Measurement of the neutron-induced total cross sections of ^(nat)Pb from 0.3 eV to 20 MeV on the Back-n at CSNS

The neutron-induced total cross sections of natural lead have been measured in a wide energy range(0.3 eV-20 MeV)on the back-streaming white neutron beamline(Back-n)at the China Spallation Neutron Source.Neutron energy was determined by the neutron total cross-section spectrometer using the time-of-flight technique.A fast multi-cell fission chamber was used as the neutron detector,and a 10-mm-thick high-purity natural lead sample was employed for the neutron transmission measurements.The on-beam background was determined using Co,In,Ag,and Cd filters.The excitation function of ^(nat)Pb(n,tot)reaction below 20 MeV was calculated using the TALYS-1.96 nuclear-reaction modeling program.The present results were compared with previous results,the evaluated data available in the five major evaluated nuclear data libraries(i.e.,ENDF/B-VIII.0,JEFF-3.3,JENDL-5,CENDL-3.2,and BROND-3.1),and the theoretical calculation curve.Good agreement was found between the new results and those of previous experiments and with the theoretical curves in the corresponding region.This measurement obtained the neutron total cross section of natural lead with good accuracy over a wide energy range and added experimental data in the resonance energy range.This provides more reliable experimental data for nuclear engineering design and nuclear data evaluation of lead.

Total cross sections for electron scattering from sulfur compounds

The original additivity rule method cannot give good results for electron scattering from SO,SO2,SO2Cl2,SO2ClF,and SO2F2 molecules at low energy,because the electron-molecule scattering is simply reduced to electron-atom scattering.Considering the difference between the bound atom in a molecule and the corresponding free atom,the original additivity rule is revised.With the revised additivity rule,the total cross sections for electron scattering from these molecules are calculated over a wide energy range below 3000 eV and compared with the available experimental and theoretical data.A better agreement between them is obtained.

A modification potential method of calculating total cross sections of electrons scattering from complex molecules C2H6, C2F6, C6H6 and C6F6 at 100 eV-5000 eV

A complex optical model potential modified by incorporating the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds between two atoms in a molecule, is first employed to calculate the total cross sections for electrons scattering from such complex molecules as C2H6, C2F6, C6H6 and C6F6 using the aclditivity rule model at Hartree-Fock level over the energy range from 100 eV to 5000 eV. The total cross sections are quantitatively compared with those obtained by experiments wherever available, and they are in good agreement with each other over a wide energy range. It is shown that the modified potential together with the additivity rule model is completely suitable for the calculation of total cross sections of electrons scattering from such complex molecules as C2H6, C2F6, C6H6 and C6F6 above 200 eV-300 eV.

Total cross sections for electrons scattering from simple molecules containing the larger atom sulfur at 30-5000eV

A complex optical model potential modified by the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds, is employed to calculate the total cross sections for electrons scattering from simple molecules （SO2, H2S, OCS, CS2 and SO3） containing the larger atom, sulfur, at 30-5000eV by using the additivity rule model at Hartree-Fock level. The quantitative molecular total cross section results are compared with those obtained in experiments and other calculations wherever available, and good agreement is obtained. It is shown that the additivity rule model together with the complex optical model potential modified by the concept of bonded atom can give the results closer to the experiments than the one unmodified by it. So, the introduction of bonded-atom concept in complex optical model potential betters the accuracy of the total cross section calculations of electrons from the molecules containing the larger atom, sulfur.

Total Cross Sections for Electron Scattering on Polyatomic Molecules （CH4, CO2,NO2, and N2O） at 10～3000 eV

A new modified formulation of the Additivity Rule (AR) was proposed to calculate the total electron scattering cross sections for CH4, CO2, NO2, and N2O, considering the overlapping between atoms in molecules and the not fully transparency of the molecules. The present calculation covers the range of impact energy from 10 to 3000 eV. The results are compared with experimental data and other theories where available. The atoms are presented by spherical complex optical potential, which is composed of static, exchange, polarization, and absorption terms.

Total cross sections for electron scattering from fluoromethanes:A revised additivity rule method

The additivity rule for electron-molecule scattering is revised by considering the difference between the free atom and the bound atom in the molecule. The total cross sections for electron scattering from fluoromethanes （CF4, CF3H, CF2H2, and CFH3） are calculated in an energy range from 100 eV to 1500 eV by the revised additivity rule. The present calculations are compared with the original additivity rule results and the available experimental data. Better agreement with each other is obtained.

A new semi-empirical formula for total cross sections of electron scattering from triatomic molecules at 30—5000 eV

Total cross sections （TCSs） of electrons scattering from triatomic molecules over the energy range from 30 to 5000 eV are investigated employing a new semi-empirical formula. The TCSs of electrons scattering from triatomic molecules SO2, NO2, and CO2 are calculated. The quantitative TCSs are in good agreement with those obtained by experiments. It is shown that the results derived from the semi-empirical formula are much closer to the measurements than other calculations.

