Tables and graphs of electron-interaction cross-sections from 10 eV to 100 GeV derived from the LLNL evaluated electron data library (EEDL), Z= 1-100, ST Perkins, DE Cullen, SM Seltzer

Tags: M. Seltzer, Data Tables, J. H. Scofield, S. T. Perkins, LLNL Evaluated Atomic Data Library, Nuclear Data Libraries, LLNL Evaluated Photon Data Library, D. E. Cullen, Lawrence Livermore Natioiwl Laboratory, Livermore, CA, Data Library, Lawrence Livermore National Laboratory
Content: UCRL--50400-VO1.31 DE92 007986 Tables and Graphs of Electron-Interaction cross sections from 10 eV to 100 GeV Derived from the LLNL Evaluated Electron Data Library (EEDL), Z = 1-100 S. T. Perkins D. E. CuUen S. M. Seltzer* Manuscript date: November 12,1991
Lawrence Livermore National Laboratory
University of California · Livermore, California · 94551
^
^Center for Radiation Research National Institute of Standards and Technology Gaithersburg, MD 20899
Dedication This volume of the UCRL-50400 series is dedicated to E. F. Plechaty. As head of the TART Monte Carlo code effort at Lawrence Livermore National Laboratory for the past 30 years, Ernie had the foresight, knowledge, and determination to significantly influence the evaluated data libraries that are described in this series. It was Ernie's resolve 10 years ago that resulted in the All-Particle Method (i.e., the ability to track all resultant particles from a given reaction within a single transport code). This volume is one of the results of that endeavor. Although Ernie retired in 1990, his interest in this field has persisted, and his contributions continue. 11
Foreword The UCRL-50400 series. An Integrated System for Production ofNeutronics and Photonics Calculational Constants, describes an integrated, computer-oriented system for the production and application of neutronics and photonics calculational constants. The system supplies reliable, up-to-date data, selects specific types of data on request, provides output in a variety of forms (ultimately in the form of input to other computer codes), and functions rapidly and efficiently. The UCRL-50400 series comprises the following volumes: · Vol. 1, Part A, Rev. 3, ECSIL: A System for Storage, Retrieval, and Display of Experimental Neutron Data, September 1976. · Vol. 1, Part B, Program ECSX4 (Version 78-1): Conversion of Experimentally Measured CrossSection Data from the Four-Center-Exchange (X4) Format to the Livermore ECSIL Format, December 1978. · Vol. 2, Rev. 2, A Bibliography of the experimental data of Neutron-Induced Interactions, July 1976. · Vol. 3, Rev. 2, An Index of the Experimental Data of Neutron-Induced Interactions, July 1976. · Vol. 4, Rev. 1, Evaluated Nuclear Data Library, September 1981. · Vol. 4, Rev. 1, Appendix C, The Neutron Library (ENDL82) in the Transmittal Format, June 1982. · Vol. 5, Part A, Rev. 1, CLYDE: A Code for the Production of Calculational Constants from Nuclear Data, September 1975. · Vol. 5, Part B, Rev. 1, Relativistic Transformations between Center-of-Mass and Laboratory Systems for Two-Body Nuclear Reactions, April 1978. · Vol. 6, Part A, Rev. 4, Tables and Graphs of Photon-Interaction Cross Sections from lOeVto 100 GeV Derived from the LLNL Evaluated Photon Data Library (EPDL), Z = lto 50, October 1989. · Vol. 6, Part B, Rev. 4, Tables and Graphs of Photon-Interaction Cross Sections from lOeVto 100 GeV Derived from the LLNL Evaluated Photon Data Library (EPDL), Z = 51to 100, October 1989. · Vol. 7, Part A, Rev. 1, Major Neutron-Induced Interactions (Z <55): Graphical, Experimental Data, July 1976. · Vol. 7, Part B, Rev. 1, Major Neutron-Induced Interactions (Z > 55): Graphical, Experimental Dflto, July 1976. · Vol. 8, Part A, Rev. 1, Supplemental Neutron-Induced Interactions (Z <35): Graphical, Experimental Data, July 1976. · Vol. 8, Part B, Rev. 1, Supplemental Neutron-Induced Interactions (Z > 35): Graphical, Experimental Data, July 1976. · Vol. 9, Thresholds of Nuclear Reactions Induced by Neutrons, Photons, Deuterons, Tritons, and Alpha Particles, September 1970. · Vol. 10, Rev. 1, Tabulated Experimental Data for Neutron-Induced Interactions, July 1976. · Vol. 11, Experimental Data, Indexes, and Techniques of Obtaining a Selected Set of Neutron Resonance Parameters, May 1972. · Vol.. 12, An Atlas of Resolved Neutron Resonance Parameters, July 1972. · Vol. 13, An Atlas of Unresolved Neutron Resonance Parameters, September 1972. · Vol. 14, TARTNP: A Coupled Neutron-Photon Monte Carlo Transport Code, February 1976. · Vol. 15, Part A, The LLL Evaluated-Nuclear-Data Library (ENDL): Evaluation Techniques, Reaction Index, and Descriptions of Individual Evaluations, September 1975. · Vol. 15, Part B, Rev. 1, The LLL Evaluated-Nuclear-Data Library (ENDL): Graphs of Cross Sections from the Library, October 1978. HI
