Maxwellian-averaged Cross Sections Research Articles

Maxwell–Boltzmann-like neutron spectrum production for Maxwellian averaged cross sections measurements

Over the years, Maxwellian Averaged Cross Sections (MACS) have been measured by neutron activation, providing a neutron energy spectrum resembling the one found inside the stars. Recently, a new method has been proposed to produce stellar spectra at different stellar temperatures (a Maxwell–Boltzmann neutron energy distribution), employing the 7Li(p,n)7Be reaction. The method is based on the idea of shaping the proton beam energy to shape the neutron beam spectrum. This method was applied to obtain a well-reproduced Maxwell–Boltzmann neutron spectrum (MBNS) at kT=28 keV. An initial proton energy of 3170 keV and an aluminum foil as a proton energy shaper were employed. Differential angular neutron energy distributions from 0 to 90 degrees in 10∘ steps were measured to obtain the 0∘–90∘ integrated neutron spectrum over a neutron flight path of 50 cm. This manuscript reports on the measurement results, confirming the method’s capability, and suggests the approach for producing a high-quality MBNS at kT=28 keV.

Investigation of 90,92Zr(n,γ)91,93Zr in the s-process nucleosynthesis

Abstract The neutron capture rates and Maxwellian-averaged cross-sections (MACS) for 90Zr(n,γ)91Zr and 92Zr(n,γ)93Zr processes have been computed within the framework of Talys v1.96. The effects of phenomenological nuclear level density (NLD) parameters and the gamma strength functions (GSFs) on Maxwellian-averaged cross-sections and neutron capture rates are examined both quantitatively and qualitatively. The present model-based computed data for MACS and reaction rates gives a good comparison with the existing literature. The fine-tuning of the statistical model’s nuclear properties (level density and gamma-ray strength) to reproduce experimental data will allow the detailed investigation of the s-process network.

Imprint of pairing correlation in (n, γ) and Maxwellian-averaged cross sections of an odd-odd 166Ho nucleus

The present paper investigates the impact of pairing correlation on the nuclear level density (NLD) and radiative strength function (RSF) of an odd-odd and rare-earth 166Ho nucleus. By employing the exact thermal pairing (EP) solution in conjunction with both the temperature-dependent independent-particle model (EP+IPM) for the NLD and the phonon damping model (EP+PDM) for the RSF, we achieve good agreement with the experimental NLD and RSF data, which have been recently extracted by using the Oslo method. Notably, without adding any extra parameters, our calculations successfully reproduce the pygmy dipole resonances (PDR) and a portion of the strength around the region of scissor resonance (SR) in the RSF. This suggests that the SR in this nucleus may be less pronounced than that obtained in the previous analysis within the phenomenological model. These features are the consequences of the EP and the couplings of the PDM phonon to all the particle-hole (ph), particle-particle (pp), and hole-hole (hh) configurations within the EP+PDM, thus insisting on the importance of the underlying physics involved in this model. Utilizing the obtained NLD and RSF, we predict the 165Ho(n,γ)166Ho and Maxwellian-averaged cross sections, which exhibit remarkable agreement with all the available experimental data from the Experimental Nuclear Reaction Data and Karlsruhe Astrophysical Database of Nucleosynthesis in Stars. These results reflect the imprint of the pairing correlation on those quantities.

Cosmic implications of the reaction: a nuclear astrophysical perspective

We conducted a comprehensive study of the neutron capture cross section of within the relevant astrophysical energy range. Through rigorous R-matrix analysis, we determined the Maxwellian-averaged cross section to be 11.98 0.25 μb at kT = 30 keV. This result is approximately four times higher than the thermal neutron capture cross section estimated in earlier studies assuming the law. The implications of our findings extend to the region of inhomogeneous Big-Bang models in nuclear astrophysics, where understanding the behaviour of neutron capture cross sections plays a crucial role in elucidating the intricate processes that shaped the early universe.

Isotopic dependence of (n,α) reaction cross sections for Fe and Sn nuclei

The (n,α) reactions play an important role for the energy generation and the synthesis of chemical elements in the stars, as well as for nuclear engineering and medical applications. The aim of this study is to explore the evolution of (n,α) reactions in Fe and Sn isotope chains in order to assess the cross section properties with the increase of neutron number in target nucleus, and to make a comparison with other relevant neutron induced reactions. The cross section calculations are based on the statistical Hauser-Feshbach and exciton models in TALYS nuclear reaction code, using global optical model potential that is additionally adjusted by the (n,α) cross section data for 54Fe and 118Sn. The calculations of (n,α) reactions in Fe and Sn isotopes provide the insight into their isotopic dependence and properties over the complete relevant range of neutron energies. The cross sections result in pronounced maxima at lower-mass isotopes, and rather strong decrease for neutron-rich nuclei consistent with the reduction of the reaction Q-value and increased contributions from other exit channels from compound nucleus. The analysis of the Maxwellian averaged cross sections at temperatures in stellar environment shows that the (n,α) reactions have significant contributions for low-mass Fe isotopes, that is opposite than for Sn isotopes. For both neutron rich isotopes γ and neutron emissions dominate, with their interplay depending on the temperature involved.

