The impact of U resonance elastic scattering approximations on thermal reactor Doppler reactivity

The effects of accurate modeling of neutron scattering in ²³⁸U resonances are analyzed for typical light water reactor (LWR) and next generation nuclear plant (NGNP) lattices. An exact scattering kernel is formulated and implemented in a newly developed Monte Carlo code, MCSD (Monte Carlo slowing down), which solves a neutron slowing down in an infinite homogeneous medium and is used to generate resonance integral data used in the CASMO-5 lattice physics code. It is shown that the exact scattering kernel increases LWR Doppler coefficients by ∼10% relative to the traditional assumption of asymptotic elastic downscatter for ²³⁸U resonances. These resonance modeling improvements are shown to decrease hot full power eigenvalues by ∼200 pcm for LWRs and ∼450 pcm for NGNPs.     

Deterministic modeling of higher angular moments of resonant neutron scattering

An exact scattering kernel formulation for anisotropic scattering up to angular order 10 has been developed and implemented into a deterministic code. The effects of accounting for lattice dynamics on the modeling of neutron scattering in ²³⁵U, ²³⁸U, ²³⁸Pu, and other nuclides have been demonstrated. The new formulation essentially reproduces other investigators previous results for isotropic scattering and quantifies the departures from the isotropic values when higher angular orders are accounted for. The correct accounting for the lattice effects influences the estimated values for the probability of neutron absorption and scattering, which in turn affect the estimation of core reactivity and burnup characteristics. It is shown that, when using the exact scattering kernel formulation, the probability for upscattering significantly increases with increasing temperatures. For example, upscattering for ²³⁸U from below the 20.67 eV resonance increases from 5.57% at 300 K to 30.41% at 1000 K, respectively. Thus, it is shown that the exact scattering kernel is strongly sensitive to temperature, a fact of major importance for High Temperature Reactor fuels. The slowing down process is important in thermal reactors because it results in the neutrons entering the thermal energy range in which the majority of fission events occur. Correctly modeling the slowing down and hence slowing down source into the thermal energy range and consequently allowing the correct modeling of the thermal energy neutron fluxes (or the correct thermal range portion of the spectrum) is paramount to the correct prediction of criticality and safety features such as the Doppler effect. These artifacts are important for all thermal spectrum reactors. In High Temperature Reactors such as the NGNP or the Deep Burn HTR these effects are even more important.     

Proof and implementation of the stochastic formula for ideal gas,energy dependent scattering kernel

The ideal gas, scattering kernel for heavy nuclei with pronounced resonances was developed [Rothenstein, W., Dagan, R., 1998. Ann. Nucl. Energy 25, 209–222], proved and implemented [Rothenstein, W., 2004 Ann. Nucl. Energy 31, 9–23] in the data processing code NJOY [Macfarlane, R.E., Muir, D.W., 1994. The NJOY Nuclear Data Processing System Version 91, LA-12740-M] from which the scattering probability tables were prepared [Dagan, R., 2005. Ann. Nucl. Energy 32, 367–377]. Those tables were introduced to the well known MCNP code [X-5 Monte Carlo Team. MCNP – A General Monte Carlo N-Particle Transport Code version 5 LA-UR-03-1987 code] via the “mt” input cards in the same manner as it is done for light nuclei in the thermal energy range. In this study we present an alternative methodology for solving the double differential energy dependent scattering kernel which is based solely on stochastic consideration as far as the scattering probabilities are concerned. The solution scheme is based on an alternative rejection scheme suggested by Rothenstein [Rothenstein, W. ENS conference 1994 Tel Aviv]. Based on comparison with the above mentioned analytical (probability S(α,β)-tables) approach it is confirmed that the suggested rejection scheme provides accurate results. The uncertainty concerning the magnitude of the bias due to the enhanced multiple rejections during the sampling procedure are proved to lie within 1–2 standard deviations for all practical cases that were analysed.     

Delayed-gamma signature calculation for neutron-induced fission and activation using MCNPX. Part II: Simulations

In Part I, we presented the theory for the MCNPX Monte Carlo delayed-gamma emission feature. This feature permits the automated execution of radiation transport simulations of delayed-gamma emission spectra at discrete (line) energies created by the products of neutron fission and activation. To illustrate and help validate the new capability, calculated delayed-gamma emissions are presented in Part II for a model based on the Fisher and Engle (1964) experiment involving ²³⁵U irradiation by a Watt-fission neutron pulse. The simulated results are in good agreement with low-resolution measured data. Simulation results involving the Beddingfield and Cecil (1998) ²³⁵U and ²³⁹Pu thermal-neutron irradiation are also presented. The structure of the high-resolution emission signature obtained using MCNPX is seen to be in good agreement with their experimental counterparts. We also show an activation result for ⁶⁰Ni bombardment by 15-MeV neutrons. The simulation results help to illustrate the use and validity of the new MCNPX delayed-gamma capability.     

