Statistical Theory Of Nuclear Reactions Research Articles

A new empirical systematic for (n, 2p) reaction cross sections around 14 MeV

In the present work, we proposed a new empirical systematic with which we can predict the (n, 2p) cross sections as an extension of the empirical rule on the basis of the statistical theory of nuclear reactions. It is obtained by fitting the experimental cross sections as a function of mass number, reaction Q–value, threshold energy and projectile energy. A new analysis of experimental data is performed for (n, 2p) reactions around 14 MeV energy. Besides, the present formula was expressed by a simple systematic with two fitting parameters. The predictions of this formula were discussed and compared with cross section measurements and empirical formulas found in the literature. Results show that the new empirical formula gives a good fit to predict the (n, 2p) cross sections around 14 MeV. This study can provide a reference to the (n, 2p) reaction channel considering the lack of measured cross section values.

Fission fragment decay simulations with the CGMF code

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 and parity. Nuclear structure and reaction input data from the RIPL3 library are used to describe fission fragment properties and decay probabilities. Characteristics of prompt fission neutrons, prompt fission γ rays, and independent fission yields can be studied consistently. Correlations in energy, angle and multiplicity among the emitted neutrons and γ rays can be easily analyzed as a function of the emitting fragments. In its current version, CGMF is limited to certain spontaneous fission reactions on Pu and Cf isotopes, as well as neutron-induced fission reactions up to 20 MeV on U, Np, and Pu isotopes. Program summaryProgram Title:CGMF 1.1CPC Library link to program files:https://doi.org/10.17632/jrtt73npzw.1Licensing provisions: BSD-3 clauseProgramming language: C++Nature of problem: Modeling of fission fragment decaySolution method: Monte Carlo implementation of the Hauser-Feshbach statistical theory of nuclear reactions to describe the de-excitation of fission fragments on an event-by-event basis.Additional comments including restrictions and unusual features: spontaneous fission reactions for 238,240,242,244Pu and 252,254Cf; neutron-induced fission reactions from thermal up to 20 MeV for n+233,234,235,238U, n+237Np, and n+239,241Pu. Binary fission only (no ternary fission).

Analysis of the reaction Q-value effect using newly evaluated empirical formulas of (n,2n) cross-sections near 14.6MeV

Empirical formulas in determining the cross-sections play an important role at the energies of which there are no experimental data scattered about. The purpose of the present communication is to further improve the formulas of the cross-section of [Formula: see text] reactions at the energies near 14.6[Formula: see text]MeV. A systematics for the evaluation of these cross-sections is studied. We present the empirical formulas based on the statistical theory of nuclear reactions in connection with the compound nucleus. The new empirical formulas are found by using the experimental cross-sections as a function of the reaction [Formula: see text]-value. Thus, the new formulas provide the best description of the existing measured data compared with systematics suggested earlier by other authors.

Experimental verification of neutron inelastic scattering cross section for iron

Results of experimental verification of results on neutron inelastic scattering cross section for iron obtained in measurements of spectra of neutrons undergoing inelastic scattering at incident neutron energies of 6.0, 7.0 and 8.0 MeV and their calculations within the framework of statistical theory of nuclear reactions and direct interactions are presented. Description is given of the methodology of measurements and simulation calculations. Spectra of neutrons undergoing inelastic scattering obtained for iron in the process of experiments are analyzed in comparison with calculated data. New measurements of neutron inelastic scattering spectra and their analysis within the framework of contemporary modeling understanding allowed formulating proposal on introduction of corrections in the indigenous BROND-2.2 library of recommended evaluated neutron data and insignificant corrections in the most recent version of the library BROND-3.

Statistical Theory of Breakup Reactions

We propose alternatives to coupled-channels calculations with loosely-bound exotic nuclei (CDCC), based on the the random matrix (RMT) and the optical background (OPM) models for the statistical theory of nuclear reactions. The coupled channels equations are divided into two sets. The first set, described by the CDCC, and the other set treated with RMT. The resulting theory is a Statistical CDCC (CDCC$_S$), able in principle to take into account many pseudo channels.

R-matrix analysis and prediction of low-energy neutron-induced fission cross sections for a range of Pu isotopes

Neutron-induced fission cross sections for the plutonium isotopes from 236 to 244 are computed for neutrons of a few keV up to 5.5 MeV incident energy, using the Hauser-Feshbach statistical theory of nuclear reactions, modified to treat the fission decay channel in the $R$-matrix formalism. The fluctuations of the fission decay widths owing to the presence of intermediate structures in the second well and to the coupling of class I and class II states are simulated by Monte Carlo sampling of the underlying model parameter distributions. The accuracy of this approach is tested relative to the results of well-known analytical formulations for the average fission cross sections. Special attention is paid to the choice and consistency of the model input parameters, in part obtained from microscopic nuclear structure calculations. The predictive capabilities offered by our method are tested against the neutron-induced fission of the very short-lived ${}^{243}$Pu (${\ensuremath{\tau}}_{1/2}=4.95$ h) for which no measurement exist. Our calculations, consistent over all the Pu isotope series, demonstrate that ${}^{243}$Pu is fissile, in contrast to what is reported in the standard ENDF/B-VII.1 and JEFF-3.1.2 evaluated libraries. No recommendations are made in the JENDL-4.0 data library for this isotope.

