Los Alamos Model Research Articles

Systematics of input parameters for the Los Alamos model with sequential emission

The application of the Point-by-Point treatment to numerous fission cases (i.e. 74 cases including many actinides fissioning spontaneously or induced by thermal neutrons and fast neutrons with energies up to the threshold of the second chance fission) has emphasized interesting systematic behaviors of different quantities characterizing the fission fragments. Such systematics can provide values of the input parameters for a new version of the Los Alamos (LA) model including the sequential emission of prompt neutrons, which was recently developed and validated. The prompt neutron spectrum results based on the systematics of input parameters are obtained in good agreement with the experimental data of many actinides. The LA model with sequential emission together with the proposed systematics of its input parameters can predict prompt neutron spectra of fissioning nuclei without any experimental information, thus it becomes an useful tool for prompt neutron spectrum evaluations.

Inclusion of sequential emission into the most probable fragmentation approach (Los Alamos model) and its validation

A new version of the Los Alamos (LA) model, based on more physical considerations than the previous versions by taking into account the sequential emission of prompt neutrons, is proposed. A residual temperature distribution for each emission sequence P $$_{\mathrm {k}}$$ (T) is considered, so that this new version can provide the prompt neutron spectrum in the center-of-mass and laboratory frames of each neutron successively emitted from the light and heavy fragment. The LA model with sequential emission is applied on 15 fission cases which were not included in the 49 cases used in the elaboration of the systematics of different quantities of residual nuclei, on which the general form of $$\hbox {P}_{\mathrm {k}}$$ (T) is based. The good description of experimental prompt neutron spectrum data of these fission cases by the model results constitutes a relevant validation of the LA model with sequential emission. Systematic behaviours of the average energies (in the center-of-mass and laboratory frames) provided by this model for each neutron sequentially emitted, are also emphasized.

Systematics of different quantities related to sequential prompt emission in fission

A deterministic treatment of sequential neutron emission, based on recursive equations of the residual temperatures, was applied to numerous fission cases (i.e. 49 cases including nuclei fissioning spontaneously or induced by thermal and fast neutrons) for which reliable experimental data of fragment distributions exist. This fact emphasizes systematics and correlations between different average quantities characterizing the initial and residual fission fragments and the sequential prompt neutron emission. The ratios of the average residual temperature following the emission of each neutron to the average temperature of initial fragments ($${ }/{ }$$) are almost constant for all studied fission cases. They do not depend on the prescriptions used for the compound nucleus cross-sections of the inverse process and the level density parameters of initial and residual fragments. This finding allows the determination of a general form of the residual temperature distribution for each emission sequence $${P}_{{k}}(T)$$ with the maximum temperature related only to the average temperature of initial fragments. In this way the sequential emission can be included into the Los Alamos model. Prompt neutron spectra in the center-of-mass and laboratory frames can be calculated for each emission sequence. The systematic of the ratios of average residual temperatures and energies to the initial ones together with other linear correlations between different prompt emission and residual quantities allow to obtain indicative values of different average prompt emission quantities in the absence of any prompt emission model.

Systematic behaviours of different quantities related to sequential prompt emission in fission

The deterministic modelling of sequential prompt emission in fission based on recursive equations of residual temperature was applied to numerous fission cases. This fact emphasized systematics and correlations between different quantities characterizing the residual fragments and the sequential emission. General forms of residual temperature distributions for each emission sequence are determined on the basis of these systematics, having as application the inclusion of sequential emission into the Los Alamos model. Also the systematics can serve to obtain indicative values of different average quantities in the absence of any prompt emission model.

Detailed validation of two deterministic models of prompt emission. Systematic behaviours of residual quantities from the sequential emission

The results of the PbP and sequential emission modellings describe very well the recent experimental data of 235U(n,f). The application of the sequential emission treatment to 49 fission cases has emphasized systematic behaviours of different quantities characterizing the fragments and the prompt emission. These allowed the determination of a general form of the residual temperature distribution for each emission sequence and the inclusion of sequential emission into the Los Alamos model.