Benchmark of Advanced Burner Test Reactor model using MCNPX 2.6.0 and ERANOS 2.1

Significant research is currently being performed whereby fast reactor cores have been designed to burn transuranic materials reducing the volume and long-term radiotoxicity of spent nuclear fuel. These core and depletion models depend on various computer codes. This research used MCNPX 2.6.0 and ERANOS 2.1 to model a standard 250 MW Advanced Burner Test Reactor (ABTR) core. The intent was to benchmark criticality and burnup results from a stochastic Monte Carlo code and a deterministic depletion code using a standard ABTR model created by Argonne National Laboratory. Because each of these codes solves the transport and burnup problem differently, there is a need to benchmark the core models in order to verify results and identify root causes for significant differences in results between codes. Flux calculations in ERANOS were performed using diffusion theory, Legendre polynomial approximations (using the VARIANT module) and discrete ordinates methods. The k-effective for the higher order transport models remained within 1000 pcm of the MCNPX model. The difference between the total heavy nuclide mass balance in ERANOS using the various flux calculations and the MCNPX depletion model was less than 0.4% out to a burnup of 1095 days (67.45 GWd/MTHM). The percent delta between the codes as a fraction of the fissioned mass was 1.34%. For the isotopes with large concentrations, such as ²³⁸U and ²³⁹Pu, the mass differences were 0.38% and 0.01% respectively. The mass difference for ²⁴¹Am was also small at 0.42%. Notable isotopes in small quantities with larger mass differences were ²⁴²Am, ²⁴²Cm, ²⁴³Cm and ²⁴⁶Cm where differences ranged from 0.1 to 0.2% after 26 days and increased to 11–136% at 1095 days.     

Monte Carlo simulation of the NaI(Tl) detector response to measure gold activated foils

This work deals with the implementation of a NaI(Tl) detector for the assessment of the specific saturation activities of pure gold foils after neutron irradiation. These gold foils can be placed in the centre of a set of polyethylene spheres with different diameters. This configuration, known as a passive Bonner sphere system, is suitable to measure neutron spectra normally extended over a wide energy range containing up to 11 decades (from thermal to a few MeV), at places where the neutron field is very intense, high frequency pulsed or where it is mixed with an important high-energy photon component. The MCNPX code was used to evaluate the NaI(Tl) responses to different incident photon energies in terms of pulse-height distributions. An experimental validation of the calculated NaI(Tl) responses, using certified standard sources at a given measurement arrangement, indicates that MCNPX is a valid tool for routine calibration and benchmarking studies of this detector. A good agreement is found between the measured pulse-height distributions of the certified standard sources and those obtained from MCNPX simulations. As a preliminary application, a bare disc Au foil was directly exposed to a Bremsstrahlung photon beam at the isocentre of an 18 MV medical LINAC, in order to test the suitability of this activation material to measure the photo-neutrons generated in such facility. Two differentiated main photo-peaks, arising from ¹⁹⁶Au and ¹⁹⁸Au predominant γ-ray emissions, were observed. The two isotopes are produced mainly by the photonuclear, ¹⁹⁷Au(γ, n)¹⁹⁶Au, and radiative capture, ¹⁹⁷Au(n, γ)¹⁹⁸Au, reactions of, respectively, high-energy photons and thermal neutrons on the gold foil. From the measured ¹⁹⁸Au saturation activity, a rough estimation of (378 ± 68) × 10⁴ cm⁻² Gy⁻¹ was derived for the thermal neutron flux within the LINAC treatment room. This value, although being very approximate, is comparable to those reported by other authors for similar LINAC facilities but with different treatment room configurations, nominal acceleration potentials and Bremsstrahlung photon irradiation areas.     

