Pre-equilibrium Exciton Model Research Articles

New semi-empirical systematic of (p,n) reaction cross section at 7.5 MeV

Abstract It is advised to use a new formula to calculate the (p, n) reaction cross section at 7.5 MeV. We propose six new parameters for the formula proposed by Broeders, C. and Konobeyev, A.Y. (2008. Systematics of (p,n) reaction crosssection. Radiochim. Acta 96: 387–397) to fit experimental data. It should be noted that our systematics is only applicable to isotopes with a ratio of 7.5 MeV to the reaction threshold above 1.3 (7.5/E th > 1.3). This is based on analytical calculations generated from the semi-empirical mass formula, the evaporation model, and the pre-equilibrium exciton model. We were able to find new parameters for the Broders et al. formula through this inquiry that guarantee a good fit with the revised experimental data (EXFOR2022) and provide a minimum value for the statistical parameters ∑ and χ 2.

A study on the estimations of (n,t) reaction cross-sections at 14.5 MeV by using artificial neural network

In this paper, calculations of the [Formula: see text] reaction cross-sections at 14.5 MeV have been presented by utilizing artificial neural network algorithms (ANNs). The systematics are based on the account for the non-equilibrium reaction mechanism and the corresponding analytical formulas of the pre-equilibrium exciton model. Experimental results, obtained from the EXFOR database, have been used to train the ANN with the Levenberg–Marquardt (LM) algorithm which is a feed-forward algorithm and is considered one of the well-known and most effective methods in neural networks. The Regression [Formula: see text] values for the ANN estimation have been determined as 0.9998, 0.9927 and 0.9895 for training, testing and for all process. The [Formula: see text] reaction cross-sections have been reproduced with the TALYS 1.95 and the EMPIRE 3.2 codes. In summary, it has been demonstrated that the ANN algorithms can be used to calculate the [Formula: see text] reaction cross-section with the semi-empirical systematics.

Investigating high-energy proton-induced reactions on spherical nuclei: Implications for the preequilibrium exciton model

Background: A number of accelerator-based isotope production facilities utilize 100- to 200-MeV proton beams due to the high production rates enabled by high-intensity beam capabilities and the greater diversity of isotope production brought on by the long range of high-energy protons. However, nuclear reaction modeling at these energies can be challenging because of the interplay between different reaction modes and a lack of existing guiding cross-section data.Purpose: A Tri-lab collaboration has been formed among the Lawrence Berkeley, Los Alamos, and Brookhaven National Laboratories to address these complexities by characterizing charged-particle nuclear reactions relevant to the production of established and novel radioisotopes.Method: In the inaugural collaboration experiments, stacked-targets of niobium foils were irradiated at the Brookhaven Linac Isotope Producer (${E}_{p}=200\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$) and the Los Alamos Isotope Production Facility (${E}_{p}=100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$) to measure $^{93}\mathrm{Nb}(p,x)$ cross sections between 50 and 200 MeV. First measurements of the $^{93}\mathrm{Nb}(p,4n)^{90}\mathrm{Mo}$ beam monitor reaction beyond 100 MeV are reported in this work, as part of the broadest energy-spanning dataset for the reaction to date. $^{93}\mathrm{Nb}(p,x)$ production cross sections are additionally reported for 22 other measured residual products. The measured cross-section results were compared with literature data as well as the default calculations of the nuclear model codes TALYS, CoH, EMPIRE, and ALICE.Results: The default code predictions largely failed to reproduce the measurements, with consistent underestimation of the preequilibrium emission. Therefore, we developed a standardized procedure that determines the reaction model parameters that best reproduce the most prominent reaction channels in a physically justifiable manner. The primary focus of the procedure was to determine the best parametrization for the preequilibrium two-component exciton model via a comparison to the energy-dependent $^{93}\mathrm{Nb}(p,x)$ data, as well as previously published $^{139}\mathrm{La}(p,x)$ cross sections.Conclusions: This modeling study revealed a trend toward a relative decrease for internal transition rates at intermediate proton energies (${E}_{p}=20$--60 MeV) in the current exciton model as compared to the default values. The results of this work are instrumental for the planning, execution, and analysis essential to isotope production.

