Beta-delayed neutron emission and $β$-delayed fission ($β$df) probabilities were calculated for heavy, neutron-rich nuclei using the Los Alamos coupled Quasi-Particle Random Phase Approximation plus Hauser-Feshbach (QRPA+HF) approach. In this model, the compound nucleus is initially populated by $β$-decay and is followed through subsequent statistical decays taking into account competition between neutrons, $γ$-rays and fission. The primary output of these calculations includes branching ratios along with neutron and $γ$-ray spectra. We find a relatively large region of heavy nuclides where the probability of $β$df is near 100%. For a subset of nuclei near the neutron dripline, delayed neutron emission and the probability to fission are both large which leads to the possibility of multi-chance $β$df (mc-$β$df). We comment on prospective neutron-rich nuclei that could be probed by future experimental campaigns and provide a full table of branching ratios in ASCII format in the supplemental material for use in various applications.
The Hauser-Feshbach fission fragment decay model, $\mathtt{HF^3D}$, which calculates the statistical decay of fission fragments, has been expanded to include multi-chance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input pre-scission quantities - fission probabilities and the average energy causing fission - and post-scission quantities - yields in mass, charge, total kinetic energy, spin, and parity. From these fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions, allowing for the calculatio…
We present an overview of the coupled-channels optical model and the Hauser-Feshbach theory code CoH$_3$, which focuses on the nuclear reaction calculations in the keV to tens of MeV region with special attention to the nuclear deformation. The code consists of three major sections that undertake the one-body potential mean-field theory, the coupled-channels optical model, and the Hauser-Feshbach statistical decay. There are other complementary segments to perform the whole nuclear reaction calculations, such as the direct/semidirect radiative capture process, pre-equilibrium process, and prom…
We incorporate the coupled-channels optical model into the statistical Hauser-Feshbach nuclear reaction theory, where the scattering matrix is diagonalized by performing the Engelbrecht-Weidenmüller transformation. This technique has been implemented in the coupled-channels optical model code ECIS by J. Raynal, and we extend this method so that all the open channels in a nucleon-induced reaction on a deformed nucleus can be calculated consistently.
The current status of optical potentials employed in the prediction of thermonuclear reaction rates for astrophysics in the Hauser-Feshbach formalism is discussed. Special emphasis is put on $α$+nucleus potentials. A novel approach for the prediction of $α$+nucleus potentials is proposed. Further experimental efforts are motivated.
Consideration of memory of spin and parity in the fissioning compound nucleus by applying the Hauser-Feshbach fission fragment decay model to photonuclear reactions
We have developed a Hauser-Feshbach fission fragment decay model, HF$^3$D, which can be applied to the statistical decay of more than 500 primary fission fragment pairs (1,000 nuclides) produced by the neutron induced fission of $^{235}$U. The fission fragment yield $Y(A)$ and the total kinetic energy TKE are model inputs, and we estimate them from available experimental data for the $^{235}$U(n$\rm_{th}$,f) system. The model parameters in the statistical decay calculation are adjusted to reproduce some fission observables, such as the neutron emission multiplicity $\overlineν$, its distributi…
A model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of scattering matrix from the coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenmüller. The ensemble average of $S$-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [Phys.Rev.C {\bf 12}, 744 (1975)] using newly parametrized channel degree-of-freedom $ν_a$ to better describe the Gaussian Orthogonal Ensemble (GOE) reference calculations. Moldauer ap…
Nuclear Astrophysics requires the knowledge of reaction rates over a wide range of nuclei and temperatures. In recent calculations the nuclear level density - as an important ingredient to the statistical model (Hauser-Feshbach) - has shown the highest uncertainties. In a back-shifted Fermi-gas formalism utilizing an energy-dependent level density parameter and employing microscopic corrections from a recent FRDM mass formula, we obtain a highly improved fit to experimental level densities. The resulting level density is used for determining criteria for the applicability of the statistical mo…