Spatial distribution of reflected gamma rays by Monte Carlo simulation

In nuclear facilities, the reflection of gamma rays of the walls and metals constitutes an unknown origin of radiation. These reflected gamma rays must be estimated and determined. This study concerns reflected gamma rays on metal slabs. We evaluated the spatial distribution of the reflected gamma rays spectra by using the Monte Carlo method. An appropriate estimator for the double differential albedo is used to determine the energy spectra and the angular distribution of reflected gamma rays by slabs of iron and aluminium. We took into the account the principal interactions of gamma rays with matter: photoelectric, coherent scattering (Rayleigh), incoherent scattering (Compton) and pair creation. The Klein-Nishina differential cross section was used to select direction and energy of scattered photons after each Compton scattering. The obtained spectra show peaks at 0.511^∗ MeV for higher source energy. The Results are in good agreement with those obtained by the TRIPOLI code [J.C. Nimal et al., TRIPOLI02: Programme de Monte Carlo Polycin?etique à Trois dimensions, CEA Rapport, Commissariat à l’Energie Atomique. [1]].     

Calculation and analysis of proton-induced reactions on Ni at incident energies from threshold to 200 MeV

Proton-induced reactions on ⁵⁸Ni have been studied in the energy range from threshold to 200 MeV. Based on experimental data of elastic scattering angular distributions and nonelastic cross section, an optimal set of proton optical potential parameters for ⁵⁸Ni has been obtained. All cross sections, elastic and inelastic scattering angular distributions, energy spectra and especially double differential cross sections for neutrons, protons, deuterons, tritons, helium particles and alpha particles emission have been calculated, using nuclear models theory. Theoretical calculations have been compared with existing experimental data, in most cases, the calculated results are in good agreement with the experimental data.     

Proton elastic scattering and proton induced γ-ray emission cross-sections on Na from 2 to 5 MeV

Differential cross-sections for proton elastic scattering on sodium and for γ-ray emission from the reactions ²³Na(p,p′γ)²³Na (E_γ = 440 keV and E_γ = 1636 keV) and ²³Na(p,α′γ)²⁰Ne (E_γ = 1634 keV) were measured for proton energies from 2.2 to 5.2 MeV using a 63 μg/cm² NaBr target evaporated on a self-supporting thin C film.The γ-rays were detected by a 38% relative efficiency Ge detector placed at an angle of 135° with respect to the beam direction, while the backscattered protons were collected by a Si surface barrier detector placed at a scattering angle of 150°. Absolute differential cross-sections were obtained with an overall uncertainty estimated to be better than ±6.0% for elastic scattering and ±12% for γ-ray emission, at all the beam energies.To provide a convincing test of the overall validity of the measured elastic scattering cross-section, thick target benchmark experiments at several proton energies are presented.     

An extended variational principle for an albedo boundary condition

The K⁺(ø⁺) variational principle for neutron transport maintained by volume and surface sources is extended so that it is applicable to an albedo boundary condition. This condition arises from the use of a forward-backward-isotropic scattering kernel and the subsequent transformation of the transport equation to an equivalent isotropic form. Thus a finite element code for neutron transport which has been established for isotropic scattering can be used to provide solutions for the forward-backward-isotropic case of anisotropic scattering. In this way benchmarks can be found to check finite element codes written specifically for anisotropic scattering.     

Electron impact excitation of the 6s S1/2 state of In atom at small scattering angles

We measured the differential cross sections (DCSs) for the electron-impact excitation of the resonance transition 5p²P_1/2-6s²S_1/2 of In atom at small scattering angles using a crossed electron-atom beam technique. The incident electron energies were E₀ = 10, 20, 40, 60, 80 and 100 eV, while the small scattering angles ranged from 1° to 10° in steps of 1°. The forward scattering function method has been used for normalizing the generalized oscillator strengths (GOS) to the known optical oscillator strength and obtaining the absolute DCS values.     

Measurement of α particle energy loss in biological tissue below 2 MeV

The energy loss of α particles crossing biological tissue at energies between 0.8 and 2.2 MeV has been measured. This energy range is very important for boron neutron capture therapy, based on the ¹⁰B(n,α)⁷Li reaction, which emits α particles with energies of 1.78 and 1.47 MeV. One of the methods used for the measurement of the boron concentration in tissue is based on the deconvolution of the α spectra obtained from neutron irradiation of thin (70 μm) tissue samples. For this technique, a knowledge of the behaviour of the energy loss of the particles in the irradiated tissue is of critical importance. In particular, the curve of the residual energy as a function of the distance travelled in the tissue must be known. In this paper, the results of an experiment carried out with an ²⁴¹Am source and a series of cryostatic sections of rat-lung tissue are presented. The experimental measurements are compared with the results of Monte Carlo calculations performed with the MCNPX code.     