· Vol. 15, Part C, The LLL Evaluated-Nuclear-Data Library (ENDL): Translation of ENDL Neutron-Induced Interaction Data into the ENDF/B Format, April 1976. · Vol. 15, Part D, Rev. 1, The LLL Evaluated-Nuclear-Data Library (ENDL): Descriptions of Individual Evaluations for Z = 0-98, May 1978. · Vol. 15, Part E, Data Testing Results for the LLL Nuclear Data Library (ENDL-78), August 1979. · Vol. 15, Part F, Experimental and Evaluated Elastic Nuclear Plus Interference Cross Sections for Light charged particles, July 1980. · Vol. 16, Rev. 2, Tabular and Graphical Presentation of 175 Neutron-Group Constants Derived from the LLL Evaluated-Nuclear-Data Library (ENDL), October 1978. · Vol. 17, Part A, Rev. 2, Program LINEAR (Version 79-1) Linearized Data in the EvaluatedNuclear-data file/Version B (ENDF/F) Format, October 1979. · Vol. 17, Part B, Rev. 2, Program SIGMAL (Version 79-1) Doppler Broadened Evaluated Cross Sections in the Evaluated-Nuclear-Data File/Version B (ENDF/B) Format, October 1979. · Vol. 17, Part C, Program RECENT: Reconstruction of Energy-Dependent Cross Sections from Resonance Parameters in the ENDF/B Format, October 1979. · Vol. 17, Part D, Program GROUPIE: Calculation of Self-Shielded Cross Sections and Multiband Parameters from Evaluated Data in the ENDF/B Format, 1980. · Vol. 17, Part E, Program EVALPLOT: Plot Data in the Evaluated-Nuclear-Data File/Version B (ENDF/B) Format, February 1979. · Vol. 17, Part F, DOWNER (Version 79-1) Group Collapse Cross Section and Transfer Matrices, January 1979. · Vol. 18, ACTL: Evaluated Neutron Activation Cross-Section Library, October 1978. · Vol. 19, Neutron-Induced Angular and energy distributions: Graphical, Experimental Data, April 1977. · Vol. 20, Bonderenko Self-Shielded Cross Sections and Multiband Parameters Derived from the LLL Evaluated-Nuclear-Data Library (EA/DL), July 1978. · Vol. 21, Part A, Maxwell-Averaged Reactions Rates (sn)for Selected Reactions between Ions with Atomic Mass <11, February 1979. · Vol. 21, Part C, Program SIGMAL (Version 79-1) Doppler-Broadened Evaluated Cross Sections in the Livermore-Evaluated Nuclear Data Library (ENDL) Format, March 1979. · Vol. 22, Rev. 1, GAMIDEN: A Program to Aid in the Identification of Unknown Materials by Gamma-Ray Spectroscopy, Jvme 1982. · Vol. 23, ENSL and CDRL: Evaluated nuclear structure Libraries, February 1981. · Vol. 23, Addendum, ENSL82 and CDRL82: The 1982 Version of Evaluated Nuclear Structure Libraries, January 1983. · Vol. 24, Thresholds and Q Values of Nuclear Reactions Induced by Neutrons, Protons, Deuterons, Tritons, ^He Ions, Alpha Particles, and Photons, March 1981. · Vol. 25, OMEGA: A CRAYl Executive Code for LLNL Nuclear Data Libraries, August 1983. · Vol. 26, A Bibliography and Index for Nuclear Reactions Among Light Charged Particles, September 1984. · Vol. 27, Calculated Neutron KERMA Factors Based on the LLNL ENDL Data File, January 1986. · Vol. 28, Index to the LLNL Evaluated Charged-Particle Library (ECPL), March 1986. · Vol. 29, Calculated Photon KERMA Factors Based on the LLNL EGDL Data File, October 1986. · Vol. 30, Tables and Graphs of Atomic Subshell and Relaxation Data Derived from the LLNL Evaluated Atomic Data Library (EADL), Z = 2-100, October 1991. · Vol 31, Tables and Graphs of Electron-Interaction Cross Sections from 10 eV to 200 GeV Derived from the LLNL Evaluated Electron Data Library (EEDL), Z = 1-100, November 1991. iv
Tables and Graphs of Electron-Interaction Cross Sections from 10 eV to 100 GeV Derived from the LLNL Evaluated Electron Data Library (EEDL), Z = 1-100 Abstract Energy-dependent evaluated electron interaction cross sections and related parameters are presented for elements H through Fm (Z = 1 to 100). Data are given over the energy range from 10 eV to 100 GeV. Cross sections and average energy deposits are presented in tabulated and graphic form. In addition, ionization cross sections and average energy deposits for each shell are presented in graphic form. This information is derived from the Livermore Evaluated Electron Data Library (EEDL) as of July, 1991. Overview The ENDL family of evaluated data libraries^ currently is being updated to include complete photon and electron Interaction data plus atomic relaxation data to couple photons and electrons. Ail of these data bases will be completely consistent; they will conserve energy and will all use the same atomic parameters (e.g., subshell binding energies). These data bases will allow complete coupled electronphoton transport calculations to be performed in a consistent manner. The current volume documents the new EEDL electron Interaction library. Earlier volumes documented the photon interaction^-^ and