The $(n,α)$ reaction contributes in many processes of energy generation and nucleosynthesis in stellar environment. Since experimental data are available for a limited number of nuclei and in restricted energy ranges, at present only theoretical studies can provide predictions for all astrophysically relevant $(n,α)$ reaction cross sections. The purpose of this work is to study $(n,α)$ reaction cross sections for a set of nuclei contributing in the weak s-process nucleosynthesis. Theory framework is based on the statistical Hauser-Feshbach model implemented in TALYS code with nuclear masses an…
The Hauser-Feshbach statistical model is applied to the de-excitation of primary fission fragments using input mass yields calculated with macroscopic-microscopic models of the potential energy surface. We test the sensitivity of the prompt fission observables to the input mass yields for two important reactions, $^{235}$U$(n_\mathrm{th},f)$ and $^{239}$Pu$(n_\mathrm{th},f)$, for which good experimental data exist. General traits of the mass yields, such as the location of the peaks and their widths, can impact both the prompt neutron and $γ$-ray multiplicities, as well as their spectra. Speci…
An Extended Hauser-Feshbach Method (EHFM) is developed for light heavy-ion fusion reactions in order to provide a detailed analysis of all the possible decay channels by including explicitly the fusion-fission phase-space in the description of the cascade chain. The mass-asymmetric fission component is considered as a complex-fragment binary-decay which can be treated in the same way as the light-particle evaporation from the compound nucleus in statistical-model calculations. The method of the phase-space integrations for the binary-decay is an extension of the usual Hauser-Feshbach formalism…
Radiative neutron capture is an important nuclear reaction whose accurate description is needed for many applications ranging from nuclear technology to nuclear astrophysics. The description of such a process relies on the Hauser-Feshbach theory which requires the nuclear optical potential, level density and $γ$-strength function as model inputs. It has recently been suggested that the M1 scissors mode may explain discrepancies between theoretical calculations and evaluated data. We explore statistical model calculations with the strength of the M1 scissors mode estimated to be dependent on th…
We investigate different formulations of the transmission coefficient $T_c$, including the form implied by Moldauer's ``sum rule for resonance reactions'' [P.A. Moldauer, Phys. Rev. Lett. 19, 1047 (1967)], the SPRT method [G. Noguere, et al. EPJ Web Conf. 146, 02036 (2017)] and the Moldauer-Simonius form [M. Simonius, Phys. Lett. 52B, 279 (1974); P.A. Moldauer, Phys. Rev. 157, 907 (1967)]. Within these different formulations, we compute the neutron transmission coefficients in the resolved and unresolved resonance regions, allowing a direct comparison with the transmission coefficients compute…
Multimessenger observations of the neutron star merger event GW170817 have re-energized the debate over the astrophysical origins of the most massive elements via the r-process nucleosynthesis. A key aspect of such studies is comparing astronomical observations to theoretical nucleosynthesis yields in a meaningful way. To perform realistic nucleosynthesis calculations, understanding the uncertainty in microphysics details such as nuclear reaction rates is as essential as understanding uncertainties in modeling the astrophysical environment. We present an investigation of neutron capture rate c…
The emission of prompt fission $γ$ rays within a few nanoseconds to a few microseconds following the scission point is studied in the Hauser-Feshbach formalism applied to the deexcitation of primary excited fission fragments. Neutron and $γ$-ray evaporations from fully accelerated fission fragments are calculated in competition at each stage of the decay, and the role of isomers in the fission products, before $β$-decay, is analyzed. The time evolution of the average total $γ$-ray energy, average total $γ$-ray multiplicity, and fragment-specific $γ$-ray spectra, is presented in the case of neu…
The Hauser-Feshbach Fission Fragment Decay (HF$^3$D) model is extended to calculate the prompt fission neutron spectrum (PFNS) for the thermal neutron induced fission on $^{235}$U, where the evaporated neutrons from all possible fission fragment pairs are aggregated. By studying model parameter sensitivities on the calculated PFNS, as well as non-statistical behavior of low-lying discrete level spin distribution, we conclude that discrepancies between the aggregation calculation and the experimental PFNS seen at higher neutron emission energies can be attributed to both the primary fission fra…
A role of β-delayed neutron emission and fission in r-process nucleosynthesis attracts a high interest. Although the number of study on them covering r-process nuclei is increasing recently, uncertainties of β-delayed neutron and fission are still large for r-process simulations. Our purpose is to make a new database on β-delayed neutron emission and fission rates. To this end, the data that are not investigated experimentally have to be predicted. Microscopic theoretical approaches based on a nuclear energy density functional and statistical models are one of the competent tools for the predi…
