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At least 307 records · Page 17

Production cross sections of cosmic antiprotons in the light of new data from the NA61 and LHCb experiments

The cosmic-ray flux of antiprotons is measured with high precision by the space-borne particle spectrometers AMS-02. Its interpretation requires a correct description of the dominant production process for antiprotons in our Galaxy, namely, the interaction of cosmic-ray proton and helium with the interstellar medium. In light of new cross section measurements by the NA61 experiment of p + p → $\bar{p}$ + X and the first ever measurement of p + He → $\bar{p}$ + X by the LHCb experiment, we update the parametrization of proton-proton and proton-nucleon cross sections. We find that the LHCb p He data constrain a shape for the cross section at high energies and show for the first time how well the rescaling from the p p channel applies to a helium target. By using p p , p He and p C data we estimate the uncertainty on the Lorentz invariant cross section for p + He → $\bar{p}$+ X . We use these new cross sections to compute the source term for all the production channels, considering also nuclei heavier than He both in cosmic rays and the interstellar medium. The uncertainties on the total source term are up to ± 20 % and slightly increase below antiproton energies of 5 GeV. This uncertainty is dominated by the p + p → $\bar{p}$ + X cross section, which translates into all channels since we derive them using the $pp$ cross sections. In conclusion, the cross sections to calculate the source spectra from all relevant cosmic-ray isotopes are provided in Supplemental Material. We finally quantify the necessity of new data on antiproton production cross sections, and pin down the kinematic parameter space which should be covered by future data.

79 ASTRONOMY AND ASTROPHYSICS↗

Poster - 18: New features in EGSnrc for photon cross sections

Purpose: To implement two new features in the EGSnrc Monte Carlo system. The first is an option to account for photonuclear attenuation, which can contribute a few percent to the total cross section at the higher end of the energy range of interest to medical physics. The second is an option to use exact NIST XCOM photon cross sections. Methods: For the first feature, the photonuclear total cross sections are generated from the IAEA evaluated data. In the current, first-order implementation, after a photonuclear event, there is no energy deposition or secondary particle generation. The implementation is validated against deterministic calculations and experimental measurements of transmission signals. For the second feature, before this work, if the user explicitly requested XCOM photon cross sections, EGSnrc still used its own internal incoherent scattering cross sections. These differ by up to 2% from XCOM data between 30 keV and 40 MeV. After this work, exact XCOM incoherent scattering cross sections are an available option. Minor interpolation artifacts in pair and triplet XCOM cross sections are also addressed. The default for photon cross section in EGSnrc is XCOM except for the new incoherent scattering cross sections, which have to be explicitly requested. The photonuclear, incoherent, pair and triplet data from this work are available for elements and compounds for photon energies from 1 keV to 100 GeV. Results: Both features are implemented and validated in EGSnrc.Conclusions: The two features are part of the standard EGSnrc distribution as of version 4.2.3.2.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

HTTR 3 D Cross Section Generation with Serpent and MAMMOTH

The High Temperature Test Reactor (HTTR) is a graphite moderated thermal reactor with a nominal power output of 30 MWth. The purpose of this work is to prepare a set of neutron cross sections for use in the transient analyses of three Loss of Forced Cooling (LOFC) events planned for this reactor. The cross sections are generated with the Serpent 2 3 D Monte Carlo code to include the axial heterogeneity and the strong axial coupling of this core. The approach yields good agreement of results when compared to previously used 2 D lattice models, which require a fine spatial discretization and, surprisingly, comes at a higher computational cost. In addition, the temperature distribution must be considered to obtain reasonable cross sections and the axial leakage component dominates the spectral effects in the core. Consequently, a temperature model as a function of the fuel and moderator temperatures is adopted, and the core is depleted to 390 effective full-power days (EFPDs). A full tabulation of cross sections is prepared at this burnup point for a variety of fuel and moderator temperatures. Next, the multiphysics reactor application MAMMOTH is used to evaluate the quality of these cross sections using a diffusion solver. As expected, the homogenization error in the cross sections is significant and the Super Homogenization (SPH) correction from MAMMOTH is necessary to preserve key reaction rates. The SPH corrected MAMMOTH results are in excellent agreement with the Serpent results and reproduce both the reference power profile and temperature coefficients at each tabulation point. This fact confirms the accuracy of the SPH corrected cross sections and demonstrates the maturity of using Serpent 2 and MAMMOTH for 3 D cross section generation, even for reactors as complex as the HTTR. Finally, the authors recommend that the cross sections should be parametrized with the local burnup and that a full core burnup calculation with coupled thermal fluids would provide a better estimate of the initial condition for any subsequent transient analysis. Unfortunately, this was not within the scope of this work, and direct analysis with these tabulations should be considered as a first order approximation, at best.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Patching EAF-2010 into CINDER2008 Cross Section Libraries