atomic relaxation*'^ libraries. As in past volumes of this publication describing evaluated data libraries, the emphasis here is on presenting an overview of the contents of the EEDL, as well as an explanation of the data contained herein, so that it may be correctly interpreted and used. For further details of the methods used to create the current library and a description of the complete contents of this library, see Ref. 6. Introduction The Livermore Evaluated Electron Library (EEDL) contains data for isolated, neutral atoms of the elements H through Fm (Z = 1 to 100) and over the energy range from 10 eV to 100 GeV. The data in this library includes cross sections, normalized angular distributions, normalized energy spectra, and energydeposition terms. The reactions considered Include bremsstrahlung, elastic scattering, excitation, and impact loruzatlon, the latter data being given on a subshell basis. This volume details the various cross sections and the energy deposition. ix
Sources of Evaluated Data Bremsstrahlung Cross Sections The bremsstrahlung cross sections were derived from the computerized data of Seltzer and Berger.'''^ The original Seltzer and Berger results were in the form of photon yield spectra for an incident electron kinetic energy from 1 keV to 10 GeV. By using systematics and cubic spline fits, these spectra were extended down to 10 eV and up to 100 GeV. For use in applications, both a cross section and a spectrumaveraged photon energy (i.e., the stopping power) are required in addition to a normalized photon spectrum. In defining a cross section, it is not possible to extend the spectra down to a photon energy, k, of zero because the spectra has a 1/it singularity. In this work, the spectra was terminated at a photon cutoff energy of 0.1 eV, which is 1% of the lowest incident electron energy considered and consistent with the accuracy to which the spectral tables were created. These cutoff spectra defined the cross section and the average photon energy in this library. Elastic Scattering Cross Sections Several different models were used for elastic scattering. Between 1 and 256 keV, Riley et al.' obtained differential cross sections by a phase-shift analysis of the Dirac equation and fit the results to an analytical expression. The coefficients in this equation were obtained from the SANDYL Monte Carlo data file^" for nine incident energies between 1 and 256 keV, for Z = 1 to 1(X). At higher energies, a factorization cross sectlon,^^ in which screening is treated separately from relativistic and spin effects, has proven satisfactory and was used here. The screening parameter was that of Mollere,^^ as empirically modified by Seltzer'^ for better low-energy behavior. The Mott-to-Rutherford cross-section ratio was obtained from Wilderman,^* whose convergence parameters were also used. The angular distribution at high energies has an extremely large forward bias. This forward component Is more appropriately treated by multiple scattering theory, which leads us to define two elastic-scattering cross sections. The total elastic-scattering cross section is defined by Integrating the angular distribution over the scattering cosine from -1 to 1. The cutoff elastic-scattering cross section is similarly obtained by Integrating over the scattering cosine from -1 to 0.999999. As previously noted, Riley's data was used from 1 to 256 keV, and the factorization cross section was used at higher energy. Of course, the two cross sections do not agree at the joining, with the difference being greater at large atomic number. A smoothing algorithm using cubic splines was therefore used to determine the cross sections between 256 keV and 10 MeV. The data between 10 eV and 256 keV were obtained by log-log extrapolation of the cross section. The transport cross section was likewise calculated and extrapolated down to 10 eV. At this energy, the extrapolated scattering and transport cross sections were approximately equal. Independent of the target atomic number. At low energy, this Indicated a symmetrical angular distribution, which for simplicity we define to be isotropic. Impact Ionization Cross Sections Sdtzer^^ divides ionization collisions into two components; close collisions and distant colUsloits. To the latter event, he suggests adding a third term that takes into account the density effect caused by the polarizability of the medium. For close collisions, the present data base uses Seltzer's modification of the Moller^^ binary collision cross section, which takes into consideration the binding of the atomic electron in a given subshell. The MoUer cross section accounts for relativistic effects, particle spin, and like-particle scattering. For distant collisions. Seltzer's modification of the Welzsacker^^-Wllliams^° method (see Ref. 19 also) was used. This cross section is described in terms of a virtual photon field interacting with the atomic electrons. The atomic data required in the present description included subshell binding energies, number of electrons, mean electron kinetic energy, and the mean radius. These were obtained X
