
XCOM Documentation

M. J. Berger and J. H. Hubbell

A computer program and data base are presented which can
be used to calculate, with a personal computer, photon
cross sections for scattering, photoelectric
absorbtion and pair production, as well as total
attenuation coefficients, in any element, compound, or
mixture, at energies from 1 keV to 100 GeV.
____________________________________________________
Table of Contents:

I.	Disclaimer
II.	Why you should use the Web
III.	Version History
IV.	Files for XCOM
V.	Setup
VI.	Running XCOM
VII.	Program Notes
____________________________________________________
I. Disclaimer:

The National Institute of Standards and Technology (NIST)
uses its best efforts to deliver a high quality copy of
the Database and to verify that the data contained therein
have been selected on the basis of sound scientific
judgement. However, NIST makes no warranties to that
effect, and NIST shall not be liable for any damage that
may result from errors or omissions in the Database.
____________________________________________________
II. Why you should use the Web:

	Simple and convenient user interface
	Graphing
	Updated regularly

Check out the online version at:

http://physics.nist.gov/XCOM
____________________________________________________
III. Version History:

	Description
	Version Number
	Date
	Programmer(s)

	Programming Update
	Version 3.1
	June 1999
	Martin J. Berger and Stephen M. Seltzer
	
	NIST Standard Reference Database 8
	Version 2.0
	June 1990
	Martin J. Berger and John H. Hubbell

	Original Release
	Version 1.2
	July 1987
	Martin J. Berger and John H. Hubbell


For more comprehensive version history information see the
online documentation:

http://physics.nist.gov/PhysRefData/Xcom/Text/version.html
____________________________________________________
IV. Files for XCOM:

XCOM.f		Fortan Source
ATWTS.DAT	Atomic Weights Data File
ENB.DAT		Data File
HASH1.DAT	Data File
HASH2.DAT	Data File
INDEX.DAT	Data File
MDATX3.xxx	Cross Sections Data for each element
		where "xxx" is the atomic number

for PC only

XCOM.exe	Photon Cross Sections Program
makedisk.bat	Application that can be used to copy the
		XCOM program to a floppy disk without
		including any extraneous files
____________________________________________________
V. Setup:

1. Make a directory for XCOM
2. Unzip the XCOM zip into that directory

Note: PC users can skip step 3

3. Compile (and link) XCOM.f

To run the program, run XCOM and follow command line
instructions
____________________________________________________
VI. Running XCOM:

Follow comand line instructions

Note on: Format for entry from prepared input file
	- First, the number of energies in the list
	- Then, energies in MeV
	- All items separated by blank spaces
____________________________________________________
VII. Program Notes:

For calculation information such as the method used
see the online documentation:

http://physics.nist.gov/PhysRefData/Xcom/Text/intro.html

================================================================================

                XCOM: Photon Cross Sections on a Personal Computer 
   
   
                       M. J. Berger and J. H. Hubbell 
                        Center for Radiation Research 
                        National Bureau of Standards 
                           Gaithersburg, MD 20899 
   
   
   
                 A computer  program and data base  are presented  
                 which can be used to calculate, with  a personal 
                 computer, photon cross  sections for scattering, 
                 photoelectric absorption and pair production, as 
                 well as total  attenuation  coefficients, in any  
                 element,  compound or mixture, at  energies from  
                 1 keV to 100 GeV. 
   
   
                                1. Introduction 
   
       Data  on the scattering and absorption of photons (x-rays,  gamma rays, 
  bremsstrahlung)  are  required for many scientific,  engineering and medical 
  applications.  The  number  of materials for which photon cross sections are 
  needed is large and ever increasing. Available tables [1-11] usually include 
  cross sections for many (but not all) elements.  Some tables [1,2,6,11] also 
  contain data for a limited number of compounds and mixtures.  In practice it 
  is  not  possible to meet all cross-section requirements adequately by means 
  of printed tables.  Moreover,  the cross sections are often needed at photon 
  energies other than those included in the tables. 
   