CINDER2008 [1] comes with multi-group cross section libraries using most recent evaluated cross section data. The multi-group cross sections are weighted with three spectra: fission, fusion and flat. However, due to data format incompatibilities with the CINDER2008library maker tool, many of the reaction cross sections adapted from EAF-2010 [2] are either truncated or completely missing. Therefore it is essential to regenerate the CINDER2008 libraries with compatible EAF-2010 data. The updated cross section libraries are compared to those of the current cross section libraries in the sections below following a brief introduction of the CINDER2008 cross section libraries and a description of the method of generating cross sections for the CINDER2008 code. In the remainder of this document, we will refer to the libraries distributed with CINDER2008before October 2016 as the "current" libraries, and those described in this work as the "updated" libraries. In figures, the current library data may be shown with the library namewith or without “cur” appended, while the updated library data may be shown with "mod" appended.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the equivalent Dancoff factor cell method performing slowing down calculations on the fly for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for pin-cell, unit-cell, and fuel assembly problems with various resonance self-shielding conditions based on very high temperature reactor, high temperature test reactor, and Empire benchmark cores, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also showed that the methodology worked well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the on-the-fly slowing down method for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Among various on-the-fly slowing down methods, the equivalent Dancoff factor cell method was employed. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for the very high temperature reactor (VHTR), high temperature test reactor (HTTR), and Empire benchmark problems with various resonance self-shielding conditions, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also show that the methodology works well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Buckling and vibration analysis of a simply supported column with a piecewise constant cross section

An analysis and sample results for the lateral buckling and vibration of a compressively loaded column is presented whose cross section is piecewise constant along its length. The column is symmetric about its mid-span and consists of three sections, the center section having a stiffer cross section than the two identical end sections. Buckling and vibration characteristics of the column are determined from numerical solution of the exact eigenvalue problems. Parametric structural efficiency analyses are performed using a nondimensionalized set of governing equations to determine the optimum ratio between the lengths of the center section and the outer sections based on both buckling load and vibration frequency requirements. In these analyses, two relationships exist. One is between cross-sectional mass and the cross section, and the other is a high-efficiency scheme. The effect of axial load on vibration frequency is also examined and compared with that of a uniform column.

Lake, Mark S.↗

The design of test-section inserts for higher speed aeroacoustic testing in the Ames 80- by 120-foot wind tunnel

An engineering feasibility study was made of aeroacoustic inserts designed for large-scale acoustic research on aircraft models in the 80- by 120-Foot Wind Tunnel at NASA Ames Research Center. The goal was to find test-section modifications that would allow improved aeroacoustic testing at airspeeds equal to and above the current 100 knots limit. Results indicate that the required maximum airspeed drives the design of a particular insert. Using goals of 200, 150, and 100 knots airspeed, the analysis led to a 30 x 60 ft open-jet test section, a 40 x 80 ft open-jet test section, and a 70 x 110 ft closed test section with enhanced wall lining respectively. The open-jet inserts would be composed of a nozzle, collector, diffuser, and acoustic wedges incorporated in the existing 80 x 120 ft test section. The closed test section would be composed of approximately 5-ft acoustic wedges covered by a porous plate attached to the test-section walls of the existing 80 x 120. All designs would require a double row of acoustic vanes between the test section and fan drive to attenuate fan noise and, in the case of the open-jet designs, to control flow separation at the diffuser downstream end. The inserts would allow virtually anechoic acoustics studies of large helicopter models, jets, and V/STOL aircraft models in simulated flight. Model scale studies would be necessary to optimize the aerodynamic and acoustic performance of any of the designs. Successful development of acoustically transparent walls, though not strictly necessary to the project, would lead to a porous-wall test section that could be substituted for any of the open-jet designs, and thereby eliminate many aerodynamic and acoustic problems characteristic of open-jet shear layers.