Several sources of angular anisotropy for fission fragments and prompt neutrons have been studied in neutron-induced fission reactions. These include kinematic recoils of the target from the incident neutron beam and the fragments from the emission of the prompt neutrons, preferential directions of the emission of the fission fragments with respect to the beam axis due to the population of particular transition states at the fission barrier, and forward-peaked angular distributions of pre-equilibrium neutrons which are emitted before the formation of a compound nucleus. In addition, there are …
The CGMF code implements the Hauser-Feshbach statistical nuclear reaction model to follow the de-excitation of fission fragments by successive emissions of prompt neutrons and $γ$ rays. The Monte Carlo technique is used to facilitate the analysis of complex distributions and correlations among the prompt fission observables. Starting from initial configurations for the fission fragments in mass, charge, kinetic energy, excitation energy, spin, and parity, $Y(A,Z,KE,U,J,π)$, CGMF samples neutron and $γ$-ray probability distributions at each stage of the decay process, conserving energy, spin an…
We present a self-consistency analysis of fission product yield evaluations. Anomalous yields are determined using a series of simple conservation checks and comparing charge distributions with common parameterizations. The total prompt neutron multiplicity as a function of product mass $\barν_T(A)$ is derived directly from the independent fission product yields using average charge conservation. This method is checked against Monte Carlo simulations of the de-excitation of the fission fragments in a Hauser-Feshbach statistical decay framework. The derived $\barν_T(A)$ is compared with experim…
We perform energy dependent calculations of independent and cumulative fission product yields for $^{235}$U, $^{238}$U, and $^{239}$Pu in the first chance fission region. Starting with the primary fission fragment distributions taken from available experimental data and analytical functions based on assumptions for the excitation energy and spin-parity distributions, the Hauser-Feshbach statistical decay treatment for fission fragment de-excitation is applied to more than 1,000 fission fragments for the incident neutron energies up to 5 MeV. The calculated independent fission product yields ar…
We present $β$-delayed neutron emission and $β$-delayed fission calculations for heavy, neutron-rich nuclei using the coupled Quasi-Particle Random Phase Approximation plus Hauser-Feshbach (QRPA+HF) approach. From the initial population of a compound nucleus after $β$-decay, we follow the statistical decay taking into account competition between neutrons, $γ$-rays, and fission. We find a region of the chart of nuclides where the probability of $β$-delayed fission is $\sim100$%, that likely prevents the production of superheavy elements in nature. For a subset of nuclei near the neutron driplin…
Modelling fission with microscopic input: excitation-energy-dependent fission paths for neutron-induced reactions
Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles（布鲁塞尔天文与天体物理研究所，布鲁塞尔自由大学）；Brussels Laboratory of the Universe - BLU-ULB（宇宙布鲁塞尔实验室）
The formation of alpha-clusters in nuclei close to the decay thresholds is discussed. These states can be considered to be boson-condensates, which are formed in a second order phase transition in a mixture of nucleons and alpha-particles. The de Broglie wavelength of the alpha-particles is larger than the nuclear diameter, therefore the coherent properties of the alpha-particles give particular effects for the study of such states. The states are above the thresholds thus the enhanced emission of multiple-alphas into the same direction is observed. The probability for the emission of multiple…
The radiative neutron capture rates for isotopes of astrophysical interest are commonly calculated within the statistical Hauser-Feshbach reaction model. Such an approach, assuming a high level density in the compound system, can be questioned in light and neutron-rich nuclei for which only a few or no resonant states are available. Therefore, in this work we focus on the direct neutron-capture process. We employ a shell-model approach in several model spaces with well-established effective interactions to calculate spectra and spectroscopic factors in a set of 50 neutron-rich target nuclei in…