from the Livermore Evaluated Atomic Data Library (EADL).* The subshell photoelectric cross sections required for the distant-collision component came from the Livermore Evaluated Photon Data Library (EPDD.^-^ Scofield's^" relativistic cross section was used for the density effect. The density-effect differential cross section is a negative correction to the differential cross section for distant collisions. When the sum of these two cross sections becomes negative, it is set to zero. This creates saturation in the subshell cross section at high energy. Differential energy spectra for the recoil electron for all subshells were obtained in this manner from 10 eV (or threshold) up to 100 GeV. These were then integrated to obtain the subshell cross sections and the average recoil electron energy. Stopping Power and Excitation For a given reaction, the stopping power, dE/dx, is defined as being the average energy loss per unit path length. The colllslonal (ionization plus excitation) stopping power, based on Bethe theory, was obtained using a computer code furnished by Seltzer^^ and was considered valid down to about 10 keV. The ionization stopping power was obtained from our data by Integration over the recoil spectra, by appropriately summing over all subshells and then converting from a per collision to a per unit path length basis. The difference between the colllslonal and the ionization stopping power was defined to be the excitation stopping power. It was noted that down to 10 keV, p2 (p = v/c, where v is the electron speed and c is the speed of light) times the excitation stopping power was almost a constant. The ratio of excitation to ionization stopping power known at higher energies was extrapolated down to lower energies to yield the excitation stopping power. Adding the stopping powers together to obtain the colllslonal stopping power yielded low-energy results that are in very good agreement with the work of Akkerman and Chemov^^ as well as with the results of Ashley et al.^ Excitation Cross Sections A very simplistic model was used for excitation. It was assumed that all excitation arises through distant collisions from the outermost subshell; this corresponds to using the distant-collision portion of the model that was used for lonization.^7-20 This approach yielded differential energy spectra that were imnormalized because the number of participating electrons was unknown. Integrating over the spectra yielded an unnormalized cross section, stopping power, and straggling. These were normalized to the excitation stopping power at 100 GeV. Energy Deposition The energy deposition terms defined here are the stopping powers, dE/dx, defined for each reaction. The energy deposition for bremsstrahlung is equal to the total average energy into the photons. The energy deposition for elastic scattering is taken to be zero, since the energy loss of the electron is negligible because of the large mass difference between incident electron and target nucleus. The energy deposition for impact ionization is based on the summation over all subshells of the sum of the subshell binding energy plus the total average knockon electron energy. As noted earlier, the excitation stopping power was taken to be the difference between the colllslonal and the ionization stopping powers. Atomic Parameters Subshell binding energies and relaxation data* have been used to define the fluorescence energy deposition presented here. These parameters are for neutral elements; initially ionized atoms and molecular binding effects have not been included. xi
Atomic Weights and Densities The atomic weights and the densities used in these calculations are presented at the tops of the tables and graphs for each element. Standard temperature and pressure (STP) values of density were used when available. If the derwity was unknown or poorly known, a value of 13.5 g/cm^ was assumed. It should be noted that the densities used here correspond to elemental densities. The density of any given element in a compound or molecule may differ greatly from that used here; this is particularly true for elements that are gaseous in their elemental form. Therefore, the mean free paths presented here should be used with caution. In any given application, it is better to calculate the mean free path directly from the cross sections and actual elemental density.