Newly developed semi-empirical formulas of nuclear excitation functions for (n,α) reactions at the energy range 12 ≤ En ≤ 20 MeV and mass number range 30 ≤ A ≤ 128

A new semi-empirical systematics of (n,α) reaction excitation functions for nuclei with mass number 30≤A≤128 at neutron induced energy range 12≤En≤20 MeV is obtained. It is based on the evaporation model and the pre-equilibrium exciton model. The Droplet model of Myers and Swiatecki was used to express the reaction energy Q. The Dostrovsky formula was introduced to formulate the expression of the inverse cross section channel.The systematics behavior of the different terms of the Droplet model involved in the reaction energy Q(n,α) was verified individually before choosing the relevant terms and setting up the formulae. By fitting these formulae to the existing cross-section data, the adjustable parameters have been determined and the systematics of the (n,α) reaction have been studied. The new semi-empirical formula has been verified for predictions of the excitation functions of nuclear reactions not used in the fitting. The calculated excitation functions were compared to the experimental data and EMPIRE-3.2 code calculations. A good agreement between excitation functions systematics and EXFOR data was observed for great number of (n,α) reactions.

State density formalism of the Iwamoto-Harada model: A suitable tool to treat cluster emission from heavy-ion collisions with account for spin variables

We study the possibility to include the cluster emission into the statistical pre-equilibrium (exciton) model suitable also for heavy ion collisions. The direct motivation of this paper is a possibility of producing superdeformed nuclei, which are easier to be detected in heavy-ion reactions than in those induced by light projectiles (nucleons, deuterons, α-particles).

Enhanced Nuclear State Density Equation in a Two-Component Pre-Equilibrium Exciton Model for Heavy Nuclei

The properties of nuclear state density which increases with increasing excitation energy are very important in many nuclear reactions. Previously, several theoretical calculations were performed and added to correct the state density equation. In this work, various corrections, i.e. the pairing effect, Pauli exclusion principle, parity, spin distribution, the finite depth and the bound state effect were added to enhance the state density results using the energy-dependent single-particle level densities (non-ESM) in 114Sn and 116Sn nuclei. The results of this work were compared to the available experimental (OSLO technique), and theoretical (E&B and HF-BCS) results. The calculations were performed for energies up to 80 MeV and show a reasonable match with experimental and theoretical results at low energies. At high energies the deformation effect affects the results and leads to mismatch between the results of this work and other results. The inclusion of the spin distribution function in case of j=1/(2 ), gives results far from the experimental data and previous theoretical results, which shows the importance of the introduction of a new formula that deals with a non-ESM system.

Evaluated gas production cross-section data for natural titanium irradiated with protons at energies up to 3 GeV

Abstract Evaluated proton, deuteron, triton, 3He and 4He production cross-section data were prepared for natural titanium irradiated with protons at the energy up to 3 GeV. The evaluated data were obtained from the analysis of results of nuclear model calculations, available measured, and systematic data. The calculations of gas production cross-sections were carried out using the intranuclear cascade model (INC), the pre-equilibrium exciton model, geometry dependence hybrid (GDH) model, Weisskopf-Ewing (WE) model, and the Hauser-Feshbach model. CASCADE, TALYS, ALICE/ASH, and ALICE/HMS codes were used for calculations. Available experimental and systematic data, model calculations were used to evaluate gas production cross-section. The evaluation was carried out using statistical methods implemented in the BEKED code package developed at KIT/INR. The evaluated cross-sections were compared with the data from evaluated data libraries.

Evaluated Activation Cross Section Data for Proton Induced Nuclear Reactions on W up to 3 GeV Incident Energy

Evaluated cross-section data files were prepared for stable tungsten isotopes with the objective to provide reliable and sound nuclear data for activation and inventory calculations of the European Spallation Source, which utilizes a tungsten target. The data files contain yields of radionuclides produced by proton induced reactions with incident energies up to 3 GeV. The calculations of cross-sections were performed using the intranuclear cascade model, the pre-equilibrium exciton model, and the Hauser-Feshbach model. The available experimental information, results of calculations and systematics were applied for the evaluation of yields of residual nuclei using statistical methods implemented in the computer code package BEKED developed at KIT.

Progress in Developing Nuclear Reaction Calculation Code CCONE for High Energy Nuclear Data Evaluation

To adapt the CCONE code to the high energy nuclear data evaluation, the preequilibrium exciton model part of the code has been extended to multiple particle emission. This is realized by sequential calculation of the decay of exciton states for all residual nuclei left by particle emissions. In addition, Iwamoto-Harada cluster coalescence model has been incorporated in the multiple-emission exciton model to improve the accuracy of calculated cluster emission spectra for deuteron, triton, 3He and α particles. The calculated light particle emission spectra are compared with experimental and evaluated data.