Revisiting the residual temperature distribution in prompt neutron emission in fission

A new triangular form of the residual temperature distribution P(T), entering the prompt emission models in which the sequential emission is globally taken into account (e.g., the Los Alamos model of Madland and Nix with subsequent improvements and the Point-by-Point model), is proposed. A deterministic treatment of the successive emission of prompt neutrons, which is based on recursive equations of the residual temperatures, was developed. This modeling was validated by the good description of many and different experimental data of prompt emission (e.g., $\overline{\nu}(A)$ , $\langle\nu\rangle$ (TKE), $\langle\varepsilon\rangle (A)$ , $\langle\varepsilon\rangle$ (TKE), $\overline{E}_{\gamma} (A)$ , etc.) and the good agreement with the results of other prompt emission models. To see a possible systematic behaviour of P(T) as a function of energy and fissioning nucleus, the deterministic treatment of sequential emission was applied to 11 nuclei undergoing fission (spontaneously or induced by thermal and fast neutrons with energies up to the threshold of the second chance fission) for which reliable experimental fission fragment distributions Y(A, TKE) exist. The shapes of all P(T) distributions for the light and heavy fragment groups and for all fragments resulting from this modeling can be approximated with a triangular form. To make possible the use of this form into the prompt emission models with a global treatment of sequential emission, a connection between the average residual temperature $\langle \mathrm{Tr} \rangle$ and the temperature of initial fragments $\langle \mathrm{Ti} \rangle$ is needed. An important finding of this study concerns the ratio $\langle \mathrm{Tr} \rangle / \langle \mathrm{Ti} \rangle$ , which is $ \approx 0.6$ for all studied fissioning systems. This result allows to obtain a new triangular form of P(T) defined only as a function of initial temperature, which is applicable to any fissioning system at any energy, in the frame of prompt emission models with a global treatment of sequential emission.

Parameterisation of the residual temperature distribution based on the modelling of successive emission of prompt neutrons

A new deterministic modelling taking into account the successive emission of prompt neutrons from initial fragments of a fragmentation range {A, Z, TKE} constructed as in the Point-by-Point (PbP) treatment is described. The good agreement of different prompt emission quantities obtained from this modelling (e.g. v(A), v(TKE), E-γ(A), E-γ(TKE), etc.) with the experimental data and the results of the PbP model and other Monte-Carlo models validates the present modelling of sequential emission. The distributions of different residual quantities, including the residual temperature distributions P(T) of light and heavy fragments allow to obtain a new parameterisation of P(T) which can be used in the PbP model and the Los Alamos model.

Comprehensive overview of the Point-by-Point model of prompt emission in fission

The investigation of prompt emission in fission is very important in understanding the fission process and to improve the quality of evaluated nuclear data required for new applications. In the last decade remarkable efforts were done for both the development of prompt emission models and the experimental investigation of the properties of fission fragments and the prompt neutrons and $\gamma$ -ray emission. The accurate experimental data concerning the prompt neutron multiplicity as a function of fragment mass and total kinetic energy for 252Cf(SF) and 235 (n, f) recently measured at JRC-Geel (as well as other various prompt emission data) allow a consistent and very detailed validation of the Point-by-Point (PbP) deterministic model of prompt emission. The PbP model results describe very well a large variety of experimental data starting from the multi-parametric matrices of prompt neutron multiplicity $\nu (A,TKE)$ and $\gamma$ -ray energy $E_{\gamma}(A,TKE)$ which validate the model itself, passing through different average prompt emission quantities as a function of A (e.g., $\nu(A)$ , $E_{\gamma}(A)$ , $\langle \varepsilon \rangle (A)$ etc.), as a function of TKE (e.g., $\nu (TKE)$ , $E_{\gamma}(TKE)$ ) up to the prompt neutron distribution $P (\nu)$ and the total average prompt neutron spectrum. The PbP model does not use free or adjustable parameters. To calculate the multi-parametric matrices it needs only data included in the reference input parameter library RIPL of IAEA. To provide average prompt emission quantities as a function of A, of TKE and total average quantities the multi-parametric matrices are averaged over reliable experimental fragment distributions. The PbP results are also in agreement with the results of the Monte Carlo prompt emission codes FIFRELIN, CGMF and FREYA. The good description of a large variety of experimental data proves the capability of the PbP model to be used in nuclear data evaluations and its reliability to predict prompt emission data for fissioning nuclei and incident energies for which the experimental information is completely missing. The PbP treatment can also provide input parameters of the improved Los Alamos model with non-equal residual temperature distributions recently reported by Madland and Kahler, especially for fissioning nuclei without any experimental information concerning the prompt emission.

