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The {gamma}-ray strength function ({gamma}SF) interconnects radiative neutron capture and photoneutron emission as a common ingredient in the statistical model. Outlined here is an indirect method of determining radiative neutron-capture cross sections for unstable nuclei based on the {gamma}-ray strength function. Application examples of the {gamma}SF method are demonstrated.
Numerous scientific fields including astrophysics, nuclear power, and nuclear forensics require a knowledge of basic nuclear properties for large numbers of short-lived, radioactive isotopes far removed from stable nuclei. Neutron-capture cross sections are one such piece of nuclear data where direct measurements are not possible and theoretical predictions can vary by orders of magnitude. A recently developed indirect technique for inferring neutron capture rates, the β-Oslo method, has been introduced but not compared against a known, directly measured neutron capture cross section. To provide this benchmark, two indirect methods based on β decay and charged-particle reactions were used to extract the nuclear level density and γ-ray strength function of 51 Ti. The nuclear level density and γ-ray strength function from the two data sets were found to be equivalent and were used to extract the neutron capture cross section of 50 Ti which agrees with previous direct measurements at high neutron energies. Here, the results demonstrate the validity of the β-Oslo method for extracting neutron capture cross sections of short-lived nuclei and provide a sufficiently small uncertainty to be used in various applications.
Mechanical properties of high polymer solid in terms of microbehavior as result of deformation and orientation, expressing anisotropic relaxation function as time dependent function
The method of pseudo-resonance cross sections is used to analyze published temperature-dependent neutron transmission and self-indication measurements on tantalum in the unresolved region. In the energy region analyzed, 1825.0 to 2017.0 eV, a direct application of the pseudo-resonance approach using a customary average strength function will not provide effective cross sections which fit the measured cross section behavior. Rather a local value of the strength function is required, and a set of resonances which model the measured behavior of the effective cross sections is derived. This derived set of resonance parameters adequately represents the observed resonance hehavior in this local energy region. Similar analyses for the measurements in other unresolved energy regions are necessary to obtain local resonance parameters for improved reactor calculations. This study suggests that Doppler coefficients calculated by sampling from grand average statistical distributions over the entire unresolved resonance region can be in error, since significant local variations in the statistical distributions are not taken into consideration.
We explore the effectiveness of the Brink–Axel hypothesis (BAH) for the computation of stellar electron capture (EC) and β-decay (BD) rates, namely that the transition strength function depends only upon the transition energy and not upon the details of the initial state. For this purpose, we calculated Gamow–Teller (GT) strength distributions for a selection of sd-shell nuclides, using two different microscopic models, namely the proton–neutron quasiparticle random phase approximation and the full configuration-interaction shell model, taking into account the first 100 states of both the initial and final nuclides. The GT transition strengths among these levels evolve with initial state energy. These transition strength functions we folded into weak-interaction mediated rates in stellar matter, specifically EC and BD rates, for a range of densities 10 g cm –3 ≤ ρ ≤ 10 11 g cm –3 and range of temperatures 1 GK ≤ T ≤ 30 GK. When transitions from excited states were approximated using the BAH, augmented by so-called 'back-resonance' transitions, the rates were affected by up to three orders of magnitude or more at high temperatures and densities. Furthermore the BAH is not a reliable approximation for the calculation of stellar rates, especially in high temperature–density environments.
Background: Photon strength functions are an important ingredient in calculations relevant for the nucleosynthesis of heavy elements. The relation to the photoabsorption cross section allows to experimentally constrain photon strength functions by investigating the photoresponse of atomic nuclei. Purpose: Here, we determine the photoresponse of 66 Zn in the energy region of 5.6 MeV to 9.9 MeV and analyze the contribution of the 'elastic' decay channel back to the ground state. In addition, for the elastic channel electric and magnetic dipole transitions were separated. Methods: Nuclear resonance fluorescence experiments were performed using a linearly polarized quasi-monoenergetic photon beam at the High Intensity γ-ray Source. Photon beam energies from 5.6 to 9.9 MeV with an energy spread of about 3% were selected in steps of 200–300 keV. Two high purity germanium detectors were used for the subsequent γ-ray spectroscopy. Results: Full photoabsorption cross sections are extracted from the data making use of the monoenergetic character of the photon beam. For the ground-state decay channel, the average contribution of electric and magnetic dipole strengths is disentangled. The average branching ratio back to the ground state is determined as well. Conclusions: The new results indicate lower cross sections when compared to the values extracted from a former experiment using bremsstrahlung on 66 Zn. In the latter, the average branching ratio to the ground state is estimated from statistical-model calculations in order to analyze the data. Corresponding estimates from statistical-model calculations underestimate this branching ratio compared to the values extracted from the present analysis, which would partly explain the high cross sections determined from the bremsstrahlung data.