       Photon  cross  sections  for compounds can of course be obtained rather 
  accurately  (except  at energies close to absorption edges) as weighted sums 
  of  the  cross sections for the atomic constituents.  However,  the required 
  numerical work  is tedious,  and the task is further complicated by the fact 
  that  photoabsorption  cross sections and total attenuation coefficients are 
  discontinuous  at  absorption  edges.  The presence of these discontinuities 
  makes  it  desirable  that cross section tables for compounds include photon 
  energies  immediately  above  and below all the absorption edges for all the 
  atomic constituents, and this requires much additional interpolation.   
   
       A convenient alternative approach is to generate the cross sections and 
  attenuation  coefficients  for  compounds   and mixtures as needed,  using a 
  personal  computer.  This  paper  describes   a computer program called XCOM 
  which  carries  out  this task quickly on IBM-compatible personal computers, 
  for any element, compound or mixture, at energies between 1 keV and 100 GeV. 
  The  program makes use of a database of cross sections for the elements that 
  is stored in compressed form on a single floppy disk. 
   
       The  XCOM program can generate cross sections on a standard energy grid 
  (spaced  approximately  logarithmically), or on a grid selected by the user, 
  or for a mix of both grids. Cross sections at energies immediately above and 
  below  all  absorption edges are automatically included.  XCOM provides  two 
  forms of output:  (a) tables which  correspond closely in format to existing 
  tables in the literature;  (b) user-selected arrays which are convenient for
  further computer calculations. 
   
       The  program provides total cross sections and attenuation coefficients 
  as  well  as partial cross sections for the following processes:  incoherent 
  scattering,   coherent  scattering,   photoelectric  absorption,  and   pair 
  production in the field of the atomic nucleus and in the field of the atomic 
  electrons.  For  compounds,  the  quantities tabulated are partial and total 
  mass  interaction  coefficients,  which   are   equal  to the product of the 
  corresponding  cross  sections times the number of target molecules per unit 
  mass of the material.  The reciprocals of these interaction coefficients are 
  the  mean free paths between scatterings,  between photo-electric absorption 
  events,  or  between  pair  production   events.  The sum of the interaction 
  coefficients  for the individual processes is equal to the total attenuation 
  coefficient.  Total  attenuation  coefficients without the contribution from 
  coherent scattering are also given, because they are often used in gamma-ray 
  transport calculations.  
   
       The  interaction  coefficients  and  total attenuation coefficients for 
  compounds  or  mixtures are obtained as sums of the corresponding quantities 
  for the atomic constituents.  The weighting factors,  that is, the fractions 
  by  weight  of  the  constituents,  are calculated by XCOM from the chemical 
  formula entered by the user. For mixtures, however, the user must supply the 
  fractions by weight of the various components. 
   
       Some  limitations  should be noted.  The cross sections for elements in 
  the  XCOM  database pertain to isolated neutral atoms,  and do not take into 
  account  molecular and solid-state effects  which modify the cross sections,
  especially  in the  vicinity  of absorption  edges.  Relatively  small cross
  sections, such as those for Delbruck scattering, two-photon Compton scatter-
  ing or photo-meson production, are not included. Also omitted is the nuclear
  photoeffect  which, in the giant-dipole  resonance region from  5 to 30 MeV, 
  can contribute a few percent to the total attenuation coefficient.  Finally, 
  XCOM does not calculate  energy  absorption  coefficients that represent the
  conversion of photon energy to kinetic energy of secondary Compton-, photo-,
  and pair-electrons. 
        
                            2. Database for Elements 
   
       A comprehensive database for all elements over a wide range of energies 
  was constructed through the combination of incoherent and coherent scattering 
  cross  sections  from  Refs. [12]  and  [13], photoelectric absorption  from 
  Scofield  [14],  and  pair  production  cross  sections  from Ref. [8].  For 
  scattering and pair production, the same cross sections are used as in other 
  recent tabulations in Refs. [6, 8, and 11], whereas for photoelectric absorp-
  tion  there is a small difference (omission of a renormalization correction)
  which is discussed below. 
   