Evaluation of the 235U prompt fission neutron spectrum including a detailed analysis of experimental data and improved model information

We present an evaluation of the 235 U prompt fission neutron spectrum (PFNS) induced by thermal to 20-MeV neutrons. Experimental data and associated covariances were analyzed in detail. The incident energy dependence of the PFNS was modeled with an extended Los Alamos model combined with the Hauser-Feshbach and the exciton models. These models describe prompt fission, pre-fission compound nucleus and pre-equilibrium neutron emissions. The evaluated PFNS agree well with the experimental data included in this evaluation, preliminary data of the LANL and LLNL Chi-Nu measurement and recent evaluations by Capote et al. and Rising et al. However, they are softer than the ENDF/B-VII.1 (VII.1) and JENDL-4.0 PFNS for incident neutron energies up to 2 MeV. Simulated effective multiplication factors k eff of the Godiva and Flattop-25 critical assemblies are further from the measured k eff if the current data are used within VII.1 compared to using only VII.1 data. However, if this work is used with ENDF/B-VIII.0β2 data, simulated values of k eff agree well with the measured ones.

Refinements in the Los Alamos model of the prompt fission neutron spectrum

This paper presents a number of refinements to the original Los Alamos model of the prompt fission neutron spectrum and average prompt neutron multiplicity as derived in 1982. The four refinements are due to new measurements of the spectrum and related fission observables many of which were not available in 1982. They are also due to a number of detailed studies and comparisons of the model with previous and present experimental results including not only the differential spectrum, but also integral cross sections measured in the field of the differential spectrum. The four refinements are (a) separate neutron contributions in binary fission, (b) departure from statistical equilibrium at scission, (c) fission-fragment nuclear level-density models, and (d) center-of-mass anisotropy. With these refinements, for the first time, good agreement has been obtained for both differential and integral measurements using the same Los Alamos model spectrum.

Evaluation of the 239Pu prompt fission neutron spectrum induced by neutrons of 500 keV and associated covariances

We present evaluations of the prompt fission neutron spectrum (PFNS) of 239Pu induced by 500keV neutrons, and associated covariances. In a previous evaluation by Talou et al. (2010), surprisingly low evaluated uncertainties were obtained, partly due to simplifying assumptions in the quantification of uncertainties from experiment and model. Therefore, special emphasis is placed here on a thorough uncertainty quantification of experimental data and of the Los Alamos model predicted values entering the evaluation. In addition, the Los Alamos model was extended and an evaluation technique was employed that takes into account the qualitative differences between normalized model predicted values and experimental shape data. These improvements lead to changes in the evaluated PFNS and overall larger evaluated uncertainties than in the previous work. However, these evaluated uncertainties are still smaller than those obtained in a statistical analysis using experimental information only, due to strong model correlations. Hence, suggestions to estimate model defect uncertainties are presented, which lead to more reasonable evaluated uncertainties. The calculated keff of selected criticality benchmarks obtained with these new evaluations agree with each other within their uncertainties despite the different approaches to estimate model defect uncertainties. The keff one standard deviations overlap with some of those obtained using ENDF/B-VII.1, albeit their mean values are further away from unity. Spectral indexes for the Jezebel critical assembly calculated with the newly evaluated PFNS agree with the experimental data for selected (n,γ) and (n,f) reactions, and show improvements for high-energy threshold (n,2n) reactions compared to ENDF/B-VII.1.

Fitting Prompt Fission Neutron Spectra Using Kalman Filter Integrated with Empire Code

Prompt fission neutron spectra (PFNS) have proven to have a significant effect on criticality of selected benchmarks, in some cases as important as cross-sections. Therefore, a precise determination of uncertainties in PFNS is desired. Existing PFNS evaluations in nuclear data libraries relied so far almost exclusively on the Los Alamos model. However, deviations of evaluated data from available experiments have been noticed at both low and high neutron emission energies. New experimental measurements of PFNS have been recently published, thus demanding new evaluations. The present work describes the effort of integrating Kalman and EMPIRE codes in such a way to allow for parameter fitting of PFNS models. The first results are shown for the major actinides for two different PFNS models (Kornilov and Los Alamos). This represents the first step towards reevaluation of both cross-section and fission spectra data considering both microscopic and integral experimental data for major actinides.