Multi-step cascade γ-ray spectra from the neutron capture at isolated resonances of 161Dy nucleus were measured at the LANSCE/DANCE time-of-flight facility in Los Alamos National Laboratory. The objectives of this experiment were to confirm and possibly extend the spin assignment of s-wave neutron resonances and get new information on photon strength functions with emphasis on the role of the M1 scissors mode vibration. The preliminary results show that the scissors mode plays a significant role in all transitions between accessible states of the studied nucleus. The photon strength functions describing well our data are compared to results from 3He-induced reactions, (n,γ) experiments on Gd isotopes, and (γ,γ’) reactions.
The cross section for neutron capture in the continuum region has been difficult to calculate accurately. Previous results for 238 U show that including an M 1 scissors-mode contribution to the photon strength function resulted in very good agreement between calculation and measurement. Our paper extends that analysis to 234 , 236 U by using γ -ray spectra measured with the Detector for Advanced Neutron Capture Experiments (DANCE) at the Los Alamos Neutron Science Center to constrain the photon strength function used to calculate the capture cross section. Calculations using a strong scissors-mode contribution reproduced the measured γ -ray spectra and were in excellent agreement with the reported cross sections for all three isotopes.
The nuclear level densities and γ-ray strength functions of 138,139,140 La were measured using the 139 La( 3 He,α), 139 La( 3 He,' 3 He), and 139La(d,p) reactions. The particle-γ coincidences were recorded with the silicon particle telescope (SiRi) and NaI(Tl) (CACTUS) arrays. In the context of these experimental results, the low-energy enhancement in the A~140 region is discussed. The 137,138,139 La(n,γ) cross sections were calculated at s- and p-process temperatures using the experimentally measured nuclear level densities and γ-ray strength functions. As a result, good agreement is found between 139 La(n,γ) calculated cross sections and previous measurements.
Background: Radiative neutron capture on thulium, which is a monoisotopic element, plays a role in different applications such as nuclear astrophysics or nuclear burning environments. Considerable discrepancies—reaching 20%—exist between evaluations in the unresolved-resonance region. Furthermore, experimental data on statistical 𝛾 decay in odd-odd rare-earth nuclei is scarce. There are still open questions about the systematics of the so-called scissors mode in the 𝑀1 photon strength function, especially in odd-odd nuclei. Purpose: This work is focused on two main topics—deriving experimental 169 Tm (𝑛,𝛾) cross section and studying statistical 𝛾 decay of 170 Tm, in particular properties of the scissors mode. Methods: The capture experiments to obtain experimental cross section were performed at the Los Alamos Neutron Science Center using the time-of-flight technique and employing the Detector for Advanced Neutron Capture Experiments. Measured coincident 𝛾-ray spectra were also compared with statistical simulations using the dicebox code to test different models of level density and photon strength functions. Results: The capture cross section was determined from 1.8 eV to 0.97 MeV, the broadest neutron-energy range ever measured for this isotope. Several new resonances have been observed. The statistical 𝛾 decay of 170 Tm cannot be reproduced without a scissors mode resonance centered at ≈ 3.3MeV. Conclusions: The measured cross section in the unresolved-resonance region is generally lower than the latest evaluations. The derived 169 Tm 𝑠-process abundance is expected to increase by a factor of 1.26, while the changes of the abundances of elements heavier than 169 Tm are in the order of 0.2%. The scissors mode properties in 170 Tm are similar to those deduced in previous analyses of neighboring nuclei 168 Er and 166 Ho .