Procedures Used to Derive Data
Cross Sections The cross sections as presented here are a subset of the contents of the EEDL. The size of the data tables has been minimized by presenting only those values that are required to allow log-log interpolation between tabulated values for all quantities on a uniform energy grid (i.e., a sufficient number of energy points are included in the tables to allow data to be interpolated to within an accuracy of about 1%). Specifically, to define a cross section at an energy E between two tabulated energies Ei and Ј3, one should use the following log-log interpolation scheme:
logia^fc^j-
log(E2/Ei)
·
^^'
Total Mean Free Path and Range The microscopic total cross section is defined by
OT(E) = aei(E) + aion(E) + Oexc(E) + Ofbreni(E)
(in bams) ,
(2)
where T refers to total, el to elastic, ion to ionization (summed over all subshells), exc to excitation, and brem to bremsstrahlung; E is the Incident electron energy (MeV). The total mean free path (the inverse of the macroscopic total cross section) and mass attenuation coefficient have been derived from the total cross section by using the relationships
ME)=--rr--7^.
(in cm)
(3)
m = ^^^ A
(incm2/g).
(4)
where
A
= atomic weight (based on carbon-12 = 12)
p
= density in g/crv?
No = Avogadro's number (0.6022137)
X{E) = the mean free path at energy Ј in cm
H(E) = the mass attenuation coefficient at energy E, in cm^/g.
The range has been derived in the continuous slowlng-down approximation by use of the expression
xii
R(Ei,Ef)= n ^ dE ,
(incm)
(5)
where
R
= range, in cm
Ei = initial energy, in MeV
Ef = final energy, in MeV
dE/dx = stopping power (colllslonal plus bremsstrahlung), in MeV/cm. In all cases, we define the final
energy, Ef as 100 eV.
Energy Deposition
Energy depositions are defined as the mean energy loss per unit path length, dE/dx, for each reaction. For ionization, the energy loss for a given collision, E - E', is
E-E' = W+Bj,
(6)
where W is the kinetic energy of the knockon electron and Bj is the subshell binding energy. The subshell atomic stopping power is given by
iE-Bj)/2
S(E)y= f(W + B / ) ^ ^ | ^ d W ,
(7)
where the differential subshell ionization cross section is on a per atom basis. The ionization stopping power is then obtained by summing over all subshells
^ ^ ^ = ^ I S{E)j
(in MeV/cm) .
(8)
For bremsstrahlung, the energy loss for a given collision is equal to the energy of the emitted photon. The atomic stopping power for this reaction is then
It
S(E)j= \k^-^dk,
(9)
0.1 eV
where k is the photon energy and the differential cross section is on a per-atom basis. The lower energy in the Integral isti\elowest bremsstrahlung spectra energy in the library. The bremsstrahlung stopping power is
^ ^ ^ 1 ^ = ^ SiE)
(in MeV/cm) .
(10)
The excitation stopping power is taken as the difference between the colllslonal stopping power of Seltzer^^ and the ionization stopping power from Eq. (8).
Impact Ionization Shell Cross Sections The ionization shell cross sections presented here have been derived by summing the subshell cross sections contained in the EEDL.
