleosynthesis processes and highlight the importance of accurate experimental nuclear data. Theoretical insights and advanced experimental techniques lay the ground work for profound understanding that can be gained of nucleosynthesis mechanisms and the origin of the elements. Recent results further underscore the effect of PSF and NLD data and its contribution to understanding abundance distributions and refining knowledge of the intricate nucleosynthesis processes. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Excitation functions of 72Ge(p,xn)72,71As reactions from threshold up to 45 MeV for production of the non-standard positron emitter 72As

Nuclear reaction cross sections for the formation of 72As and 71As in proton-induced reactions on enriched 72Ge targets were measured up to 45 MeV utilizing three different cyclotrons at the Forschungszentrum Jülich. The stacked-thin sample activation technique in combination with high-resolution γ-ray spectrometry was used. The major γ-ray peaks of 72As and 71As formed via the 72Ge(p,n)72As and 72Ge(p,2n)71As reactions, respectively, were analyzed. The incident proton energy and flux on a foil were determined using several monitor reactions. Based on integrated counts, irradiation data and the nuclear decay data, the reaction cross sections were measured. All data describe the first measurements. Theoretical nuclear model calculations were then carried out by using the codes TALYS 1.96, EMPIRE 3.2 and ALICE-IPPE. A very good agreement between the measured data and calculated values was found. The new data enabled us to calculate the thick target yields and estimate the radionuclidic impurities for a given energy range. Over the optimum energy range Ep = 14 → 7 MeV, the calculated thick target yield of 72As amounts to 272 MBq/μAh with no 71As impurity at all. The 72Ge(p,n)72As reaction on the enriched 72Ge is thus very suitable for clinical scale production of 72As at a medical cyclotron.

Yield estimation of radionuclides from 6,7Li-induced reactions: A comparative analysis for 97,95Ru

The article reports the production yields of the medically relevant Ru radionuclides and other co-produced radionuclides from 6,7Li-induced reactions on 93Nb target within the 20-45 MeV energy range. The residues were measured employing the activation technique followed by the offline γ-spectroscopy. Statistical model calculations using EMPIRE3.2.2 code are employed to assess the optimized nuclear model parameters and production mechanisms of the residues. As an outcome, new data from 6Li reaction suggests 9720 MBq/C of thick target yield (TTY) for the production of 95Ru with minimal impurities. While 7Li reaction may be relied upon for producing 97Ru, yielding 813 MBq/C TTY within the studied energy range.

Activation cross section for the (n,2n) and (n,p) reactions on 103Rh, 48Ti and 52Cr from reaction threshold up to 25 MeV energy region

Activation and off-line γ-ray spectrometric methods were used to measure the ground and isomeric state (n,2n) reaction cross section for 103Rh at two different neutron energies. The standard 27Al (n,α)24Na reference reaction was used to normalise neutron flux. The proton beam from the 14UD BARC-TIFR Pelletron facility in Mumbai, India, was utilised to create high-energy quasi-monoenergetic neutrons via the 7Li (p,n) reaction. Statistical model calculations including the level density, pre-equilibrium and optical potential model were performed using the TALYS (ver. 1.95) and EMPIRE (ver. 3.2.3) reaction codes. In addition, because of considerable discrepancies in measured data, the literature (n,p) reaction cross section of 52Cr and 48Ti targets were examined theoretically in the present work. The measured cross sections are discussed and compared with the latest evaluated data of the FENDL-3.2b, CENDL-3.2, TENDL-2019, JENDL-5.0, and ENDF/B-VIII.0 libraries, and experimental data based on the EXFOR compilation. The theoretical investigation of the (n,2n) reaction cross section was performed for the ground and isomeric state for the first time from reaction threshold to 25 MeV energies. The experimental data corresponding to the ground, isomeric state and isomeric ratio were reproduced consistently by the theoretical calculations. The present experimental results are good with certain literature data and theoretical values.