Statistical Theory of Nuclear Reactions: Comparisons with Unimolecular Reactions and Microcluster Productions

Statistical reaction processes of nuclei, of molecules and of microclusters are compared with each other. Bohr and Weisskopf's theory of compound nuclear reactions is reviewed together with recent developments in this field, which will be one of the bases for understanding statistical reactions in general. Further sophistication of the theory including pre-equilibrium processes is briefly reviewed.

PRE-EQUILIBRIUM EFFECTS IN THE SECONDARY PARTICLE SPECTRA IN THE REACTIONS WITH HEAVY IONS

Theoretical description of the experimentally obtained spectra for protons and α-particles and model calculations for the neutron spectra in the reactions with heavy ions has been presented. The hybrid model of non-equilibrium processes was used. Equilibrium evaporation process was analyzed in the framework of the statistical theory of nuclear reactions with Monte-Carlo simulation including certain dynamical and kinematical characteristics. This approach was included in PACE code, which permits to simulate Monte-Carlo de-excitation nuclear process. The Fermi-gas model and level-density phenomenological model for the variation of the nuclear level density parameters was used. In this approach data on 16 O +116 Sn reaction with Ebeam = 130, 250 MeV were analyzed. Double-differential light charged particle spectra for this reaction were measured using the GARFIELD apparatus in coincidence with evaporation residues. The experimental data were collected in four angular ranges from 29 to 41, 41 to 53, 53 to 67 and 67 to 82 degrees in the laboratory system. The results of the calculations are shown and discussed for these four angular ranges. The contributions from the evaporative and pre-equilibrium processes were analyzed in connection with different nucleus equilibration mechanisms.

Time characteristics and odd-even effects in nucleus deexcitation process

An approach based on the statistical theory of nuclear reactions and Monte Carlo method is used for evaluations of excited nuclear system characteristics like probability of decay channel (light particle, γ-quanta emission, or fission), energy, emission angle of decay products, and time characteristics of deexcitation processes. This method permits the direct simulation of the experimental situation, in particular, nuclear-lifetime measurements by the crystal blocking technique. Decay times of compound nuclei formed in the fusion reactions 12C+28Si → 40Ca and 19F+28Si → 47V are estimated.

Decay time characteristics of the U-like excited nuclei

The unified energy dependence of the induced fission times obtained by the crystal blocking technique for heavy nuclei with Z=91–94 in the range of initial excitation energy from 5 to 250 MeV was analyzed. It was demonstrated that, for excitation energies of the investigated heavy fissionable nuclei up to 60–70 MeV, the fission times can be described in the framework of the statistical theory of nuclear reactions taking into account the double-humped structure of the fission barrier and the lifetimes of both classes of excited nuclear states realized in the first and second potential wells. However, for excitation energies above 70 MeV, there is a need to consider the dynamical effects in the fission channel.

Fission time in the 28Si + natPt reaction

The experimental fission times are analyzed for excited nuclei produced in the 28Si + natPt reaction. Experimental lifetimes obtained by the crystal-blocking technique range between 10−17 and 10−18 s at bombarding energies between 140 and 170 MeV, respectively. Experimental data are analyzed within the statistical theory of nuclear reactions and the double-humped-fission-barrier model with allowance for preequilibrium processes and the nuclear-dissipation phenomenon. It is shown that fission barriers retain their double-humped structure for nuclear temperatures up to about 1.7–1.8 MeV and that the lifetimes of excited strongly deformed states in the second potential well contribute substantially to the observed delay times in the fission decay channel.

Blocking technique measurements of the induced fission time of U nuclei

The blocking technique was used to measure lifetimes of the excited 234,235U nuclei produced in the 232Th+α reaction at the energy of bombarding α-particles in the range 20.0–31.2 MeV. The resulting experimental data are analyzed in the statistical theory of nuclear reactions with allowance for the lifetimes of the excited states of the first and second potential wells of the double-humped fission barrier. The absolute values of the level densities in the second potential well, fission barrier parameters and type of shape symmetry in the second well were determined.