Measurement of the Tb159(n,γ) cross section at the CSNS Back-n facility

The stellar ($n,\ensuremath{\gamma}$) cross section data for the mass numbers around $A\ensuremath{\approx}160$ are of key importance to nucleosynthesis in the main component of the slow neutron capture process, which occurs in the thermally pulsing asymptotic giant branch (TP-AGB). The new measurement of ($n,\ensuremath{\gamma}$) cross sections for $^{159}\mathrm{Tb}$ was performed using the ${\mathrm{C}}_{6}{\mathrm{D}}_{6}$ detector system at the back streaming white neutron beam line (Back-n) of the China spallation neutron source with neutron energies ranging from 1 eV to 1 MeV. Experimental resonance capture kernels are reported up to 1.2 keV neutron energy with this capture measurement. Maxwellian-averaged cross sections (MACS) are derived from the measured $^{159}\mathrm{Tb}(n,\ensuremath{\gamma})$ cross sections at $kT=5$--100 keV and are in good agreement with the recommended data of KADoNiS-v0.3 and JEFF-3.3, while KADoNiS-v1.0 and ENDF-VIII.0 significantly overestimate the present MACS up to $40%$ and $20%$, respectively. A sensitive test of the $s$-process nucleosynthesis is also performed with the stellar evolution code mesa. Significant changes in abundances around $A\ensuremath{\approx}160$ are observed between the ENDF/B-VIII.0 and present measured rate of $^{159}\mathrm{Tb}(n,\ensuremath{\gamma})^{160}\mathrm{Tb}$ in the mesa simulation.

Neutron capture cross section of ^{83}Kr

The neutron capture cross section of ^{83}Kr has been measured via the time-of-flight technique between 25 meV and 500 keV. The experiment used the DANCE array at the Los Alamos National Laboratory. Maxwellian Averaged Cross Sections have been derived for a range of stellar temperatures and are found to be in good agreement with previous data. The impact of the new cross sections on stellar nucleosynthesis has been investigated.

Nuclear level densities and γ-ray strength functions of 120,124Sn for astrophysical purposes

The nuclear level densities (NLDs) and γ-ray strength functions (GSFs) of 120,124Sn were extracted with the Oslo method, compared and combined with other experimental data to be used as inputs in the TALYS reaction code to constrain the Maxwellian-averaged cross sections (MACS) for the 119,123Sn(n, γ)120,124Sn reactions. For 120Sn, the MACS are in relatively good agreement with the JINA REACLIB, BRUSLIB libraries, while no clear agreement was found for 124Sn. In addition, the pygmy dipole resonance (PDR) was found to contribute with up to ≈ 3 − 8% of the total MACS in these nuclei.

The Stellar 72Ge(n, γ) Cross Section for weak s-process: A First Measurement at n_TOF

The slow neutron capture process (s-process) is responsible for producing about half of the elemental abundances heavier than iron in the universe. Neutron capture cross sections on stable isotopes are a key nuclear physics input for s-process studies. The 72Ge(n, γ) Maxwellian-Averaged Cross Section (MACS) has an important influence on the production of isotopes between Ge and Zr in the weak s-process in massive stars and so far only theoretical estimations are available. An experiment was carried out at the neutron time-of-flight facility n_TOF at CERN to measure the 72Ge(n, γ) reaction for the first time at stellar neutron energies. The capture measurement was performed using an enriched 72GeO2 sample at a flight path length of 184 m, which provided high neutron energy resolution. The prompt gamma rays produced after neutron capture were detected with a set of liquid scintillation detectors (C6D6). The neutron capture yield is derived from the counting spectra taking into account the neutron flux and the gamma-ray detection efficiency using the Pulse Height Weighting Technique. Over 70 new neutron resonances were identified, providing an improved resolved reaction cross section to calculate experimental MACS values for the first time. The experiment, data analysis and the new MACS results will be presented including their impact on stellar nucleosynthesis, which was investigated using the post-processing nucleosynthesis code mppnp for a 25 solar mass model.