Measurement of the [Formula: see text]Ta([Formula: see text]) cross sections up to stellar s-process temperatures at the CSNS Back-n

The neutron capture cross section of [Formula: see text]Ta is relevant to s-process of nuclear astrophysics, extraterrestrial samples analysis in planetary geology and new generation nuclear energy system design. The [Formula: see text]Ta([Formula: see text]) cross section had been measured between 1 eV and 800 keV at the back-streaming white neutron facility (Back-n) of China spallation neutron source(CSNS) using the time-of-flight (TOF) technique and [Formula: see text] liquid scintillator detectors. The experimental results are compared with the data of several evaluated libraries and previous experiments in the resolved and unresolved resonance region. Resonance parameters are extracted using the R-Matrix code SAMMY in the 1-700 eV region. The astrophysical Maxwell average cross section(MACS) from kT = 5 to 100 keV is calculated over a sufficiently wide range of neutron energies. For the characteristic thermal energy of an astrophysical site, at kT = 30keV the MACS value of [Formula: see text]Ta is 834 ± 75 mb, which shows an obvious discrepancy with the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADoNiS) recommended value 766 ± 15 mb. The new measurements strongly constrain the MACS of [Formula: see text]Ta([Formula: see text]) reaction in the stellar s-process temperatures.

TENDL-based evaluation and adjustment of p+111Cd between 1 and 100 MeV

Proton induced reaction data are needed in the optimization of various radioisotope production routes, among others. In this work, the evaluation of proton-induced reactions on ¹¹¹Cd between 1 and 100 MeV using the TALYS code system within an iterative Bayesian Monte Carlo (iBMC) framework, is presented. The method involves the simultaneous variation of a large number of nuclear reaction models included in the TALYS code system as well as their parameters. Each random TALYS calculation yields a vector of calculated values of cross section observables as well as the angular distributions, among others, which were compared with corresponding vectors of carefully selected differential experimental data for reaction channels where data were available. The random nuclear data file with the maximum likelihood function value obtained from combining the individual χ²s computed for the considered reaction channels was chosen as the parent vector and the starting point for the generation of a further set of random TALYS calculations. This was repeated multiple times until a targeted convergence of 5% was reached. The final evaluated file was compared with available experimental data from the EXFOR database as well as with the evaluations from the TENDL-2021 and JENDL5.0 libraries, and found to compare favorably.

Statistical (n, γ ) cross section model comparison for short-lived nuclei

Neutron-capture cross sections of neutron-rich nuclei are calculated using a Hauser-Feshbach model when direct experimental cross sections cannot be obtained. A number of codes to perform these calculations exist, and each makes different assumptions about the underlying nuclear physics. We investigated the systematic uncertainty associated with the choice of Hauser-Feshbach code used to calculate the neutron-capture cross section of a short-lived nucleus. The neutron-capture cross section for 73 Zn (n, γ ) 74 Zn was calculated using three Hauser-Feshbach statistical model codes: TALYS, CoH, and EMPIRE. The calculation was first performed without any changes to the default settings in each code. Then an experimentally obtained nuclear level density (NLD) and γ -ray strength function ( γ SF ) were included. Finally, the nuclear structure information was made consistent across the codes. The neutron-capture cross sections obtained from the three codes are in good agreement after including the experimentally obtained NLD and γ SF , accounting for differences in the underlying nuclear reaction models, and enforcing consistent approximations for unknown nuclear data. It is possible to use consistent inputs and nuclear physics to reduce the differences in the calculated neutron-capture cross section from different Hauser-Feshbach codes. However, ensuring the treatment of the input of experimental data and other nuclear physics are similar across multiple codes requires a careful investigation. For this reason, more complete documentation of the inputs and physics chosen is important.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1140/epja/s10050-023-00920-0.