Soderman, Paul T.↗

Maximum Mean Lift Coefficient Characteristics at Low Tip Mach Numbers of a Hovering Helicopter Rotor Having an NACA 64(1)A012 Airfoil Section

An investigation has been conducted on the Langley helicopter test tower to determine experimentally the maximum mean lift-coefficient characteristics at low tip Mach number and a limited amount of drag- divergence data at high tip Mach number of a helicopter rotor having an NACA 64(1)AO12 airfoil section and 8 deg of linear washout. Data are presented for blade tip Mach numbers M(t) of 0.29 to 0.74 with corresponding values 6 6 of tip Reynolds number of 2.59 x 10(exp 6) and 6.58 x 10(exp 6). Comparisons are made between the data from the present rotor with results previously obtained from two other rotors: one having NACA 0012 airfoil sections and the other having an NACA 0009 airfoil tip section. At low tip Mach numbers, the maximum mean lift coefficient for the blade having the NACA 64(1)AO12 section was about 0.08 less than that obtained with the blade having the NACA 0009 tip section and 0.21 less than the value obtained with the blade having the NACA 0012 tip section. Blade maximum mean lift coefficient values were not obtained for Mach number values greater than 0.47 because of a blade failure encountered during the tests. The effective mean lift-curve slope required for predicting rotor thrust varied from 5.8 for the tip Mach nuniber range of 0.29 to 0.55 to a value of 6.65 for a tip Mach number of 0.71. The blade pitching-moment coefficients were small and relatively unaffected by changes in thrust coefficient and Mach number. In the instances in which stall was reached, the break in the blade pitching-moment curve was in a stable direction. The efficiency of the rotor decreased with an increase in tip speed. Expressed as figure of merit, at a tip Mach number of 0.29 the maximum value was about 0.74. Similar measurements made on another rotor having an NACA 0012 airfoil and with a rotor having an NACA 0009 tip section, showed a value of 0.75. Synthesized section lift and profile-drag characteristics for the rotor-blade airfoil section are presented as an aid in predicting the high-tip-speed performance of rotors having similar airfoils.

Powell, Robert D., Jr.↗

Inclined Bodies of Various Cross Sections at Supersonic Speeds

To aid in assessing effects of cross-sectional shape on body aerodynamics, the forces and moments have been measured for bodies with circular, elliptic, square, and triangular cross sections at Mach numbers 1.98 and 3.88. Results for bodies with noncircular cross sections have been compared with results for bodies of revolution having the same axial distribution of cross-sectional area (and, thus, the same equivalent fineness ratio). Comparisons have been made for bodies of fineness ratios 6 and 10 at angles of attack from 0 deg to about 20 deg and for Reynolds numbers, based on body length, of 4.0 x 10(exp 6) and 6.7 x 10(exp 6). The results of this investigation show that distinct aerodynamic advantages can be obtained by using bodies with noncircular cross sections. At certain angles of bank, bodies with elliptic, square, and triangular cross sections develop considerably greater lift and lift-drag ratios than equivalent bodies of revolution. For bodies with elliptic cross sections, lift and pitching-moment coefficients can be correlated with corresponding coefficients for equivalent circular bodies. It has been found that the ratios of lift and pitching-moment coefficients for an elliptic body to those for an equivalent circular body are practically constant with change in both angle of attack and Mach number. These lift and moment ratios are given very accurately by slender-body theory. As a result of this agreement, the method of NACA Rep. 1048 for computing forces and moments for bodies of revolution has been simply extended to bodies with elliptic cross sections. For the cases considered (elliptic bodies of fineness ratios 6 and 10 having cross-sectional axis ratios of 1.5 and 2), agreement of theory with experiment is very good. As a supplement to the force and moment results, visual studies of the flow over bodies have been made by use of the vapor-screen, sublimation, and white-lead techniques. Photographs from these studies are included in the report.