A survey of some results in the modern microscopic theory of properties of nuclear reactions with gamma rays is given. First of all, we discuss the impact of Phonon Coupling (PC) on the Photon Strength Function (PSF) because it represents the most natural physical source of additional strength found for Sn isotopes in recent experiments that could not be explained within the standard HFB + QRPA approach. The self-consistent version of the Extended Theory of Finite Fermi Systems in the Quasiparticle Time Blocking Approximation is applied. It uses the HFB mean field and includes both the QRPA and PC effects on the basis of the SLy4 Skyrme force. With our microscopic E1 PSFs, the following properties have been calculated for many stable and unstable even–even semi-magic Sn and Ni isotopes as well as for double-magic {sup 132}Sn and {sup 208}Pb using the reaction codes EMPIRE and TALYS with several Nuclear Level Density (NLD) models: (1) the neutron capture cross sections; (2) the corresponding neutron capture gamma spectra; (3) the average radiative widths of neutron resonances. In all the properties considered, the PC contribution turned out to be significant, as compared with the standard QRPA one, and necessary to explain the available experimental data. The results with the phenomenological so-called generalized superfluid NLD model turned out to be worse, on the whole, than those obtained with the microscopic HFB + combinatorial NLD model. The very topical question about the M1 resonance contribution to PSFs is also discussed.Finally, we also discuss the modern microscopic NLD models based on the self-consistent HFB method and show their relevance to explain the experimental data as compared with the phenomenological models. The use of these self-consistent microscopic approaches is of particular relevance for nuclear astrophysics, but also for the study of double-magic nuclei.
Background: A handful of neutron-deficient stable nuclei, known as the “p nuclei,” cannot be produced through astrophysical neutron capture processes. Instead, some of these nuclei are proposed to be produced by 𝛾-induced reactions on existing r- and s-process seeds. The specific astrophysical site or sites are not yet identified, however, with uncertainties in the cross sections of these 𝛾-induced reactions playing a role. Databases of reaction rates for astrophysical simulations often rely on theoretical statistical model calculations, such as Hauser-Feshbach, for rates where no experimental information is known. However, reasonable variations in the choice of parametrizations of various nuclear properties can create order-of-magnitude variations in the final predicted cross sections and reaction rates, which are then propagated through the models to the predicted final abundances. Purpose: To better constrain these statistical model calculations and ultimately reduce the uncertainties from the nuclear physics on our understanding of the p nuclei, a measurement of the cross sections of 𝛾-induced reactions on the p-nucleus 102 Pd was undertaken. This work represents the first measurement of its kind, using segmented silicon detectors to measure prompt charged particle emission from 𝛾-induced reactions. Methods: Quasimonoenergetic gamma beams from the High Intensity 𝛾 Source facility bombarded an enriched 102 Pd target. A segmented silicon array was arranged to detect the particles emitted from (𝛾,𝑝) and (𝛾,𝛼) reactions. Results: Reaction cross sections were deduced at multiple 𝛾-beam energies between 10 and 19 MeV, and compared to statistical model calculations using talys-1.96. The 102 Pd (𝛾,𝑝) 101 Rh reaction cross section was reasonably well reproduced by a subset of photon strength functions and level densities, though the strength to the ground state of 101 Rh was underestimated at higher incident gamma energies. The 102 Pd (𝛾,𝛼) 98 Ru was in general overpredicted by the various alpha-nucleus optical model potentials. Conclusions: While the theoretical cross sections used to model the (𝛾,𝑝) reactions for the p process may be reasonable, a more careful approach is needed in the case of (𝛾,𝛼). Further work to probe gamma-induced reaction cross sections at and near the p nuclei is warranted.
We combine the thermal QRPA approach with the Skyrme energy density functional theory (Skyrme–TQRPA) for modelling the process of electron capture on nuclei in supernova environment. For a sample nucleus, {sup 56}Fe, the Skyrme–TQRPA approach is applied to analyze thermal effects on the strength function of GT{sub +} transitions which dominate electron capture at E{sub e} ≤ 30 MeV. Several Skyrme interactions are used in order to verify the sensitivity of the obtained results to the Skyrme force parameters. Finite-temperature cross sections are calculated and the results are comparedwith those of the other model calculations.
The recently developed particle-hole dispersive optical model is applied to describe properties of high-energy isoscalar monopole excitations in medium-heavy mass spherical nuclei. In particular, the double transition density averaged over the energy of the isoscalar monopole excitations is considered for {sup 208}Pb in a wide energy interval, which includes the isoscalar giant monopole resonance and its overtone. The energy-averaged strength functions of these resonances are also analyzed.