Stellar neutron spectra at 28 keV thermal temperature

To calculate the reaction rate in the neutron capture processes it is common to work with the Maxwellian Average Cross Section (MACS), defined as the reaction rate scaled by the most probable neutron velocity of the Maxwell-Boltzmann distribution. For MACS determination with lower uncertainties, the need of a neutron spectrum as similar as possible to the stellar one motivates this work. At the CN Van der Graaff accelerator of the LNLINFN laboratories, an experimental measurement is performed to produce a Maxwell-Boltzmann neutron spectrum with 28 keV of thermal temperature. The neutron time-of-flight spectrometry is implemented to determine 0°-90° integrated neutron spectrum, employing the 7Li(p,n)7Be reaction as neutron source, an initial proton energy of 3.17 MeV and a 51 µm thickness aluminum foil, as proton energy shaper.

Stellar s-process neutron capture cross sections on ASe and ACe

We report on experiments at the Soreq Applied Research Accelerator Facility Liquid-Lithium Target (SARAF-LiLiT) laboratory dedicated to the study of s-process neutron capture reactions. The kW-power proton beam at 1.92 MeV (1-2 mA) from SARAF Phase I yields high-intensity 30 keV quasi-Maxwellian neutrons (3-5 1010 n/s). The high neutron intensity enables Maxwellian averaged cross sections (MACS) measurements of samples with short-lived decay products. Neutron capture reactions on natSe and natCe were investigated by activation in the LiLiT neutron beam and γ-spectrometry measurements of their decay products.

Indirect measurement of the (n, γ)127Sb cross section

Sensitivity studies of the i process have identified the region around 135I as a bottleneck for the neutron capture flow. Nuclear properties such as the Maxwellian-averaged cross section (MACS) are key to constrain the uncertainties in the final abundance patterns. With the Oslo method, we are able to indirectly measure such properties for the nuclei involved in this process. From the 124Sn(α, pγ)127Sb reaction data we extract the nuclear level density and γ-ray strength function for 127Sb. The level density at higher excitation energies is compatible with the constant-temperature model, while the γ-ray strength function presents features like an upbend and a pygmy-like structure below S n. From these two quantities we can calculate the MACS for the 126Sb(n, γ)127Sb reaction using the Hauser-Feshbach formalism, and constrain its uncerainties from the theoretical ones. Libraries such as JINA REACLIB, TENDL and BRUSLIB agree well with the experimental results, while ENDF/B-VIII.0 predicts a higher rate.

Indirect measurement of the (n,γ)127Sb cross section

Sensitivity studies of the i process have identified the region around 135I as a bottleneck for the neutron capture flow. Nuclear properties such as the Maxwellian-averaged cross section (MACS) are key to constrain the uncertainties in the final abundance patterns. From the 124Sn(α, pγ)127Sb reaction we are able to indirectly measure the nuclear level density and γ-ray strength function for 127Sb using the Oslo method. From these two quantities we can calculate the MACS for the 126Sb(n, γ)127Sb reaction using the Hauser-Feshbach formalism, constrain its uncertainties and compare it to libraries such as JINA REACLIB, TENDL and BRUSLIB.

Nuclear level densities and γ-ray strength functions of 120,124Sn and their application in astrophysics

Nuclear level densities (NLDs) and γ-ray strength functions (GSFs)of 120;124Sn have been extracted with the Oslo method and additionally constrained with the novel Shape method. The GSFs were found to be in excellent agreement with the strengths from the inelastic relativistic proton scattering experiment. This comparison suggests the validity of the Brink-Axel hypothesisused as one of the key assumptions in astrophysical calculations. The extracted NLDs and GSFs were further used as experimental inputs to constrain the Maxwellian-averaged cross sections (MACS) for the radiative neutron capture process 119;123Sn (n, γ)120;124Sn using the the nuclear reaction code TALYS.

Direct reactions for nuclear astrophysics

The neutron activation technique is a well established method to measure neutron capture cross sections relevant for the s-process. The7Li(p,n) reaction at Ep= 1912 keV is often used as a neutron source since the energy distribution of the emitted neutrons closely resembles a Maxwell-Boltzmann spectrum ofkBT= 25 keV, mimicking the22Ne(α,n) phase in TP-AGB stars. The weak s-process, which takes place in massive stars, can reach energies up tokBT = 90 keV. Neutron spectra corresponding to a Maxwell-Boltzmann distribution withkBT> 25 keV cannot be produced by the7Li(p,n) reaction directly. We developed a method to obtain quasi-Maxwellian neutron capture cross sections over a wide energy range by combining a set of spectrum average cross sections measured at six different proton energies and distances between the lithium target and the sample. The measured spectrum averaged cross section can be used to calculate the Maxwellian-Averaged cross-section (MACS) fromkBT= 25 keV tokBT= 90 keV. Over the last two years neutron capture cross sections on over 20 isotopes have been measured at Goethe University Frankfurt using this methodology. An overview of the current experimental method, challenges during data analysis and the first results are presented.