Jorgensen, Leland H.↗

Turbine airfoil having outboard and inboard sections

A turbine airfoil usable in a turbine engine and formed from at least an outboard section and an inboard section such that an inner end of the outboard section is attached to an outer end of the inboard section. The outboard section may be configured to provide a tip having adequate thickness and may extend radially inward from the tip with a generally constant cross-sectional area. The inboard section may be configured with a tapered cross-sectional area to support the outboard section.

42 ENGINEERING↗

Interactive Visualization of Multi-Group Cross Sections on High-Fidelity Spatial Meshes

Core simulation tools utilizing Monte Carlo transport methods represent the 'Holy Grail' for nuclear reactor analysis. However, deterministic transport methods pose a number of advantages to Monte Carlo from a computational perspective, which seems likely to make these methods more viable in the near to intermediate term. Deterministic methods almost universally discretize the energy domain in a few to hundreds of energy groups. One of the key challenges for deterministic transport-based methods to be viable is accurate, reactor agnostic multi-group cross section generation. This paper describes tools for data processing and visualization of multigroup cross sections generated on high-fidelity spatial meshes from the OpenMC Monte Carlo code. Next generation deterministic transport reactor core modeling tools will require multi-group cross section (MGXS) generation on high-fidelity spatial meshes. High-fidelity MGXS are necessary for the accurate simulation of neutron physics in nuclear reactors with a high degree of spectral heterogeneity - e.g., large localized neutron flux gradients throughout a reactor core. Although many local (e.g., pin cell) approximations have been developed to model the scalar flux to compute spectral-averaged MGXS, these techniques cannot account for complex intra-pin and intra-assembly spatial self-shielding effects. Monte Carlo presents the most accurate method for reactor agnostic multi-group cross section generation since it does not require the use of local approximations to the flux. Monte Carlo has been proposed as a highly desirable framework for reactor agnostic cross section generation for many years. Monte Carlo methods can effectively embed all of the relevant spectral effects into the MGXS through the random particle tracking and interaction sampling processes. Previous work has applied MCNP and Serpent to compute few-group constants for diffusion calculations, and OpenMC to compute multi-group cross sections for transport-based methods. The primary difficulty with using Monte Carlo for MGXS generation is the tremendous computational resources required to adequately converge multi-group cross sections in each spatial region and energy group. Recent development of the OpenMC Monte Carlo code for high-performance computing platforms has made multigroup cross section generation from Monte Carlo more tractable in the foreseeable future. The recent release of OpenMC v0.7.1 includes a new Python-based module for MGXS generation. The MGXS generation module leverages many of the algorithms and features for 'big data' analysis of large tally datasets on complex spatial meshes. This paper describes the data management workflow and visualization tools which have been developed to explore the plethora of MGXS data generated with OpenMC. It is the authors' hope that the development of the visualization tool described in this paper will ultimately enable the design of machine learning algorithms to accelerate the convergence rate of high-fidelity multi-group cross section generated with Monte Carlo. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Free molecular collision cross section calculation methods for nanoparticles and complex ions with energy accommodation

The structures of nanoparticles, macromolecules, and molecular clusters in gas phase environments are often studied via measurement of collision cross sections. To directly compare structure models to measurements, it is hence necessary to have computational techniques available to calculate the collision cross sections of structural models under conditions matching measurements. However, presently available collision cross section methods contain the underlying assumption that collision between gas molecules and structures are completely elastic (gas molecule translational energy conserving) and specular, while experimental evidence suggests that in the most commonly used background gases for measurements, air and molecular nitrogen, gas molecule reemission is largely inelastic (with exchange of energy between vibrational, rotational, and translational modes) and should be treated as diffuse in computations with fixed structural models. In this work, we describe computational techniques to predict the free molecular collision cross sections for fixed structural models of gas phase entities where inelastic and non-specular gas molecule reemission rules can be invoked, and the long range ion-induced dipole (polarization) potential between gas molecules and a charged entity can be considered. Specifically, two calculation procedures are described detail: a diffuse hard sphere scattering (DHSS) method, in which structures are modeled as hard spheres and collision cross sections are calculated for rectilinear trajectories of gas molecules, and a diffuse trajectory method (DTM), in which the assumption of rectilinear trajectories is relaxed and the ion-induced dipole potential is considered. Collision cross section calculations using the DHSS and DTM methods are performed on spheres, models of quasifractal aggregates of varying fractal dimension, and fullerene like structures. Techniques to accelerate DTM calculations by assessing the contribution of grazing gas molecule collisions (gas molecules with altered trajectories by the potential interaction) without tracking grazing trajectories are further discussed. The presented calculation techniques should enable more accurate collision cross section predictions under experimentally relevant conditions than pre-existing approaches, and should enhance the ability of collision cross section measurement schemes to discern the structures of gas phase entities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Charge exchange and ionization cross sections of H{sup +}+H collision in dense quantum plasmas