xiii
Accuracy of the Data Bremsstrahlung Based on our extrapolations and Seltzer's and Berger's'^-* estimates, our stated uncertainties in the bremsstrahlung cross section are · lOeVtolkeV, 10 to 25% · 1 keV to 2 MeV, 5 to 10% · 2 to 50 MeV, <10% · 50 MeV to 10 GeV, =3% · 10 to 100 GeV, «5%. At low energies, however, coherent solid-state and molecular effects can increase this greatly. Fortunately, because the bremsstrahlung cross section and energy loss are a small part of the total at low energy, uncertainties in these data will have littie effect on applications. Elastic Scattering For elastic scattering, theory seems to be adequate except at low energies. However, Berger and Wang2* indicate that no theory exists that will in general calculate the differential cross section above 1 keV for molecules or in solids. Here, theory predicts too high a cross section at small angles, and experiment shows diffraction effects. At 10 eV, we have compared the transport cross section calculated from our data to the semi-empirical values of Itikawa.^^ From this comparison, it appears that our results, because of neglecting resonance effects, can overestimate the transport cross section by up to 10(X)% at low energies. The error in our elastic data would be at least this large. Ionization Comparing our K-shell ionization cross section to the compiled experimental data of Tawara and Kato^^ and Long et al.,^'' we find that the uncertainties in our data appear to be ^30 to 40% at low energies. The error might be as large as a factor of 2 above several hundred MeV for Intermediate-Z elements because of the uncertainty in the onset in energy of the density effect. Errors in the outer subshells are probably at least as much. Finally, our neglect of solid-state effects will introduce even larger uncertainties at low energies. Stopping Power Berger's and Seltzer's^^ colllslonal stopping-power errors are · lOtolOOkeV, 2 to 3% for low-Z material 5 to 10% for high-Z material · abovelOOkeV, lto2%. Our estimated ionization stopping-power errors are · 10 to 100 eV, up to 1000% · 100 eV to 1 keV, 10 to 20% · ItolOkeV, 5tol0% · 100 keV to 100 GeV, 2 to 5%. Chir estimated excitation stopping-power errors are · 10 to 100 eV, up to 1000% · 100 eV to 100 GeV, 20 to 50%. xiv
Subshell Parameters By comp>aring subshell parameters from a number of different sources, one can see that there is still a disagreement of about 1% between the edge energies. For use in applications, particularly coupled electron-photon transport, knowing the exact edge energies is not as important as ensuring that the same edge energies are used throughout. Therefore, Scofield's subshell parameters* are consistentiy used for both photon and electron data. Associated Libraries and Availability of the Data EEDL contains only the data necessary to describe the interactions of electrons with matter. For performing coupled photon-electron calculations, two additional libraries are available. · The Livermore Evaluated Photon Data Library (EPDL),^ to describe the interaction of photons with matter. · The Livenrwre Evaluated Atomic Data Library (EADL),* to describe the relaxation of singly ioiuzed atoms. All three of these libraries are available in the ENDL format.^ Explanation of Graphs and Tables The electron data in this report are in the form of graphs and tables; Included are cross sections, energy depositions, mean free paths, and particle ranges. Data are presented in order of increasing Z (atonuc number). For each element, four figures are followed by tabulated data. In the first figure, "Cross Sections," the Integrated cross sections are plotted. The total cross section is defined by Eq. (2). For elastic scattering, results are presented for the total elastic (defined by integrating the angular distribution over - 1 5 n S1) and the cutoff elastic (defined by integrating the angular distribution over -1 ^ |i ^ 0.999999). The second figure, "Energy Deposition," shows the various energy-deposition terms for electron Interactions. Results are given both as the stopping power, dE/dx (in MeV/cm), and as the mass stopping power, (l/p)(dE/ix) (in MeV-cm^/g). The fluorescence deposition is the component of the ionization that yields x rays. The difference between the ionization and the fluorescence deposition is the electron deposition, which includes both the original knockon contribution as well as the contribution from the subsequent orbital electrons in the relaxation of the atom back to neutrality. (Editor's note: We know that "Bremsstrahlung" is misspelled in