Delayed-gamma signature calculation for neutron-induced fission and activation using MCNPX, Part I: Theory

The capability to conduct automated radiation-transport simulations of delayed-gamma emission spectra at discrete (line) energies created by the products of neutron fission and activation has been developed for MCNPX. To do so, the CINDER'90 isotopic transmutation code has been merged into MCNPX to seamlessly supply time-dependent, decay-chain atom densities for 3400 nuclides. A new dataset containing ENDF/B-VI emission-probability line data for 979 nuclides has been created for MCNPX, with the balance of the 3400 nuclides treated using existing 25-group emission spectra. Cumulative distribution sampling functions have been developed to accommodate line and multigroup emission data. Fission-product sampling for fissions induced by sub-20-MeV neutrons uses fission-yield data for thermal (E < 1 eV), fission-spectrum (1 eV ≤ E < 14 MeV), and high-energy (E ≥ 14 MeV) neutrons for isotopes of uranium, plutonium, thorium, americium, californium, curium, einsteinium, fermium, and neptunium. For higher-energy neutrons, LAHET, a physics package that is also a part of MCNPX, generates a list of residual nuclides. In Part II, we present simulation results for models based on experiments conducted by Fisher and Engle (1964) and Beddingfield and Cecil (1998) to validate the new capability. As will be seen therein, the MCNPX results are in good agreement with the measured data. Finally, in Part III we augment the Monte Carlo presentation with a transport-theory formulation to provide a succinct encapsulation of the relevant physics. The new MCNPX delayed-gamma development offers a powerful new tool for fission-related signature recognition.     

Method based on isotope ratio mass spectrometry for evaluation of carbon activation in the reactor graphite

The general idea of this work is to introduce an evaluation method to restore the irradiation parameters of graphite or other carbonaceous materials using experimental and modelling results of ¹³C generation in the irradiated material. The method is based on coupling of stable isotope ratio mass spectrometry and computer modelling of the reactor core to evaluate the realistic characteristics of the reactor core such as the neutron fluence in any position of the reactor graphite stack or other graphite constructions.The generation of carbon isotopes ¹³C and ¹⁴C in the irradiated graphite of the RBMK-1500 reactor has been estimated by modelling of the reactor core with computer codes MCNPX and CINDER90. Good agreement of simulated and measured Δ¹³C/¹²C values in graphite of the central part of the reactor core indicates that the neutron flux (1.40 × 10¹⁴ n/cm² s) is modelled accurately in the graphite sleeve of the fuel channel. The simulated activity of ¹⁴C is compared with the one measured by the β spectrometry technique. Results indicate that production of ¹⁴C from ¹⁴N in the RBMK-1500 reactor is considerable and has to be taken into account in order to make proper evaluation of ¹⁴C activity. Measured ¹⁴C specific activity values correspond to 15 ± 4 ppm impurity of ¹⁴N in graphite samples from the RBMK-1500 reactor core.     

Scattering of 14.1 MeV Neutrons by 6Li, 7Li, 9Be, 10B and 11B

Using a time-of-flight spectrometer, the differential cross sections were measured for the elastic and inelastic scattering of 14.1 MeV neutrons by ⁶Li, ⁷Li, ⁹Be, ¹⁰B and ¹¹B. In the case of elastic scattering by ⁷Li and ¹⁰B, correction was applied to subtract the contribution of inelastic scattering from the unresolved first excited state, after which, the elastic scattering data were compared with predictions based on the optical model. The potential parameters derived with a seven-parameter search yielded angular distributions agreeing with the present experimental data. The expressions for these parameters are presented as a function of mass number.

The experimental data on inelastic scattering were analyzed with the distorted wave Born approximation. The deformation parameters were estimated to be nearly equal to or larger than unity for these nuclei.     

Neutralization effect for Ne+ scattering from a Cu(110) surface

Intensity and structure of the energy spectra of Na⁺ and Ne⁺ ions scattered from a Cu(110) surface are governed by multiple scattering and neutralization effects. These were studied for ion energies between 600 eV and 1 keV and in the temperature range from 100 to 600 K in the experiment and by computer simulation. Na⁺ scattering directly reflects the crystallographic structure of the (110) surface. The temperature effects can be used to analyze thermal motions of surface atoms in terms of a surface Debye temperature for specific vibrational directions. The contributions of single and multiple scattering events to the energy spectra are analyzed and for Ne⁺ a strong trajectory-dependent neutralization is found. The comparison of the neutralization of Ne⁺ and Na⁺ leads to a Ne⁺ ion survival probability of a few percent for single scattering, less than 1% for double scattering, and a value of less than 10⁻³ for scattering from atoms below the top atomic layer. A simple neutralization model is developed to explain the observed survival probabilities.     