       The  incoherent  (Compton) scattering  cross sections in Ref. [12] were 
  obtained from a combination of the Klein-Nishina formula and nonrelativistic 
  Hartree-Fock incoherent scattering functions.  Radiative and double Compton-
  scattering   corrections  were  also  included.   The   coherent  (Rayleigh)
  scattering cross sections in Ref. [13] were calculated from a combination of 
  the Thompson formula and relativistic Hartree-Fock atomic form factors.  The 
  photoelectric cross sections were obtained by Scofield [14] by a phase-shift
  calculation  for  a  central  potential  and a Hartree-Slater atomic  model.  
  Scofield's results extend only up to 1.5 MeV.  At higher energies, where the
  photoelectric  cross section is quite small, a  semi-empirical  formula from
  Ref. [2] connects Scofield's values at 1.5 MeV to the asymptotic high-energy
  limit calculated by Pratt [15].  Cross sections for pair production given in
  Ref. [8] are  based on  complicated  combinations  of formulas  from  Bethe-
  Heitler  theory with various other  theoretical models to  take into account
  screening, Coulomb, and radiative  corrections.  Different combinations were
  used in the  near-threshold, intermediate and high-energy  regions to obtain
  the best possible agreement with experimental cross sections. 
   
       For  elements with atomic numbers from 2 to 54, Scofield [14] presented 
  correction  factors   for  individual  atomic  subshells,   with  which  the  
   photo-effect cross  sections  can be  renormalized so  that they  correspond 
  approximately  to a relativistic Hartree-Fock model rather than the Hartree- 
  Slater model used in the original calculation.  This renormalization is most 
  significant for the outer atomic shells;  the total cross section is lowered 
  by  no  more  than  10  percent   at energies above 1 keV.  Scofield did not 
  actually  apply  the  renormalization   to   the cross sections given in his 
  tables.  The  renormalization   was   used,  however,  in the tabulations in 
  Refs. [6, 8, and 11].  Recent reviews [16,17]  indicate that,  on the whole, 
  agreement with experiment is better when the renormalization is not done. We 
  have  therefore  omitted  the renormalization  in the database  for the XCOM 
  program. 
   
                        3. Interpolation and Combination 
   
       For  the  purpose  of interpolation with respect to photon energy,  the 
  coherent  and incoherent scattering cross sections and the total attenuation 
  coefficients  are  approximated by log-log cubic-spline fits as functions of 
  energy.  For the pair-production cross sections,  the fitted quantity is the 
  logarithm of the quantity ((1-E'/E)**3)*SPAIR(E), where E is the photon energy, 
  E' the  threshold  energy  for pair  production,  and SPAIR(E)  is the cross 
  section.  The fitting is done separately for pair production in the field of 
  the atomic nucleus (E' = 1.022 MeV) and in the field of the atomic electrons
  (E' = 2.044 MeV). 
   
       The  combined  photoelectric absorption cross section for all shells is 
  similarly  interpolated  with use of log-log cubic-spline fits,  but only at 
  energies above the K-shell absorption edge. Below this energy, interpolation 
  is  applied  to  the logarithm of the photoelectric absorption cross section 
  for each separate shell, fitted as a linear function of the logarithm of the 
  photon energy. The separate fitting for each shell is necessary to avoid the 
  error  that  would  be   incurred  by interpolating across absorption edges. 
  Linear  log-log  fitting  is  equivalent  to assuming that the photoelectric 
  cross section is proportional to a power of the photon energy, and was found 
  to  provide  more satisfactory fits than a log-log cubic-spline fit near the 
  absorption edges. 
   