The development of a modern and more realistic nuclear energy density functional (EDF) for accurate predictions of properties of nuclei is the subject of enhanced activity, since it is very important for the study of properties of nuclear matter (NM), giant resonances and, in particular, of properties of rare nuclei with unusual neutron-to-proton ratios. Here, we provide a short review of the current status of the nuclear EDF and the theoretical results obtained for properties of nuclei and nuclear matter. We will first describe a method for determining the parameters of the EDF, associated with the Skyrme type effective interaction, by carrying out a Hartree-Fock based fit to extensive set of data of ground state properties and constraints. Next we will describe the fully self-consistent Hartree-Fock (HF) based random-phase-approximation (RPA) theory for calculating the strength functions S(E) and centroid energies E CEN of giant resonances and the folding model (FM) distorted wave Вorn approximation (DWBA) to calculate the excitation cross section of giant resonances by α scattering. Then we will provide results for: (i) the Skyrme parameters of the KDE0v1 EDF; (ii) consequences of violation of self-consistently in HF-based RPA; (iii) FM-DWBA calculation of excitation cross section; (iv) values of the E CEN of isoscalar and isovector giant resonances of multipolarities L=0–3 for a wide range of spherical nuclei, using 33 EDFs associated with standard form of the Skyrme type interactions, commonly employed in the literature; and (v) the sensitivities E CEN of the giant resonances to bulk properties of NM. We also determine constraints on NM properties, such as the incompressibility coefficient and effective mass, by comparing with experimental data on E CEN of giant resonances.
β{sup −}-decay rates are of crucial importance in stellar evolution and nucleosynthesis, as they are a key component in stellar processes. Tabulated values of the decay rates as functions of both temperature T and density ρ are necessary input to stellar evolution codes such as MESA, or largescale nucleosynthesis simulations such as those performed by the NuGrid collaboration. Therefore, it is interesting to know the uncertainties in these rates and the effects of these uncertainties on stellar structure and isotopic yields. We have calculated β-strength functions and reaction rates for nuclei ranging from {sup 16}O to {sup 339}136, extending from the proton drip line to the neutron drip line based on a quasi-particle random-phase approximation (QRPA) in a deformed folded-Yukawa single-particle model. Q values are determined from the finite-range droplet mass model (FRDM). We have investigated the effect of model uncertainty on astrophysical β{sup −}-decay rates calculated by the FRDM. The sources of uncertainty considered are Q values and deformation. The rates and their uncertainties are generated for a variety of temperature and density ranges, corresponding to key stellar processes. We demonstrate the effects of these rate uncertainties on isotopic abundances using the NuGrid network calculations.
During the last decade, a theoretical method based on the energy–density functional theory and quasiparticle–phonon model, including up to three-phonon configurations was developed. The main advantages of themethod are that it incorporates a self-consistentmean-field and multi-configuration mixing which are found of crucial importance for systematic investigations of nuclear low-energy excitations, pygmy and giant resonances in an unified way. In particular, the theoretical approach has been proven to be very successful in predictions of new modes of excitations, namely pygmy quadrupole resonance which is also lately experimentally observed. Recently, our microscopically obtained dipole strength functions are implemented in predictions of nucleon-capture reaction rates of astrophysical importance. A comparison to available experimental data is discussed.
An extended version of the interacting boson model (IBM), encompassing two-particle–two-hole (2p-2h) excitations originating from below a valence shell and one-particle–one-hole (1p-1h) excitations extending to the upper next-nearest major shell, is developed to investigate cross-shell excitation effects in the transitional nucleus 98 Mo. This extended IBM framework is utilized to reproduce experimentally observed properties such as low-lying positive-parity level energies, 𝐵(𝐸2) values, and the electric quadrupole moment of the 2$^{+}_{1}$ state, 𝜌 2 (𝐸0, 0$^{+}_{2}$ → 0$^{+}_{g}$), as well as the strength functions of the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant quadrupole resonance (ISGQR) in 98 Mo. It is shown that the extended consistent-𝑄 IBM, incorporating configuration mixing of both 2p-2h excitations from below the valence shell and 1p-1h excitations to the upper next-nearest major shell, describes the low-lying structural properties and the ISGMR and ISGQR strength distributions of 98 Mo quite well, with the ISGMR and the ISGQR strength distributions comparable to the results of the self-consistent quasiparticle random-phase approximation with Skyrme interactions.