Positron total cross sections for collisions with N_2 and CO_2 at 30-3000 eV

The total （elastic plus inelastic） cross sections for positron scattering from N2 and CO2 over the incident energy range from 30 to 3000eV are calculated using the additivity rule model at Hartree-Fock level. A complex optical model potential modified by incorporating the concept of bonded atom, which takes into account the overlapping effect of electron clouds between two atoms in a molecule, is employed to calculate the total cross section of positron-molecule scattering. The calculated total cross sections are in good agreement with those reported by experiments and other theories over a wide energy range.

Conceptual design of a Cs2LiLaBr6 scintillator‑based neutron total cross section spectrometer on the back‑n beam line at CSNS

To reduce the experimental uncertainty in the 235 U resonance energy region and improve the detection efficiency for neutron total cross section measurements compared with those obtained with the neutron total cross section spectrometer(NTOX), a dedicated lithium-containing scintillation detector has been developed on the Back-n beam line at the China Spallation Neutron Source. The Fast Scintillator-based Neutron Total Cross Section(FAST) spectrometer has been designed based on a Cs2Li La Br6(CLLB) scintillator considering the γ-ray flash and neutron environment on the Back-n beam line. The response of the CLLB scintillator to neutrons and γ-rays was evaluated with different 6Li/7 Li abundance ratios using Geant4. The neutron-γdiscrimination performance of the CLLB has been simulated considering different scintillation parameters, physical designs,and light readout modes. A cubic 6Li-enriched( > 90%) CLLB scintillator, which has a thickness of 4-9 mm and side length of no less than 50 mm to cover the Φ 50 mm neutron beam at the spectrometer position, has been proposed coupling to a side readout SiPM array to construct the FAST spectrometer. The developed simulation techniques for neutron-γ discrimination performance could provide technical support for other neutron-induced reaction measurements on the Back-n beam line.

Elastic scattering and total reaction cross sections of^(6)Li examined via a microscopic continuum discretized coupled-channels model

We present a systematic study of 6Li elastic scattering and total reaction cross sections at incident energies around the Coulomb barrier within the continuum discretized coupled-channels(CDCC)framework,where 6Li is treated in anα+d two-body model.Collisions with 27Al,64Zn,138Ba,and 208Pa are analyzed.The microscopic optical potentials(MOP)based on Skyrme nucleon-nucleon interaction forαand d are adopted in CDCC calculations and satisfactory agreement with the experimental data is obtained without any adjustment on MOPs.For comparison,αand d global phenomenological optical potentials(GOP)are also used in CDCC analysis and a reduction of no less than 50%on the surface imaginary part of deuteron GOP is required for describing the data.In all cases,the 6Li breakup effect is significant and provides repulsive correction to the folding model potential.The reduction on the surface imaginary part of GOP of deuteron reveals a strong suppression of the reaction probability of deuteron as a component of 6Li when compared with that of a free deuteron.Further investigation is performed by considering the d breakup process equivalently within the dynamic polarization potential approach,and the results show that d behaves in a manner similar to a tightly bound nucleus in 6Li induced reactions.

Additivity rule for electron-molecule total cross section calculations at 50-5000 eV: a new geometrical approach

Taking into consideration the changes of the geometric shielding effect in a molecule as the energy of incident electrons varies, this paper presents an empirical fraction, which depends on the energy of incident electrons, the target＇s molecular dimension and the atomic and electronic numbers in the molecule. Using this empirical fraction, it proposes a new formulation of the additivity rule. Employing the new additivity rule, it calculates the total cross sections of electron scattering by C2H4, C6H6, C6H14 and C8H18 over the energy range from 50 to 5000eV. In order to exclude the calculation deviations caused by solving the radial Schrodinger equation of electron scattering by atoms, here the atomic cross sections are derived from the experimental total cross section results of simple molecules （H2, O2, CO） via the inversion algorithm. The quantitative total cross sections are compared with those obtained by experiments and other theories, and good agreement is obtained over a wide energy range, even at energy of several tens of eV.

A Modified Potential Method for Electrons Scattering Total Cross Section Calculations on Several Molecules at 30 ～ 5000 eV： CF4, CCl4, CFCl3, CF2Cl2, and CF3Cl

A complex optical model potential modified by the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds between two atoms in a molecule, is employed to calculate the total cross sections （TCS5） for electrons scattering from several molecules （CF4, CCl4, CFCl3, CF2 Cl2, and CF3 Cl） over an incident energy range 30 - 5000 eV using the additivity rule model at Hartre-Fock level. The quantitative TCS5 are compared with those obtained by experiments and other theories wherever available, and good agreement is obtained above 100 eV. It is shown that the modified potential can successfully calculate the TCS5 of electron-molecule scattering over a wide energy range, especially at lower energies.