Evaluation and Uncertainty Quantification of Prompt Fission Neutron Spectra of Uranium and Plutonium Isotopes

The prompt fission neutron spectra (PFNS) of the low-incident-energy neutron-induced fission reactions n + 229-238U and n + 235-242Pu have been systematically evaluated using differential experimental data and the Los Alamos model (LA model). Using the first-order, linear Kalman filter, the LA model parameters are constrained using the experimental data and an evaluation of the PFNS and its uncertainties across a suite of isotopes’ results. Correlations between isotopes of each actinide are presented through the model parameter correlations, and the resulting evaluations can be used to fill in inconsistencies within the ENDF/B-VII.1 library where PFNS data are scarce or in need of an update.

Development of Neutron Detector Arrays for Neutron-Induced Reaction Measurements

The outgoing neutron energy spectra from neutron-induced fission of various actinides are important for basic understanding of the fission process near the scission point as well as playing a large role in neutron transport codes, which are heavily relied upon in the design of advanced nuclear reactors and simulations of critical assemblies. The reliability of the results of neutron transport models is a strong function of the quality of the nuclear data used as input. Currently, the world's experimental database of fission neutron spectra is severely incomplete (especially for higher incident neutron energies) with large uncertainties in key portions of the outgoing energy spectra. Many transport codes use evaluated data libraries, which are based on the approach of the Los Alamos model. Other theoretical models have been developed, but the available data cannot distinguish the results of different models (as is the case for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{239}$</tex> </formula> Pu). Better measurements are needed for all incident and outgoing neutron energies, but most urgently in the low-energy (below 1 MeV) and high-energy (above 6 MeV) portions of the outgoing spectra where theoretical model results differ greatly. We present the design considerations (and some characterization results) of the two Chi-Nu neutron detector arrays: one array of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{6}$</tex></formula> Li-glass detectors and one array of liquid-scintillator detectors. These detector arrays are being constructed to meet the challenge of measuring the prompt fission neutron spectra (for a few common actinides) to a higher accuracy and precision than achieved previously and over a larger incident energy range than has been covered by previous experimenters. We see a significant reduction in neutron-scattering backgrounds with our new array designs.

234U(n,f) Model Description of Sub-barrier Fission Cross-section Resonances and Calculation of Prompt Neutron Emission Data

Abstract Neutron induced cross-sections of 234 U are calculated, focusing on the description of sub-barrier resonances in the fission cross-section. The correlation between the resonant behaviour of fission cross-section of fertile actinides (characterizing the pre-scission stage) and the visible fluctuations of their fission fragment and prompt neutron data (characterizing the post-scission stage), already discussed for the case of 238 U(n,f), is outlined and quantitatively supported in this case, too. The recently measured fission fragment distributions of 234 U(n,f) at incident energies covering the range 0.2-5 MeV, allow the averaging of multi-parametric matrices provided by the Point-by-Point (PbP) model, leading to interesting behaviours of prompt neutron data. For the first time the average prompt neutron multiplicity as a function of TKE is calculated at many incident energies (En) revealing interesting facts: the slope dTKE/dν does not vary with En and the flattening of at low TKE values is more pronounced at low En. Average model parameters (like energy release, neutron separation energy from fragments, level density of fragments) as a function of TKE exhibit nice and regular behaviours that can be fitted very well. The obtained average parameter dependences on TKE allow the use of the most probable fragmentation approach (Los Alamos model with subsequent improvements) having as advantages a very short computing time compared to the PbP and Monte Carlo treatments and the possibility to extend the lower and upper limits of the TKE range.

Point-by-Point model description of experimental average prompt neutron multiplicity as a function of total kinetic energy of fission fragments

The present Point by Point (PbP) model calculations of average prompt neutron multiplicity as a function of total kinetic energy 〈ν〉(TKE), performed for three fissioning systems 252Cf(SF), 239Pu(nth, f) and 235U(nth, f), describe very well the experimental data over the entire TKE range, including not only the slope dTKE/dν but also the flattening of experimental 〈ν〉 data at low TKE values.Present deterministic PbP model results of 〈ν〉(TKE) are analyzed comparatively with previous PbP 〈ν〉(TKE) results based on the same multi-parametric matrix ν(Z, A, TKE) and different manners of averaging this matrix over the fission fragment distributions, as well as with previous and recent results of probabilistic Monte Carlo treatments.The average model parameters as a function of TKE provided by the PbP treatment exhibit nice and regular behaviours and can be fitted well. The resulted model parameter dependences on TKE allow the use of the most probable fragmentation approach (Los Alamos model with subsequent improvements) having the advantages to provide results at many TKE values in a very short calculation time (compared to the PbP model and Monte Carlo treatments) and also outside the TKE range where the PbP model is applicable.Possible explanations of discrepancies between the slopes of different sets of experimental 〈ν〉(TKE) data are mentioned, too.