       The  interaction  coefficients  and  total attenuation coefficients for 
  compounds  are obtained as weighted sums over the corresponding coefficients 
  for  elements.  XCOM automatically calculates the weight  factors, i.e., the 
  fractions  by weights of the atomic constituents,  from the chemical formula 
  for the compound entered by the user.  For mixtures, the user must enter the 
  fractions by weight of the components. 
   
   
                       4. Overview of the XCOM Program 
   
       The hardware requirements for running the XCOM program are moderate. It 
  is  sufficient  to have an IBM-compatible personal computer with a memory of 
  at least 256K bytes,  and with at least one 5.25-inch floppy-disk drive.  It 
  is  assumed  that  the  computer  is   operated with the PC-DOS or an MS-DOS 
  operating system,  version 2.0 or later.  A mathematical co-processor (Intel 
  8087  or  80287 chip) is not required,  but is highly desirable,  because it 
  speeds up to execution of XCOM by a factor of twenty or better. 
   
       The  XCOM program is distributed on two 5.25-inch floppy disks.  One of 
  these  is  the  Database  Disk,  and   contains 100 data files designated as 
  MDAT.001,  MDAT.002, ..., MDAT.100.  These  files,  generated  by  a Fortran 
  program and written in binary format, contain the cross-section database for
  the  elements  with  atomic  numbers  Z = 1 to 100.  The  other disk  is the
  Program Disk, and contains an executable file called XCOM.EXE.  
   
       The Program Disk also contains a copy of this report, in file XCOM.DOC, 
  and  the Fortran source code for XCOM.  The source code is not needed to run 
  XCOM.  It  is  included  to make it possible for the user to make modify the 
  program,  and  to  adapt  the  program to for use with a different operating 
  system or computer. 
   
  The main program, XCOM, uses the following subroutines: 
   
    SPEC    Allows the user to specify the composition of the material, 
            the energy list, desired output etc. 
   
    FORM    Translates the chemical symbols for elements or chemical 
            formulas for compounds into the composition of the material 
            specified in terms of atomic numbers, atomic weights, and  
            fractions by weight of the atomic constituents. 
   
    MERGE   Creates a merged energy list arranged according to magnitude. 
            This list combines a standard energy grid (approximately 
            logarithmic) with the set of absorption-edge energies for 
            all the atomic constituents for a given compound or mixture, 
            and with the set of additional energies which the user wishes  
            to add. 
   
    REV     Utility routine for reversing the order of certain arrays. 
   
    SCOF    Routine for generating coefficients for cubic-spline fits. 
   
    BSPOL   Interpolation routine (based on binary search) making use of 
            cubic-spline interpolation coefficients from SCOF.FOR. 
   
    BLIN    Linear interpolation routine, based on binary search.  
               
       Also  included  on the Program Disk are five additional files which are 
  "included" in the main program or in subroutines at the time of compilation. 
  ENB.DAT and INDEX.DAT are for inclusion in XCOM,  HASH1.DAT and HASH2.DAT in 
  FORM, and ATWTS.DAT in XCOM and FORM. 
   
   
   
                       5. How to Run the XCOM Program 
   
       If  the program is to be run using only floppy disks,  the Program Disk 
  should be inserted into drive A.  After the appearance of the A> prompt, the 
  program can be started by entering "XCOM". 
   
       If the program is to be run from a hard disk,  it is recommended that a 
  special  subdirectory  be created for running XCOM.  First,  the user should 
  copy  the  file  XCOM.EXE  from  the  Program  Disk  and  the   data   files 
  MDAT.001, MDAT.002, ..., MDAT.100  from the  Database Disk  into the special 
  directory.  After  the special directory is made the current  directory, the 
  program can be started by entering XCOM. 
   
       From this point on,  the program proceeds interactively.  The user must 
  respond to prompts (indicated by -->) by entering requested input data or by 
  making  choices from various options.  The requested information pertains to 
  the name and characterization of the substance of interest,  the desired set 
  of energies at which cross sections are to be computed,  and the form of the
  output. 
   