A systematic study of (n, p) excitation functions at 14.5 MeV neutrons

A semi-empirical formula is proposed for (n, p) reaction cross-sections at 14.5 MeV neutron energy based on the statistical model, considering the Q-value dependence due to asymmetry parameter and utilizing pre-equilibrium exciton model. Predictions of this formula agree well with those of the existing formulae and with experimental data and have good agreement with it.

Differential Cross Section Comparison Calculated from Kalbach and Iwmoto-Harada Models for Alpha Emission in Pre-equilibrium Region

α-cluster cross section production by proton/neutron induced reactions was calculated at different energies using Kalbach PRECO6 program and an analysis in the framework of pre-equilibrium exciton model made with Iwamoto-Harada [IH] model depend on pickup mechanism. Comparison with our calculation give remarkable agreement with experimental data. The cross section have been estimated for the targets 54Fe, 63Cu, 120Sn with different energies.

Calculations of Double Differential Deuteron Emission Cross Sections at 62 MeV Proton Induced Reactions

In this study, double differential deuteron emission cross sections for 27Al, 54,56Fe, 197Au, 208Pb and 209Bi target nuclei have been calculated by the TALYS code at 62 MeV proton energy. The use of TALYS involved calculations by the pre-equilibrium exciton model and the Hauser–Feshbach model. The calculated double differential cross sections have been compared with the experimental data taken from the literature.

Use of Covariance Matrices in a Consistent (Multiscale) Data Assimilation for Improvement of Basic Nuclear Parameters in Nuclear Reactor Applications: from Meters to Femtometers

A new approach is proposed, the consistent data assimilation, that allows to link the integral data experiment results to basic nuclear parameters employed by evaluators to generate ENDF/B point energy files in order to improve them. A practical example is provided where the sodium neutron propagation experiments, EURACOS and JANUS-8, are used to improve via modifications of {sup 23}Na nuclear parameters (like scattering radius, resonance parameters, Optical model parameters, Statistical Hauser-Feshbach model parameters, and Preequilibrium Exciton model parameters) the agreement of calculation versus experiments for a series of measured reaction rate detectors slopes. Future work involves comparison of results against a more traditional multigroup adjustments, and extension to other isotope of interest in the reactor community as {sup 56}Fe, actinides, and fission products.

Systematics of (p, n) reaction cross-section

Semi-empirical systematics of the (p, n) reaction cross-section was obtained at incident proton energies 7.5 MeV, 12.4 MeV and 24.8 MeV. Systematics is based on analytical formulas derived using the pre-equilibrium exciton model, evaporation model and semi-empirical mass formula Parameters of systematics were fitted to the data obtained from the analysis of available measured (p, n) reaction cross-section.

EMPIRE: Nuclear Reaction Model Code System for Data Evaluation

EMPIRE is a modular system of nuclear reaction codes, comprising various nuclear models, and designed for calculations over a broad range of energies and incident particles. A projectile can be a neutron, proton, any ion (including heavy-ions) or a photon. The energy range extends from the beginning of the unresolved resonance region for neutron-induced reactions (∽ keV) and goes up to several hundred MeV for heavy-ion induced reactions. The code accounts for the major nuclear reaction mechanisms, including direct, pre-equilibrium and compound nucleus ones. Direct reactions are described by a generalized optical model (ECIS03) or by the simplified coupled-channels approach (CCFUS). The pre-equilibrium mechanism can be treated by a deformation dependent multi-step direct (ORION + TRISTAN) model, by a NVWY multi-step compound one or by either a pre-equilibrium exciton model with cluster emission (PCROSS) or by another with full angular momentum coupling (DEGAS). Finally, the compound nucleus decay is described by the full featured Hauser-Feshbach model with γ-cascade and width-fluctuations. Advanced treatment of the fission channel takes into account transmission through a multiple-humped fission barrier with absorption in the wells. The fission probability is derived in the WKB approximation within the optical model of fission. Several options for nuclear level densities include the EMPIRE-specific approach, which accounts for the effects of the dynamic deformation of a fast rotating nucleus, the classical Gilbert-Cameron approach and pre-calculated tables obtained with a microscopic model based on HFB single-particle level schemes with collective enhancement. A comprehensive library of input parameters covers nuclear masses, optical model parameters, ground state deformations, discrete levels and decay schemes, level densities, fission barriers, moments of inertia and γ-ray strength functions. The results can be converted into ENDF-6 formatted files using the accompanying code EMPEND and completed with neutron resonances extracted from the existing evaluations. The package contains the full EXFOR (CSISRS) library of experimental reaction data that are automatically retrieved during the calculations. Publication quality graphs can be obtained using the powerful and flexible plotting package ZVView. The graphic user interface, written in Tcl/Tk, provides for easy operation of the system. This paper describes the capabilities of the code, outlines physical models and indicates parameter libraries used by EMPIRE to predict reaction cross sections and spectra, mainly for nucleon-induced reactions. Selected applications of EMPIRE are discussed, the most important being an extensive use of the code in evaluations of neutron reactions for the new US library ENDF/B-VII.0. Future extensions of the system are outlined, including neutron resonance module as well as capabilities of generating covariances, using both KALMAN and Monte-Carlo methods, that are still being advanced and refined.