CONRAD – a code for nuclear data modeling and evaluation

The CONRAD code is an object-oriented software tool developed at CEA since 2005. It aims at providing nuclear reaction model calculations, data assimilation procedures based on Bayesian inference and a proper framework to treat all uncertainties involved in the nuclear data evaluation process: experimental uncertainties (statistical and systematic) as well as model parameter uncertainties. This paper will present the status of CONRAD-V1 developments concerning the theoretical and evaluation aspects. Each development is illustrated with examples and calculations were validated by comparison with existing codes (SAMMY, REFIT, ECIS, TALYS) or by comparison with experiment. At the end of this paper, a general perspective for CONRAD (concerning the evaluation and theoretical modules) and actual developments will be presented.

Investigation of fission product isomeric ratios and angular momenta of 132Sn populated in the 241Pu(nth,f) reaction

During an experimental campaign performed at the LOHENGRIN recoil spectrometer of the Institut Laue-Langevin (ILL), a kinetic energy dependence of 132Sn fission product isomeric ratio (IR) has been measured by inducing thermal fission of 241Pu. The IRs are deduced using gamma ray spectrometry in coincidence with the ionisation chamber. To interpret these data, we use the FIFRELIN Monte-Carlo code to simulate the de-excitation of the fission fragments. Combining the IRs with the FIFRELIN calculations, the angular momentum distribution with kinetic energy of the doubly magic nucleus of 132Sn was deduced. This will be compared with the angular momentum distribution obtained for the reaction 235U(nth,f) for 132Sn.

GEANT4 simulation of a range verification method using delayed γ spectroscopy of a 92Mo marker

In this work, we propose a novel technique for in-vivo proton therapy range verification. This technique makes use of a molybdenum hadron tumour marker, implanted at a short distance from the clinical treatment volume. Signals emitted from the marker during treatment can provide a direct measurement of the proton beam energy at the marker's position. Fusion-evaporation reactions between the proton beam and marker nucleus result in the emission of delayed characteristic γ rays, which are detected off-beam for an improved signal-to-noise ratio. In order to determine the viability of this technique and to establish an experimental setup for future work, the Monte Carlo package GEANT4 was used in combination with ROOT to simulate a treatment scenario with the new method outlined in this work. These simulations show that the intensity of delayed γ rays produced from competing reactions yields a precise measurement of the range of the proton beam relative to the marker, with sub-millimetre uncertainty.

Simultaneous Determination of Neutron-Induced Fission and Radiative Capture Cross Sections from Decay Probabilities Obtained with a Surrogate Reaction

Reliable neutron-induced-reaction cross sections of unstable nuclei are essential for nuclear astrophysics and applications but their direct measurement is often impossible. The surrogate-reaction method is one of the most promising alternatives to access these cross sections. In this work, we successfully applied the surrogate-reaction method to infer for the first time both the neutron-induced fission and radiative capture cross sections of ^{239}Pu in a consistent manner from a single measurement. This was achieved by combining simultaneously measured fission and γ-emission probabilities for the ^{240}Pu(^{4}He,^{4}He^{'}) surrogate reaction with a calculation of the angular-momentum and parity distributions populated in this reaction. While other experiments measure the probabilities for some selected γ-ray transitions, we measure the γ-emission probability. This enlarges the applicability of the surrogate-reaction method.

Accurate determination of production data of the non-standard positron emitter 86Y via the 86Sr(p,n)-reaction

In view of several significant discrepancies in the excitation function of the 86Sr(p,n)86g+xmY reaction which is the method of choice for the production of the non-standard positron emitter 86Y for theranostic application, we carried out a careful measurement of the cross sections of this reaction from its threshold up to 16.2 MeV at Forschungszentrum Jülich (FZJ) and from 14.3 to 24.5 MeV at LBNL. Thin samples of 96.4% enriched 86SrCO3 were prepared by sedimentation and, after irradiation with protons in a stacked-form, the induced radioactivity was measured by high-resolution γ-ray spectrometry. The projectile flux was determined by using the monitor reactions natCu(p,xn)62,63,65Zn and natTi(p,x)48V, and the calculated proton energy for each sample was verified by considering the ratios of two reaction products of different thresholds. The experimental cross section data obtained agreed well with the results of a nuclear model calculation based on the code TALYS. From the cross section data, the integral yield of 86Y was calculated. Over the optimum production energy range Ep = 14 → 7 MeV the yield of 86Y amounts to 291 MBq/μA for 1 h irradiation time. This value is appreciably lower than the previous literature values calculated from measured and evaluated excitation functions. It is, however, more compatible with the experimental yields of 86Y obtained in clinical scale production runs. The levels of the isotopic impurities 87mY, 87gY, and 88Y were also estimated and found to be <2% in sum.