A Correlation Potential Method for Electron Scattering Total Cross Section Calculations on Several Diatomic and Polyatomic Molecules over Energy Range 10～5000eV

A complex optical model potential correlated by the concept of bonded atom, which considers the overlapping effect of electron clouds between two atoms in a molecule, is firstly employed to calculate the total cross sections for electron scattering on several molecules (NH3, H2O, CH4, CO, N2, O2, and C2H4) over the energy range 10 ～ 5000 eV using the additivity rule model at Hartree-Fock level. The difference between the bonded atom and the free one in states is that the overlapping effect of electron clouds of bonded atoms in a molecule is considered. The quantitative total cross sections are compared with the experimental data and with the other calculations wherever available and good agreement is obtained over the energy range 10 ～ 5000 eV. It is shown that the correlated calculations are much closer to the available experimental data than the uncorrelated ones at lower energies, especially below 500 eV. Therefore,considering the overlapping effect of electron clouds in the complex optical model potential could be helpful for the better accuracy of the total cross section calculations of electron scattering from molecules.

Theoretical Analysis of Neutron Double-Differential Cross Sections of n ＋^9Be Reactions

By using the nuclear reaction model for light nuclei, the calculations of the double-differential cross sections of outgoing neutrons from n ＋^9Be reactions are performed. The total outgoing neutrons are only come from the （n, 2n）2a reaction channel. The （n, 2n）2a reaction channel is achieved through six different reaction approach, which are illustrated in this paper. The calculated results agree very well with the measured data at En = 7.1, 8.09, 8.17, 9.09, 9.97 and 10.26 MeV, because the updated level schemes related to the n ＋ ^9Be reactions have been employed in this calculations.

Measurement of the neutron total cross section of^(9)Be at the Back-n white neutron source of CSNS

The neutron total cross section data of^(9)Be are essential in the nuclear structure model research of light nuclei and nuclear power installations.The neutron total cross section of^(9)Be in the 0.3 eV−120 MeV energy region has been measured using time-of-flight and transmission methods with the Neutron Total Cross Sectional Spectrometer(NTOX)based on the multi-cell fast fission chamber at the China Spallation Neutron Source(CSNS)-Back-n white neutron source(Back-n).The fission count-neutron energy distributions of ^(235)U and ^(238)U without samples and with Be samples with three thicknesses were measured in the double-bunch operation mode for a beam power of 100 kW.The Bayesian method was used to eliminate the influence of the double-bunch problem on neutron measurement in the energy region above 10 keV.The neutron total cross section of^(9)Be results was consistent with ENDF/B-VIII.0 evaluation library data in the 0.3 eV−20 MeV energy region.In the energy ranges of 0.3 eV to 10 keV and 0.01 to 20 MeV,the deviations between our results and the evaluation results of ENDF/B-VIII.0 were within 2.5%and 15%,respectively.In the resonance energy region,the measured resonance energies in our experiment were 0.63,0.82,and 2.8 MeV,respectively.The results showed that the total cross section uncertainties of three Be samples were within 2.2%in the energy region below 1 MeV.The total cross section uncertainty of 30 mm Be from ^(235)U was the smallest and less than 5%in the energy region of 0.3 eV−120 MeV.The results of this experiment can provide technical support for further data analysis and related nuclear data evaluation.

Electron-impact ionization cross section calculations for lithium-like ions

The electron-impact ionization of lithium-like ions C^(3+),N^(4+),O^(5+),Ne^(7+),and Fe2^(3+)is studied using a combination of two-potential distorted-wave and R-matrix methods with a relativistic correction.Total cross sections are computed for incident energies from 1 to 10 times of ionization energy and better agreements with the experimental results are obtained in comparison with the theoretical data available.It is found that the indirect ionization processes become significant for the incident energy larger than about four times of the ionization energy.Contributions from the exchange effects along the isoelectronic sequence are also discussed and found to be important.The present method can be used to obtain systematic ionization cross sections for highly charged ions across a wide incident energy range.

Analysis of total reaction cross sections for deuterons on 1p-shell-nuclei

This study aims to analyze the differential cross sections （DCSs） of elastic scattering and total reaction cross sections （TRCSs） of the loosely-bound deuteron projectile impinging on lp-shell nuclei, such as 9Be, 12C, and 160, at incident energies ranging between 10.6 and 171 MeV using the continuum discretized coupled channel （CDCC） method. By fitting the experimental data for the DCSs and TRCSs, energy-dependent renormalization factors for the real and imaginary parts of the nucleon-nucleus optical-model potentials deduced from the studies proposed by Koning and Delaroche （KD02） and by Watson, Singh, and Segel （WSS）, are obtained. It is found that with the WSS potential, which was obtained specifically for lp-shell nuclei, the CDCC calculations can simultaneously reproduce both the DCSs and the TRCSs. The results show that it is important to choose appropriate optical potentials to describe deuteron-induced reactions.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments

The (180)3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3rd-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3rd-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3rd-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: II. Computed Sensitivities

This work presents the results of the exact computation of (180)3 = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3rd-order sensitivities are significantly larger than their corresponding 1st- and 2nd-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3rd-order relative sensitivity is the mixed sensitivity of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of 1H (“isotope 6”) and 239Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1st-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope 1H, having the value , while the largest 2nd-order sensitivity is . The 3rd-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.

Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.