This article describes an original approach to analyze simultaneously cross sections and surrogate data measurements using efficient Monte Carlo extended $\mathcal{R}$-matrix theory algorithm based on unique set of nuclear structure parameters. The alternative analytical path based on the manifold Hauser-Feshbach equation was intensively used in this work to gauge the errors carried by the surrogate-reaction method commonly taken to predict neutron-induced cross sections from observed partial decay probabilities. Present paper emphasizes in particular a dedicated way to treat direct reaction e…
The fully energy-damped yields from the $^{35}$Cl+$^{12}$C reaction have been systematically investigated using particle-particle coincidence techniques at a $^{35}$Cl bombarding energy of $\sim$ 8 MeV/nucleon. The fragment-fragment correlation data show that the majority of events arises from a binary-decay process with rather large numbers of secondary light-charged particles emitted from the two excited exit fragments. No evidence is observed for ternary break-up events. The binary-process results of the present measurement, along with those of earlier, inclusive experimental data obtained …
Cross sections for the photon-induced particle-emission reactions (gamma,n), (gamma,p), and (gamma,alpha) are given for all natural isotopes from Ti to Bi. The target nuclei are assumed to be in their ground states, except for 180Ta which is naturally occurring as the isomer 180mTa. The cross sections are calculated in a statistical model (Hauser-Feshbach) approach and covering an energy range from threshold up to 7.35 MeV above the threshold (14.7 MeV above threshold for (gamma,alpha) reactions). The results are intended to aid conception and analysis of experiments which can also be used to …
We present a coupled Quasi-particle Random Phase Approximation and Hauser-Feshbach (QRPA+HF) model for calculating delayed particle emission. This approach uses microscopic nuclear structure information which starts with Gamow-Teller strength distributions in the daughter nucleus, and then follows the statistical decay until the initial available excitation energy is exhausted. Explicitly included at each particle emission stage is $γ$-ray competition. We explore this model in the context of neutron emission of neutron-rich nuclei and find that neutron-gamma competition can lead to both increa…
We have computed dipole strength distributions for nickel and tin isotopes within the Relativistic Quasiparticle Time Blocking approximation (RQTBA). These calculations provide a good description of data, including the neutron-rich tin isotopes $^{130,132}$Sn. The resulting dipole strengths have been implemented in Hauser-Feshbach calculations of astrophysical neutron capture rates relevant for r-process nucleosynthesis studies. The RQTBA calculations show the presence of enhanced dipole strength at energies around the neutron threshold for neutron rich nuclei. The computed neutron capture rat…
A new shell model Hamiltonian for p-shell nuclei which properly takes into account important roles of spin-isospin interactions is used to obtain cross sections of neutrino-^12C reactions induced by decay-at-rest (DAR) neutrinos as well as supernona neutrinos. Branching ratios to various decay channels are calculated by the Hauser-Feshbach theory. Neutrino-^4He reactions are also investigated by using recent shell model Hamiltonians. The reaction cross sections are found to be enhanced for both ^12C and ^4He compared with previous calculations. As an interesting consequence of this, a possible…
The isospin dependence of nuclear level density has been investigated by analyzing the spectra of evaporated neutrons from excited $^{116}$Sn and $^{116}$Te nuclei. These nuclei are populated via $p$ + $^{115}$In and $^{4}$He + $^{112}$Sn reactions in the excitation energy range of 18 - 26 MeV. Because of low excitation energy, the neutron spectra are predominantly contributed by the first-chance decay leading to the $β$-stable $^{115}$Sn and neutron-deficient $^{115}$Te as residues for the two cases. Theoretical analysis of the experimental spectra have been performed within the Hauser-Feshba…
In order to study the processes creating intermediate and heavy nuclei in massive stars it is necessary to provide neutron capture cross sections and reaction rates close to stability and for moderately unstable neutron-rich nuclei. Furthermore, one has to know the efficiency of neutron-releasing reactions in the main evolutionary phases of a massive star. We present simulations of the nucleosynthesis in a 15 and 25 solar mass star, for the first time followed completely from main sequence hydrogen burning until the type II supernova explosion including all nuclides up to Bi. Theoretical react…
The prediction of cross sections for nuclei far off stability is crucial in the field of nuclear astrophysics. For spherical nuclei close to the dripline the statistical model (Hauser-Feshbach) approach is not applicable and direct contributions may dominate the cross sections. For neutron-rich, even-even Sn targets, we compare the resulting neutron capture cross sections when consistently taking the input for the direct capture calculations from three different microscopic models. The results underline the sensitivity of cross sections calculated in the direct model to nuclear structure model…