Systematics of (p,α) (p,nα), and (p,np) reaction cross-sections

Semi-empirical systematics of (p,α) (p,nα), and (p,np) reaction cross-sections were obtained at various incident proton energies from 17.9 to 28.5 MeV. Systematics are based on analytical formulas derived using the pre-equilibrium exciton model, evaporation model and semi-empirical mass formula. Parameters of systematics were fitted to the data obtained from the analysis of available measured cross-sections for (p,α) (p,nα), and (p,np) reactions.

Semi-empirical systematics of (n, 3He) reaction cross-section at 14.6 and 20 MeV

A new semi-empirical formula for the evaluation of (n, 3He) reaction cross-sections at the energy of 14.6 and 20 MeV is presented. Formula was derived using the analytical expression for the evaluation of the 3He spectrum within the frame of pre-equilibrium exciton model. The systematics obtained is compared with the empirical formula for the (n, 3He) reaction cross-section.

Semi-empirical systematics of [formula omitted] reaction cross-section at 14.5, 20, and 30 MeV

A new semi-empirical formula for the evaluation of the ( n , p ) reaction cross-section is discussed. The formula was derived using analytical expressions for the calculation of the proton emission spectrum in nuclear reactions within the framework of the preequilibrium exciton model and the evaporation model. A new analysis of experimental ( n , p ) reaction cross-sections was performed. The experimental data and model calculations were used to get the ( n , p ) reaction cross-section systematics at 14.5, 20, and 30 MeV. The systematics provides the best description of experimental data compared with formulas proposed earlier by other authors.

Nuclear models for proton induced upsets: a critical comparison

This work studies the status of the nuclear models used for estimating single event upsets sensitivity and other radiation effects, induced by protons in microelectronic devices. An extended comparison is made between the calculations of the two most developed models, the intranuclear cascade model (used for instant by the HETC code) and the pre-equilibrium exciton (PEqEx) model. The new data base ENDF/B-VI (calculated using PEqEx) is used to clarify the role of the various interactions of primary protons with Si nuclei in the energy deposition in silicon. In particular, we consider the light nuclear reaction products: secondary protons and /spl alpha/ particles. A comparison of simulated deposition spectra of surface barrier detectors with experimental data is shown. The role of reaction products created in the surrounding of the sensitive volume is discussed.

Model calculations of the radiative capture process and the Brink–Axel hypothesis

Using the consistent Direct–SemiDirect (DSD) and the improved Preequilibrium (PEQ) exciton model we analyzed the excitation functions for the neutron radiative capture transitions to the isolated single-particle states in 141 Ce and 209 Pb in order to study the energy positions of the peaks belonging to the Brink–Axel Giant Resonances (BA GDR) built on single-particle states. The PEQ calculations of γ transitions to discrete levels have been performed for the first time. The PEQ model peaks appear at energies lower than those of the BA GDRs for about 0.2 MeV for low-spin states, and for about 0.4 MeV for high-spin ones. The DSD model energies are higher than the BA GDR ones for about 0.3 MeV (1 MeV for high-spin states). Both models reproduce the available experimental peak energies within about 0.25 MeV.