The plasma screening effects of dense quantum plasmas on H{sup +}+H charge exchange and ionization cross sections are calculated by the classical trajectory Monte Carlo method. For charge exchange cross sections, it is found that the screening effects reduce cross sections slightly in weak screening conditions. However, cross sections are reduced substantially in strong screening conditions. For ionization cross sections, with the increase of screening effects, cross sections for low energies increase more rapidly than those for high energies. When the screening effects are strong enough, it is found that ionization cross sections decrease with the increase of incident H{sup +} energy. In addition, the cross sections have been compared with those in weakly coupled plasmas. It is found that in weak screening conditions, plasma screening effects in the two plasmas are approximately the same, while in strong screening conditions, screening effects of dense quantum plasmas are stronger than those of weakly coupled plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

MC 2 -3: Multigroup Cross Section Generation Code for Fast Reactor Analysis

This paper presents the methods and performance of the MC2 -3 code, which is a multigroup cross-section generation code for fast reactor analysis, developed to improve the resonance self-shielding and spectrum calculation methods of MC2 -2 and to simplify the current multistep schemes generating region-dependent broad-group cross sections. Using the basic neutron data from ENDF/B data files, MC2 -3 solves the consistent P1 multigroup transport equation to determine the fundamental mode spectra for use in generating multigroup neutron cross sections. A homogeneous medium or a heterogeneous slab or cylindrical unit cell problem is solved in ultrafine (2082) or hyperfine (~400 000) group levels. In the resolved resonance range, pointwise cross sections are reconstructed with Doppler broadening at specified temperatures. The pointwise cross sections are directly used in the hyperfine group calculation, whereas for the ultrafine group calculation, self-shielded cross sections are prepared by numerical integration of the pointwise cross sections based upon the narrow resonance approximation. For both the hyperfine and ultrafine group calculations, unresolved resonances are self-shielded using the analytic resonance integral method. The ultrafine group calculation can also be performed for a two-dimensional whole-core problem to generate region-dependent broad-group cross sections. Verification tests have been performed using the benchmark problems for various fast critical experiments including Los Alamos National Laboratory critical assemblies; Zero-Power Reactor, Zero-Power Physics Reactor, and Bundesamt für Strahlenschutz experiments; Monju start-up core; and Advanced Burner Test Reactor. Verification and validation results with ENDF/B-VII.0 data indicated that eigenvalues from MC2 -3/DIF3D agreed well with Monte Carlo N-Particle5 MCNP5 or VIM Monte Carlo solutions within 200 pcm and regionwise one-group fluxes were in good agreement with Monte Carlo solutions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Application of Neutron Multiplicity Counting Experiments to Optimal Cross-Section Adjustments