An experimental campaign has been undertaken at INFN Laboratori Nazionali di Legnaro, Italy, in order to progress in our understanding of the statistical properties of light nuclei at excitation energies above particle emission threshold, by measuring exclusive data from fusion-evaporation reactions. A first reaction 12C+12C at 7.9 AMeV beam energy has been measured, using the GARFIELD+Ring Counter experimental setup. Fusion-evaporation events have been exclusively selected. The comparison to a dedicated Hauser-Feshbach calculation allows us to give constraints on the nuclear level density at …
Radiative thermal neutron capture cross sections for nuclei participating in s-process and p-process nucleosynthesis in and around $N=50$ closed neutron shell have been calculated in statistical semi-microscopic Hauser-Feshbach approach for the energy range of astrophysical interest. A folded optical model potential is constructed utilizing the standard DDM3Y real nucleon-nucleon interaction. The folding of the interaction with target radial matter densities, obtained from the relativistic-mean-field approach, is done in coordinate space using the spherical approximation. The standard nuclear …
A statistical theory of light nucleus reaction (STLN) is proposed to describe both neutron and light charged particle induced nuclear reactions with 1p-shell light nuclei involved. The dynamic of STLN is described by the unified Hauser-Feshbach and exciton model, of which the angular momentum and parity conservations are considered in equilibrium and pre-equilibrium processes. The Coulomb barriers of the incident and outgoing charged particles, which seriously influence the open reaction channels, could be reasonably considered in the incident channel and the different outgoing channels. In ki…
Various theories beyond the standard model of particle physics predict the existence of baryon number violating processes resulting in nucleon decay. When occurring within an atomic nucleus, such a decay will be followed by secondary decays of the daughter nucleus unless its ground state is directly populated. In this paper, we estimate branching ratios for processes associated with dinucleon decays of the $^{16}$O nucleus. To this end, we use a simple shell model for the ground state of $^{16}$O. For decays from the 1$s_{1/2}$ configuration, which result in highly excited states in the daught…
Neutrino-induced reactions on $^{16}$O are investigated by shell-model calculaions with new shell-model Hamiltonians, which can describe well the structure of $p$-shell and $p$-$sd$ shell nuclei. Distribution of the spin-dipole strengths in $^{16}$O, which give major contributions to the $ν$-$^{16}$O reaction cross sections, is studied with the new Hamiltonians. Muon-capture reaction rates on $^{16}$O are also studied to discuss the quenching of the axial-vector coupling in nuclear medium. Charged-current and neutral-current reaction cross sections are evaluated in various particle and $γ$ emi…
Method: To examine signatures of this alpha-condensation, a compound nucleus reaction using 160, 280, and 400 MeV 16O beams impinging on a carbon target was used to investigate the 12C(16O,7a) reaction. This permits a search for near-threshold states in the alpha-conjugate nuclei up to 24Mg. Results: Events up to an alpha-particle multiplicity of 7 were measured and the results were compared to both an Extended Hauser-Feshbach calculation and the Fermi break-up model. The measured multiplicity distribution exceeded that predicted from a sequential decay mechanism and had a better agreement wit…
We present a new approach for calculating electromagnetic excitation of nuclei as well as probabilities of emission and distributions of neutrons from decays of excited nuclear systems for ultrarelativistic, ultraperipheral heavy ion collisions. Excitation functions for $γ$ + Pb $\to$ Pb$^*$ are parametrized using physics-motivated components: excitation of giant resonances, quasi-deuteron absorption mechanism, excitation of nucleon resonances as well as high-energy dissociation of protons and neutrons. Neutron emission (up to 10 neutrons) from low-energy excitations of $^{208}$Pb is modelled …
The path towards the production of \textit{r}-process seed nuclei follows a course where the neutron-rich light and medium mass nuclei play a crucial role. The neutron capture rates for these exotic nuclei could dominate over their $α$-capture rates, thereby enhancing their abundances at or near the drip line. We calculate the radiative neutron capture cross-section for the $^{33}$Na(n,$γ)^{34}$Na reaction via the Coulomb dissociation of $^{34}$Na as it undergoes elastic breakup on $^{208}$Pb when directed at a beam energy of 100 MeV/u using the entirely quantum mechanical theory of finite ran…