Evaluation of gamma-ray strength function based on measured gamma-ray pulse-height spectra in time-of-flight neutron capture experiments

In order to develop an evaluation method of gamma-ray strength function (GSF), neutron capture pulse-height (PH) spectrum of gold was employed, where it was measured with the NaI(Tl) spectrometer of AN-NRI installed at the Material and Life Science Experimental Facility in J-PARC. The neutron capture gamma-ray spectrum of gold was calculated using the nuclear reaction model code CCONE. In order to obtain the information on GSF from the measured data, a gamma-ray response function for the NaI(Tl) spectrometer was calculated by the Monte-Carlo particle-transport simulation code PHITS. As a result, the PH spectrum comparable with measured one was derived by applying the gamma-ray response function to the calculated gamma-ray spectrum. By evaluation with measured PH spectra, we obtained GSF which reasonably explains measured PH spectrum in the continuum region.

PROFIL-2 Experiment and neutron capture cross sections of Europium isotopes

Neutron-induced cross section is one of the key quantities in nuclear physics and nuclear engineering. The integral experiment can give good feedback to the cross sections with low uncertainties. Using the optical model and statistical model, the neutron-induced total and capture cross sections of153Eu are revaluated according to the experimental microscopic total cross sections and the PROFIL-2 integral experiment. The corresponding uncertainties and covariances are determined with the data assimilation method implemented in CONRAD code. On the other hand, the previous interpretation of the PROFIL-2 experiment showed that JEFF-3.1 overestimates the neutron-induced capture cross section of 151 Eu by a factor of 2. Further analysis performed in the present work points out that the large difference between calculation and experimental data is mainly due to the lack of152m1 Eu in ERANOS code, which was used to interpret the PROFIL-2 experiment. The correction of 152m1Eu on the interpretation largely reduces the difference between JEFF-3.1 and PROFIL-2 and shows the agreement between the PROFIL-2 integral experiment and other microscopic measurements. The revaluated neutron-induced total and capture cross sections of 151 Eu and 153Eu correspond well with both the microscopic experimental measurements and the PROFIL-2 integral experiment.

Neutron inelastic cross section measurements on 58,60Ni

A natural nickel sample was used at the GELINA (Geel Electron LINear Accelerator) neutron source of the European Commission, Joint Research Centre, Geel to measure the neutron inelastic cross sections. The GAINS (Gamma Array for Inelastic Neutron Scattering) spectrometer was employed to detect the emitted γ rays while a 235U fission chamber monitored the neutron flux. We report the preliminary production cross sections corresponding to the first transitions in 58,60Ni in comparison with previously reported data and with TALYS 1.9 calculations performed using the default input parameters.

Excitation functions of the Zn(p,xn)Ga reactions

The excitation functions for ^{64,66,67,68,70}Zn(p,n)^{64,66,67,68,70}Ga and ^{64,66,67,68,70}Zn(p,2n)^{63,65,66,67,69}Ga have been calculated for incident proton energies from threshold values to 30 MeV using the statistical model code TALYS-1.6. The (p,n) and (p,2n) cross sections have been calculated using both phenomenological Koning and Delaroche (KD) and semimicroscopic Jeukenne-Lejeune-Mahaux-Bruyeres (JLMB) optical model potentials. The phenomenological back-shifted Fermi gas model (BFM) and microscopic Hartree-Fock (HF) approaches for calculation of level densities have been compared in the present work. The pre-equilibrium process has been treated using exciton model. The sensitivity of cross section data to different models of optical model potential and level density have been investigated. It is found that the (p,n) and (p,2n) cross section calculations with semimicroscopic JLMB optical model potential and microscopic HF level density show agreement with the data. The (p,n) and (p,2n) cross section calculations have been compared with corresponding cross sections from nuclear data library, TENDL-2019. The (p,xn) cross sections obtained will be useful in several applications, particularly, for optimization of production routes for Ga isotopes.