This paper presents the first application of model calibration to neutron multiplicity counting (NMC) experiments for cross-section optimization that is informed by adjoint-based sensitivity analysis (SA) and first-order uncertainty quantification (UQ). We summarize previous work on SA applied to NMC and describe notable modifications and additions. We give the procedure for first-order UQ and Bayesian-inference-based parameter estimation (PE). We then discuss model calibration applied to NMC of a 4.5-kg sphere of weapons-grade, alpha-phase plutonium metal (the BeRP ball) with the nPod neutron multiplicity counter. For the BeRP ball in bare and polyethylene-reflected configurations, we discuss the sensitivity of the first- and second-moment detector responses (i.e., first and second moments of the NMC distribution, respectively) to the cross sections. We describe the sources of uncertainty in the measured and simulated responses. Specifically, uncertainty in the measured responses is due to both random and systematic sources. Uncertainty in the simulated responses is due to the cross-section covariances. We describe in detail the adjustment to the cross sections and cross-section covariances due to the optimization. Due to the contribution of systematic uncertainties to the measured response uncertainties, the adjustment to the cross sections is similar in trend but larger in magnitude compared to that recommended by previous work. We compare the measured responses to responses simulated with nominal and optimized cross sections, demonstrating that the best-estimate cross sections produce simulations of NMC experiments that are more accurate with reduced uncertainty.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Semi-empirical scaling for ion–atom single charge exchange cross sections in the intermediate velocity regime

We present a semi-empirical scaling law for non-resonant ion–atom single charge exchange cross sections for collisions with velocities from ${10}^{7}\,{\rm{t}}{\rm{o}}\,{10}^{9}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$ and ions with positive charge $q\lt 8$. Non-resonant cross sections tend to have a velocity peak at collision velocities $v\lesssim 1\ {\rm{a}}{\rm{u}}$ with exponential decay around this peak. We construct a scaling formula for the location of this peak then choose a functional form for the cross section curve and scale it. The velocity at which the cross section peaks, v m , is proportional to the energy defect of the collision, ${\rm{\Delta }}E$, which we predict with the decay approximation. The value of the cross section maximum is proportional to the charge state q, inversely proportional to the target ionization energy I T , and inversely proportional to v m . For the shape of the cross section curve, we use a function that decays exponentially asymptotically at high and low velocities. We scale this function with parameters ${v}_{{\rm{m}}},{I}_{{\rm{T}}},{Z}_{{\rm{T}}},\mathrm{and}\ {Z}_{{\rm{P}}}$, where the ${Z}_{{\rm{T}},{\rm{P}}}$ are the target and projectile atomic numbers. In conclusion, for the more than 100 cross section curves that we use to find the scaling rules, the scaling law predicts cross sections within a little over a factor of 2 on average.

74 ATOMIC AND MOLECULAR PHYSICS↗

SU-E-I-43: Photoelectric Cross Section Revisited

Purpose: The importance of the precision in photoelectric cross-section value increases for recent developed technology such as dual energy computed tomography, in which some reconstruction algorithms require the energy dependence of the photo-absorption in each material composition of human being. In this study, we revisited the photoelectric cross-section calculation by self-consistent relativistic Hartree-Fock (HF) atomic model and compared with that widely distributed as “XCOM database” in National Institute of Standards and Technology, which was evaluated with localdensity approximation for electron-exchange (Fock)z potential. Methods: The photoelectric cross section can be calculated with the electron wave functions in initial atomic state (bound electron) and final continuum state (photoelectron). These electron states were constructed based on the selfconsistent HF calculation, where the repulsive Coulomb potential from the electron charge distribution (Hartree term) and the electron exchange potential with full electromagnetic interaction (Fock term) were included for the electron-electron interaction. The photoelectric cross sections were evaluated for He (Z=2), Be (Z=4), C (Z=6), O (Z=8), and Ne (Z=10) in energy range of 10keV to 1MeV. The Result was compared with XCOM database. Results: The difference of the photoelectric cross section between the present calculation and XCOM database was 8% at a maximum (in 10keV for Be). The agreement tends to be better as the atomic number increases. The contribution from each atomic shell has a considerable discrepancy with XCOM database except for K-shell. However, because the photoelectric cross section arising from K-shell is dominant, the net photoelectric cross section was almost insensitive to the different handling in Fock potential. Conclusion: The photoelectric cross-section program has been developed based on the fully self-consistent relativistic HF atomic model. Due to small effect on the Fock potential for K-shell electrons, the difference from XCOM database was limited: 1% to 8% for low-Z elements in 10keV-1MeV energy ranges. This work was partly supported by the JSPS Core-to-Core Program (No. 23003)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