The impact of n_TOF data on s-process modelling

We show examples of the impact of the Maxwellian averaged capture cross sections determined at n_TOF over the past 20 years on AGB stellar nucleosynthesis models. In particular, we developed an automated procedure to derive MACSs from evaluated data libraries, which are subsequently used as input to stellar models computed by means of the FuNS code. In this contribution, we present a number of s-process abundances obtained using different data libraries as input to stellar models, with a focus on the role of n_TOF data.

The ASTRAL database for neutron-capture nucleosynthesis studies

Present nuclear reaction network computations for astrophysical simulations involve many different types of rates, including neutron-capture reactions of interest for the modeling of heavy-element nucleosynthesis. While for many of them we still have to rely on theoretical calculations, an increasing number of experimentally-determined cross sections have now become available. In this contribution, we present “ASTrophysical Rate and rAw data Library” (ASTRAL), a new online database for neutron-capture cross sections based on experimental results, mainly obtained through activation and timeof-flight measurements. For the evaluation process, cross sections were re-calculated starting from raw data and by considering recent changes in physical properties of the involved isotopes (e.g., half-life and γ-ray intensities). We show the current status of the database, the techniques adopted to derive the recommended Maxwellian-averaged cross sections, and future developments.

^{74}Ge(n,gamma ) cross section below 70 keV measured at n_TOF CERN

Neutron capture reaction cross sections on ^{74}Ge are of importance to determine ^{74}Ge production during the astrophysical slow neutron capture process. We present new resonance data on ^{74}Ge(n,gamma ) reactions below 70 keV neutron energy. We calculate Maxwellian averaged cross sections, combining our data below 70 keV with evaluated cross sections at higher neutron energies. Our stellar cross sections are in agreement with a previous activation measurement performed at Forschungszentrum Karlsruhe by Marganiec et al., once their data has been re-normalised to account for an update in the reference cross section used in that experiment.

Application of kernel ridge regression in predicting neutron-capture reaction cross-sections

This article provides the first application of the machine-learning approach in the study of the cross-sections for neutron-capture reactions with the kernel ridge regression (KRR) approach. It is found that the KRR approach can reduce the root-mean-square (rms) deviation of the relative errors between the experimental data of the Maxwellian-averaged cross-sections and the corresponding theoretical predictions from 69.8% to 35.4%. By including the data with different temperatures in the training set, the rms deviation can be further significantly reduced to 2.0%. Moreover, the extrapolation performance of the KRR approach along different temperatures is found to be effective and reliable.

Measurement of neutron-capture cross sections of Ge70,72 using the DANCE facility

Background: Approximately half of all atomic nuclei heavier than iron are synthesized by the slow neutron-capture process. The weak component of this process is not well understood and the reaction rates of each isotope in the s-process path affect nucleosynthesis abundances downstream.Purpose: To measure the neutron-capture cross sections of two weak s-process nuclei, $^{70,72}\mathrm{Ge}$, using the neutron time-of-flight technique. Measuring the capture cross sections for isotopes in this region of the chart of nuclides has proven challenging due to dominant scattering cross sections.Method: Samples consisted of pellets made of pressed enriched metallic powders. The $^{70,72}\mathrm{Ge}$ neutron-capture cross sections were measured as a function of neutron energy using the Detector for Advanced Neutron Capture Experiments at Los Alamos National Laboratory.Results: Neutron-capture cross sections were measured from 10 eV to 1 MeV. These are the first measurements for $^{70,72}\mathrm{Ge}$ between 300 keV and 1 MeV neutron energy. Maxwellian-averaged cross sections were calculated in the astrophysically relevant neutron energy range (5 keV $\ensuremath{\le}kT\ensuremath{\le}$ 100 keV). Their value at $kT=30$ keV was found to be $89\ifmmode\pm\else\textpm\fi{}11$ mb for $^{70}\mathrm{Ge}$ and $58\ifmmode\pm\else\textpm\fi{}5$ mb for $^{72}\mathrm{Ge}$. Both values are in agreement with recent time-of-flight measurements at n_TOF (neutron Time-Of-Flight facility at the European Organization for Nuclear Research).Conclusions: The average cross section results from this work for $^{70}\mathrm{Ge}$ show minor ($<1\ensuremath{\sigma}$) disagreement with a recent measurement by the n_TOF collaboration at higher neutron energies. This corresponds to the neutron energy region that had previously never been measured ($>300$ keV). Two reaction library databases underestimate the $^{72}\mathrm{Ge}$ average cross section below 30 keV according to n_TOF and DANCE. This is likely due to capture resonances that are missing from the theoretical cross sections in the databases that were identified in both time-of-flight measurements. Additionally, a rudimentary analysis of the impact of both cross section measurements on stellar nucleosynthesis abundances using the NETZ nucleosynthesis tool is presented.