Analysis of neutron induced (n,γ) and (n,2n) reactions on 232Th from reaction threshold to 20 MeV

Excitation functions for ²³²Th(n,γ) and ²³²Th(n,2n) reactions from reaction threshold to 20 MeV were calculated using TALYS-1.9 nuclear code by invoking suitable options for the level densities, optical model potentials, pre-equilibrium effects and γ-ray strength functions. In earlier studies, theoretical plots for ²³²Th(n,γ) and ²³²Th(n,2n) reaction cross-sections were obtained by using EMPIRE 3.2 and TALYS 1.9 codes with default parameters, however none of the reported plots could match with the corresponding experimental cross-sections reported in EXFOR data particularly between 14-20 MeV. The results of the present study reveal that by using a combination of specific input parameters in TALYS 1.9 code, the theoretical evaluation of the cross sections favour a higher pre-equilibrium rate for the harder spectrum. Moreover the estimated cross-sections match fairly well with the corresponding experimental data (EXFOR database) as well as with the evaluated data files (ENDF/VII.0, JENDL-4.0). The results of the present study are important for the validation of nuclear model approaches with increased predictive power for (n,xn) cross-sections and particularly for the application of thorium based fuel in Accelerator-Driven Sub-critical System.

An investigation of effects of level density models and gamma ray strength functions on cross-section calculations for the production of 90Y, 153Sm, 169Er, 177Lu and 186Re therapeutic radioisotopes via (n,γ) reactions

One of the methods used to treat different cancer diseases is the employment of therapeutic radioisotopes. Therefore, many clinical, theoretical and experimental studies are being carried out on those radioisotopes. In this study, the effects of level density models and gamma ray strength functions on the theoretical production cross-section calculations for the therapeutic radioisotopes 90Y, 153Sm, 169Er, 177Lu and 186Re in the (n,γ) route have been investigated. TALYS 1.9 code has been used by employing different level density models and gamma ray strength functions. The theoretically obtained data were compared with the experimental data taken from the literature. The results are presented graphically for better interpretation.

The Gogny-HFB+QRPA dipole strength function and its application to radiative neutron capture cross section

Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we extend our large-scale calculations of the E1 and M1 absorption γ-ray strength function obtained in the framework of the axially-symmetric deformed quasiparticle random phase approximation (QRPA) based on the finite-range D1M Gogny force to the determination of the de-excitation strength function. To do so, shell-model calculations of the de-excitation dipole strength function as well as experimental data are considered to provide insight in the low-energy limit and to complement the QRPA estimate phenomenologically. We compare our final prediction of the E1 and M1 strengths with available experimental data at low energies and show that a relatively good agreement can be obtained. Its impact on the average radiative width as well as radiative neutron capture cross section is discussed.

Impact of FIFRELIN input parameters on fission observables

Evaluated nuclear data are essential for nuclear reactor studies. In order to significantly improve the precision of nuclear data, more and more fundamental fission models are used in the evaluation processing. Therefore, tests of fission models become a central issue. In this framework, FIFRELIN (FIssion Fragments Evaporation Leading to an Investigation of Nuclear data) is a Monte Carlo code developed in order to modelize fission fragments de-excitation through the emission of neutrons, γ and conversion e-. To be performed, a FIFRELIN calculation relies on several models such as gamma strength function and nuclear level density and of more empirical hypothesis such as total excitation energy repartition or angular momentum given by the fission reaction. Moreover, pre-emission mass yield and kinetic energy distribution per mass are necessary to process the simulation. A set of five free parameters are chosen to reproduce a target observable. Often this observable corresponds to the mean neutron multiplicity for heavy and light fragment. In this work, the impact of the set of parameters on different output observables (neutron emission probability, neutron multiplicity as function of the fission fragment mass) is investigated.

Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum

Statistical γ-decay from highly excited states is determined by the nuclear level density (NLD) and the γ-ray strength function (γSF). These average quantities have been measured for several nuclei using the Oslo method. For the first time, we exploit the NLD and γSF to evaluate the γ-width in the energy region below the neutron binding energy, often called the quasi-continuum region. The lifetimes of states in the quasi-continuum are important benchmarks for a theoretical description of nuclear structure and dynamics at high temperature. The lifetimes may also have impact on reaction rates for the rapid neutron-capture process, now demonstrated to take place in neutron star mergers.

Potential sources of uncertainties in nuclear reaction modeling

Nowadays, reliance on nuclear models to interpolate or extrapolate between experimental data points is very common, for nuclear data evaluation. It is also well known that the knowledge of nuclear reaction mechanisms is at best approximate, and that their modeling relies on many parameters which do not have a precise physical meaning outside of their specific implementations in nuclear model codes: they carry both specific physical information, and effective information that is related to the deficiencies of the model itself. Therefore, to improve the uncertainties associated with evaluated nuclear data, the models themselves must be refined so that their parameters can be rigorously derived from theory. Examples of such a process will be given for a wide sample of models like: detailed theory of compound nucleus decay through multiple nucleon or gamma emission, or refinements to the width fluctuation factor of the Hauser-Feshbach model. All these examples will illustrate the reduction in the effective components of nuclear model parameters, through the reduced dynamics of parameter adjustment needed to account for experimental data. The significant progress, recently achieved for the non-fission channels, also highlights the difficult path ahead to improve our quantitative understanding of fission in a similar way: by relying on microscopic theory.

Study of photon strength functions via (γ→, γ′, γ″) reactions at the γ3-setup

One of the basic ingredients for the modelling of the nucleosynthesis of heavy elements are so-called photon strength functions and the assumption of the Brink-Axel hypothesis. This hypothesis has been studied for many years by numerous experiments using different and complementary reactions. The present manuscript aims to introduce a model-independent approach to study photon strength functions via γ-γ coincidence spectroscopy of photoexcited states in 128Te. The experimental results provide evidence that the photon strength function extracted from photoabsorption cross sections is not in an overall agreement with the one determined from direct transitions to low-lying excited states.

Evaluation of neutron capture cross section on 205Pb with photonuclear data

The neutron capture cross section of long-lived radioactive 205Pb is derived by using the nuclear reaction calculation code CCONE, based on photonuclear data. The present result is smaller than that of TENDL-2015 by a factor of 4. The derived Maxwellian averaged capture cross section (MACS) is the smallest compared to the existing data. The produced amount of 205Pb is explored with a simulated neutron flux in the Pb-Bi eutectic (LBE) target. The continuous use of the system in 25 years creates 205Pb with about 6 kg at maximum in the LBE (including natural Pb of 103 kg). The impact of the derived MACS on the stellar nucleosynthesis is investigated. It is found that the abundance of Tl is slightly enhanced due to the increase in the remaining abundance of 205Pb.

Experimental Neutron Capture Rate Constraint Far from Stability

Nuclear reactions where an exotic nucleus captures a neutron are critical for a wide variety of applications, from energy production and national security, to astrophysical processes, and nucleosynthesis. Neutron capture rates are well constrained near stable isotopes where experimental data are available; however, moving far from the valley of stability, uncertainties grow by orders of magnitude. This is due to the complete lack of experimental constraints, as the direct measurement of a neutron-capture reaction on a short-lived nucleus is extremely challenging. Here, we report on the first experimental extraction of a neutron capture reaction rate on ^{69}Ni, a nucleus that is five neutrons away from the last stable isotope of Ni. The implications of this measurement on nucleosynthesis around mass 70 are discussed, and the impact of similar future measurements on the understanding of the origin of the heavy elements in the cosmos is presented.