Performance modeling of Deep Burn TRISO fuel using ZrC as a load-bearing layer and an oxygen getter

The effects of design choices for the TRISO particle fuel were explored in order to determine their contribution to attaining high-burnup in Deep Burn modular helium reactor fuels containing transuranics from light water reactor spent fuel. The new design features were: (1) ZrC coating substituted for the SiC, allowing the fuel to survive higher accident temperatures; (2) pyrocarbon/SiC “alloy” substituted for the inner pyrocarbon coating to reduce layer failure and (3) pyrocarbon seal coat and thin ZrC oxygen getter coating on the kernel to eliminate CO. Fuel performance was evaluated using General Atomics Company’s PISA code. The only acceptable design has a 200-μm kernel diameter coupled with at least 150-μm thick, 50% porosity buffer, a 15-μm ZrC getter over a 10-μm pyrocarbon seal coat on the kernel, an alloy inner pyrocarbon, and ZrC substituted for SiC. The code predicted that during a 1600 °C postulated accident at 70% FIMA, the ZrC failure probability is <10^?4.     

On the use of S(α,β) tables for nuclides with well pronounced resonances

The use of S(α,β) tables for evaluating the secondary energy distribution is restricted in the MCNP code [Briesmeister, J.F. (Ed.), 1997. MCNP – A General Monte Carlo N-Particle Transport Code, LA-12625-M] to light isotopes only. The reason is the free gas model in NJOY, [Macfarlane, R.E., Muir, D.W., 1994. The NJOY Nuclear Data Processing System Version 91, LA-12740-M] which does not account for heavy isotopes with strongly energy dependent cross-sections. The joint scattering kernel developed by [Rothenstein, W., Dagan, R., 1998. Ann. Nucl. Energ. 25, 209–222] improved the secondary energy distribution treatment in a manner consistent with the BROADR module in NJOY. [Rothenstein, W., 2004. Ann. Nucl. Energ. 31, 9–23] enabled the generation of S(α,β) by implementing a new formalism for the modified kernel into the NJOY module THERMR.The new generated S(α,β) tables for heavy isotopes with pronounced resolved resonances were added to the MCNP library data files and the MCNP code itself, was modified accordingly. The quantitative effects of using scattering kernel tables in the vicinity of resonances were analyzed by introducing them into the Tellier et al. [Tellier, H., Costa, M., Raepsaet, C., Van der Gucht, C., 1993. 113, 20–30] benchmark problem. The absorption rate and the Doppler effect were calculated for the pronounced eight S-type resonances of ²³⁸U within the energy range 2.7–210 eV. The introduced S(α,β) tables for ²³⁸U increases the Doppler effect by 23.5% in comparison with the existing MCNP calculation method. Over the entire Resolved Resonance Region (RRR) this means an increase of 17.5%. The overall absorption rate over the entire RRR is increased by 1.4% at 1200 K and by 2.1% at 1800 K.     

Theoretical calculation and analysis of the p+Co reaction

All cross sections, elastic and inelastic scattering angular distributions, energy spectra, and double differential cross sections of neutron, proton, deuteron, triton, helium and alpha particle emission for the p+⁵⁹Co reaction have been calculated and analyzed at incident energies from threshold to 200 MeV. The optical model, the intra-nuclear cascade model, direct, pre-equilibrium and equilibrium reaction theories are used. It is found that the theoretical calculated results are in good agreement with experimental data.     

Calculation and evaluations for n+Cu reactions

All cross sections of neutron induced reactions, angular distributions, energy spectra and double differential cross sections are consistently calculated and analyzed for n+^63,65,nat.Cu reactions at incident neutron energies below 200 MeV based on the nuclear theoretical models. The optical model, preequilibrium and equilibrium reaction theories, the distorted wave Born approximation theory are used. Theoretical calculated results are compared with existing experimental data and the evaluated results in ENDF/B-VII and JENDL-3 libraries. The optical model potential parameters are obtained according to the experimental data of total, nonelastic scattering cross sections and elastic scattering angular distributions.