Study of Gamma Radiation from the Interaction of 14.6-MeV Neutrons with 27Al

The gamma radiation from the interaction of 14.6-MeV neutrons with aluminum has been investigated by high-resolution germanium-detector gamma-ray spectroscopy. Cross sections for gamma lines from the 27Al(n,n’γ), (n,pγ), and (n,npγ) reactions have been measured at an emission angle of 125 deg. The results are compared with previous measurements and with predictions based on the statistical theory of nuclear reactions (including direct and precompound contributions). The current results are within the range of values reported in the widely discrepant previous measurements and thus allow the resolution of these discrepancies. The relative intensities of the gamma lines analyzed in this work are in good agreement with the results of a white neutron source measurement performed by two of the authors at Los Alamos National Laboratory. The measured gamma-ray production cross sections were compared with the results of nuclear model calculations using the GNASH code. The agreement with the calculated cross sections is unsatisfactory. The results of the statistical calculations are on average ∼20% below the measured cross sections, and there are also some discrepancies between the calculated and measured relative intensities for the different lines from the (n,n’γ) reaction.

Study of Gamma Radiation from Interaction of 14.7-MeV Neutrons with208Pb

The gamma radiation from the interaction of 14.7-MeV neutrons with {sup 208}Pb is investigated by high-resolution germanium-detector gamma-ray spectroscopy by using an enriched {sup 208}Pb sample. Cross sections for 14 gamma-ray lines from the {sup 208}Pb(n,n{prime}{gamma}) and {sup 208}Pb(n,2n{gamma}) reactions are measured at an emission angle of 124 deg. The results are compared with measurements from previous studies and with predictions based on the statistical theory of nuclear reactions (including direct and precompound contributions). The current results, especially for the {sup 208}Pb(n,n{prime}{gamma}) reaction, are considerably smaller than the results of most of the measurements of the previous studies probably because of the neglect of important sources of background, e.g., gamma-ray production in lead shielding, in the previous studies. Agreement with theory is adequate for the strong transitions between the lowest levels in {sup 207}Pb and {sup 208}Pb, but large discrepancies exist for the weaker transitions, especially for gamma-ray transitions from levels where experimental knowledge of branching ratios is missing. The study of the gamma radiation from the interaction of 14-MeV neutrons with lead is essential for accurate prediction of the gamma-ray heating in such devices. In addition, the nucleus {sup 208}Pb is especially studied as a test case for detailedmore » comparison of the predictions of nuclear reaction theory with experiments.« less

Structure of 75Se.

The low-lying low-spin levels of {sup 75}Se have been investigated. These levels were populated via the {sup 75}As({ital p},{ital n}{gamma}){sup 75}Se reaction with proton energies between 3.0 and 4.0 MeV. Angular distribution measurements have been used to assign spin values and to determine multipole mixing ratios via compound statistical theory of nuclear reactions. Lifetimes for 17 states in {sup 75}Se were obtained by the Doppler-shift attenuation method for the first time. For several of the transitions in {sup 75}Se, values or limits for {ital B}({ital M}1) and {ital B}({ital E}2) were obtained. The negative-parity sequence of levels up to about 2.5 MeV could be predicted well on the basis of the collective model with Coriolis perturbation. An effective moment-of-inertia parameter under the effect of Coriolis perturbation is used to predict these states. The results compare quite well with experimental values.

The statistical theory of nuclear reactions in the limit of isolated resonances III

In two earlier papers, the statistical theory was considered in the limit of isolated resonances. The calculated quantity was essentially the compound nucleus cross section. Here, we complete those considerations with the correlation betweenS-matrix elements taken at different energies.

The statistical theory of nuclear reactions in the limit of isolated resonances II

The statistical theory of nuclear reactions in the limit of isolated resonances II

Parity violation in compound-nucleus reactions.

A formalism is developed that incorporates parity violation into the statistical theory of nuclear reactions. It allows the calculation of average square values of observables sensitive to parity breaking starting from well known average parameters (transmission coefficients and level densities) as input. For the case of low-energy neutron resonance scattering, a systematic study of the expected size of the effect is presented. An enhanced sensitivity of these reactions to parity violation is borne out.

Scattering theory and conductance fluctuations in mesoscopic systems

A random-matrix model developed originally in the framework of the statistical theory of nuclear reactions is (via the many-channel approximation of Landauer's formula) applied to universal conductance fluctuations (UCF) in a disordered sample connected to two or three leads. The leads are modelled as ideal conductors. For large sample lengths, the results agree with those obtained by other approaches. This shows that UCF can be modelled successfully in terms of random matrices. For sample lengths of several tens of elastic mean free paths, the conductance fluctuations are seen to depend sensitively on the coupling to the leads. This is due to the appearance of a new energy scale, the width Γ for emission of an electron from the disordered sample into the leads. This quantity Γ also influences the autocorrelation function of the conductance. Results are presented for the three canonical random-matrix ensembles: The Gaussian orthogonal, unitary, and symplectic ensembles.

The statistical theory of nuclear reactions in the limit of isolated resonances

The random matrix theory of statistical nuclear reactions — formulated by Verbaarschot, Weidenmüller and Zirnbauer — is considered in the limit of isolated resonances. This means more technically: the correlation between the elmentsS ab andS cd * of the scattering matrix is calculated in the limit of very small transmission coefficientsT c in all open channelsc.