these figures, but the effort to redo 200 figures to correct it would be prohibitive.) The final two plots are the ionization shell quantities. The third figure, "Shell Cross Sections," shows the total ionization cross section and the components for each atomic shell. The final figure, "Energy Deposition," shows the corresponding divisions for energy deposition. The tables cover the energy range from 10 eV to 100 GeV. Included in the table are enough points to allow log-log interpolation between tabulated values as well as element subshell binding energies (e.g., L2) and the decade marks. The tabulated energy points will not necessarily be the same for all elements. Under "Mean Free Path" are the mean free path, Eq. (3), and the mass attenuation coefficient, Eq. (4). The range is from an incident energy, E, down to an energy of 100 eV. The cross sections and energy depositions include both the total and the various components. XV
References 1. R. J. Howerton et al., OMEGA: A Cray 1 Executive Code for LLNL Nuclear Data Libraries, Vol. 25, Lawrence Livermore Natioiwl Laboratory, Livermore, CA, UCRL-50400 (1983). 2. D. E. Cullen, M. H. Chen, J. H. Hubbell, S.T. Perkins, E.F. Plechaty, J. A. Rathkopf, and J. H. Scofield, Tables and Graphs of Photon-Interaction Cross Sections from 10 eV to 100 GeV Derived from the LLNL Evaluated Photon Data Library (EPDL), Lawrence Livermore National Laboratory, Livermore, CA, UCRL-50400, Vol. 6, Rev. 4, Part A: Z = 1 to 50, Part B: Z = 51 to 100 (1989). 3. D. E. Cullen, S. T. Perkins, and J. A. Rathkopf, The 1989 Livermore Evaluated Photon Data Library (EPDL), Lawrence Livermore National Laboratory, Livermore, CA, UCRL-ID-103424 (1990). 4. S. T. Perkins et al.. Tables and Graphs of Atomic Subshell and Relaxation Data Derived from the LLNL Evaluated Atomic Data Library (EADL), Z = 1-100, Lawrence Livermore National Laboratory, Livermore, CA, UCRL-50400,Vol. 30 (1991). 5. S. T. Perkins and D. E. Cullen, The 1991 Evaluated Atomic Data Library (EADL), Lawrence Livermore National Laboratory, Livermore, CA (to be published). 6. S. T. Perkins and D. E. Cullen The 1991 Livermore Evaluated Electron Data Library (EEDL), Lawrence Livermore National Laboratory, Livermore, CA, (to be published). 7. M. Seltzer and M. J. Berger, Nucl. Instrum. and Meth. in Phys. Res., B12,95 (1985). 8. M. Seltzer and M. J. Berger, At. Data and Nucl. Data Tables 35,345 (1986). 9. M. E. Riley et al.. At. and Nucl. Data Tables 15,443 (1975). See also At. and Nucl. Data Tables 28,379 (1983). 10. A. J. Antolak, Private communication, ^andia National Laboratories, Livermore, CA (1987). 11. M. J. Berger, Methods in Comp. Phys. Vol. 1 (Academic Press, New York, 1963), p. 35. 12. G. Moll^re, Z. Naturforsch. 2a, 113 (1947). 13. S. M. Seltzer, "An (Overview of ETRAN Monte Carlo Methods," in Monte Carlo Transport of Electrons and Photons, Chapt. 7 (T. M. Jenkins et al, eds.) (Plenum Press, New York, 1988). 14. S. Wilderman, Private communication. University of Michigan, Ann Arbor, MI (1988). 15. S. M. Seltzer, "Cross Sections for Bremsstrahlung Production and for Electron Impact Ionization," in Monte Carlo Transport of Electrons and Photons, Chapt. 4 (T. M. Jenkins et al., eds.) (Plenum Press, New York, 1988). 16. C. MoUer, Ann. Phys. 14,568 (1932). 17. C. F. Weizsacker, Z. Physik 88,612 (1934). 18. E. J. Williams, Kgl. Danske Videnskab. Mat.-fys. Medd. Xni, 4 (1934). 19. J. D. Jackson, Classical Electrodyrumks, 2nd ed. (Wiley Press, 1975), p. 719. 20. J. H. Scofield, Phys. Reo. A18,963 (1978). Note that Eq. (20) has a typographical error. 21. S. M. Seltzer, Private communication. National Institute of Standards and Technology, Gaithersburg, MD (1988). See also M. J. Berger and S. M. Seltzer, "Stopping Powers and Ranges of Electrons and Positrons," National Institute of Standards and Technology, Gaithersburg, MD, NBSIR 82-2550 (1982). 22. A. F. Akkerman and G. Ya.Chemov, Phys. Stat. Sol. (b) 89,329 (1978). 23. J. C. Ashley, C. J. Tung, and R. H. Ritchie, Surface Science 81,409 (1979). 24. M. J. Berger and R. Wang, "Multiple-Scattering Angular Deflections and Energy-Loss Straggling," in Monte Carlo Transport of Electrons and Photons, Chapt. 2 (T. M. Jenkins et al., eds.) (Plenum Press, New York, 1988). 25. Y. Itlkawa, At. Data and Nucl. Data Tables 21,69 (1978). See also Y. Itikawa, At. Data and Nucl. Data Tables 14,1(1974). 26. H. Tawara and T. Kato, At. Data and Nucl. Data Tables 36,167 (1987). 27. X. Long et al.. At. Data and Nucl. Data Tables 45,353 (1987). XVI

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