Calculation of Prompt Fission Neutron from 233U(n, f) Reaction by Multi-Modal Los Alamos Model

An attempt is made to improve the evaluation of the prompt fission neutron emission from 233U(n, f) reaction for incident neutron energies below 6 MeV. The multi-modal fission approach is applied to the improved version of Los Alamos model and the point by point model. The prompt fission neutron spectra and the prompt fission neutron as a function of fragment mass (usually named “sawtooth" data) υ(A) are calculated independently for the three most dominant fission modes (standard I, standard II and superlong), and the total spectra and υ(A) are synthesized. The multi-modal parameters are determined on the basis of experimental data of fission fragment mass distributions. The present calculation results can describe the experimental data very well, and the proposed treatment is thus a useful tool for prompt fission neutron emission prediction.

Calculation of prompt fission neutron spectra for 235U(n,f)

The prompt fission neutron spectra for the neutron-induced fission of 235U at En < 5 MeV are calculated using nuclear evaporation theory with a semi-empirical model, in which the nonconstant and constant temperatures related to the Fermi gas model are taken into account. The calculated prompt fission neutron spectra reproduce the experimental data well. For the n(thermal)+ 235U reaction, the average nuclear temperature of the fission fragment, and the probability distribution of the nuclear temperature, are discussed and compared with the Los Alamos model. The energy carried away by γ rays emitted from each fragment is also obtained and the results are in good agreement with the existing experimental data.

Two detector arrays for fast neutrons at LANSCE

The neutron spectrum from neutron-induced fission needs to be known in designing new fast reactors, predicting criticality for safety analyses, and developing techniques for global security application. The experimental data base of fission neutron spectra is very incomplete and most present evaluated libraries are based on the approach of the Los Alamos Model. To validate these models and to provide improved data for applications, a program is underway to measure the fission neutron spectrum for a wide range of incident neutron energies using the spallation source of fast neutrons at the Weapons Neutron Research (WNR) facility at the Los Alamos Neutron Science Center (LANSCE). In a double time-of-flight experiment, fission neutrons are detected by arrays of neutron detectors to increase the solid angle and also to investigate possible angular dependence of the fission neutrons. The challenge is to measure the spectrum from low energies, down to 100 keV or so, to energies over 10 MeV, where the evaporation-like spectrum decreases by 3 orders of magnitude from its peak around 1 MeV. For these measurements, we are developing two arrays of neutron detectors, one based on liquid organic scintillators and the other on 6Li-glass detectors. The range of fission neutrons detected by organic liquid scintillators extends from about 600 keV to well over 10 MeV, with the lower limit being defined by the limit of pulse-shape discrimination. The 6Li-glass detectors have a range from very low energies to about 1 MeV, where their efficiency then becomes small. Various considerations and tests are in progress to understand important contributing factors in designing these two arrays and they include selection and characterization of photomultiplier tubes (PM), the performance of relatively thin (1.8 cm) 6Li-glass scintillators on 12.5 cm diameter PM tubes, use of 17.5 cm diameter liquid scintillators with 12.5 cm PM tubes, measurements of detector efficiencies with tagged neutrons from the WNR/LANSCE neutron beam, and efficiency calibration with 252Cf spontaneous fission neutrons. Design considerations and test results are presented.

Systematic Quantification of Uncertainties for Evaluated Prompt Fission Neutron Spectra and Multiplicities

Uncertainties associated with evaluated average prompt fission neutron spectra and multiplicities are obtained for a suite of actinides in the Los Alamos model formalism. Systematics for the model input parameters are taken from the literature and used as prior values in a Bayesian updating procedure. Posterior systematics as well as associated posterior uncertainties are inferred. In addition, cross-isotope correlations are evaluated for the first time. The quantification of uncertainties associated with advanced Monte Carlo Hauser-Feshbach calculations of prompt fission neutron spectra is also discussed.