       The  prompts are largely self-explanatory.  In order to indicate to the 
  user  what  to  expect,  we show  in this  report  a record  of prompts  and
  responses  that  appeared  on the  monitor screen  in three  sample runs  of
  XCOM,  for  an  element  (lead)  in  Appendix A,  for  a  compound  (calcium
  tungstate) in Appendix B, and for a mixture (pyrex glass) in Appendix C. The
  XCOM program could probably be run without further explanations.  Additional
  information  is provided in  the remainder of this  Section, which will help 
  the user to formulate his responses to the prompts. 
   
  5.1. Name of Substance. 
   
       The  name can be freely chosen,  may include imbedded blanks,  and must 
  consist  of  no more than 72 characters.  The name will appear on the top of 
  the output table.
    
  5.2. Elements, Compounds and Mixtures. 
   
       The  substance  for  which  cross   sections  are to be computed can be 
  designated to be an element, compound or mixture. Elements can optionally be 
  indicated  by  their   atomic   number,  or by their chemical  symbol. These 
  symbols,  or chemical formulas for compounds,  should be entered in standard 
  chemical notation,  with appropriate upper and lower case.  However, because 
  of  hardware limitations,  subscripts must be written on line.  For example, 
  the formula for calcium tungstate must be entered as CaWO4. 
   
       Substances  consisting of molecules with only a single species of atoms 
  can be designated as either as elements or compounds. For example, molecular 
  nitrogen  could  be treated as an "element" with symbol N,  or as a compound 
  with formula N2 (entered as N2). 
   
  5.3. Mixtures. 
   
       Mixtures  are  assumed  to  consist of two or more components,  each of 
  which can be either an element or a compound.  Whether the mixture is broken 
  down  into  "elemental"  components  or "compound" components is a matter of 
  convenience  (depending on the readily available information),  but does not 
  change the results.  
   
       The user  must indicate  how many components  there are in the mixture,
  and must specify the chemical symbol or formula, as well as  the fraction by 
  weight,  for each component,  as prompted. The program then uses these input 
  data  to  compute  the   fractions   by  weight of for the individual atomic 
  constituents,  as  well  as the sum of these fractions.  This information is 
  displayed on the monitor screen. The input data might be faulty in the sense 
  that  the  sum of the fractions by weight does not add up to unity.  In this 
  case the user is given two choices:  1) The input data can be "accepted", in 
  which  case  the program renormalizes all of the fractions by weight so that 
  they add up to unity;  2) Another set of fractions by weight for the mixture
  can be entered.  
   
  5.4. Quantities and Units. 
   
       For  elements,  the  user is  given  three  choices:  1) the output can
  consist  of  cross  sections  for  individual  processes,  and  total  cross 
  sections, in units of  barns/atom, where 1 barn =10E-24 cm2;  2) the output 
  can consist of cross sections for individual processes,  in barns/atom,  and 
  mass  attenuation  coefficients,  in  cm2/g;  3)   the output can consist of 
  partial  mass  interaction  coefficients   and,  total   mass    attenuation 
  coefficients,  in  cm2/g.  For   compounds   and  mixtures the output always 
  consists  of  partial  mass interaction coefficients,  and total attenuation 
  coefficients, in cm2/g. 
   
  5.5. Energy List. 
   
       The user can 1) limit the output to the standard energy grid, 2) add to 
  the standard grid selected energies of his choice, or 3) request output only 
  for the set of energies selected by him.  In case 2) the additional energies 
  are merged into the standard energy grid according to magnitude. In case 3), 
  the  energies  will  appear  in  the output table exactly in the sequence in 
  which they were entered by the user. 
   
       If  additional  energies  are  entered  by the user,  this can be done, 
  optionally,  either  from the keyboard,  or from a previously prepared input 
  file.  This  file (stored in any desired directory on a floppy or hard disk) 
  should contain, as first item, the number of additional energies, and then a 
  list of energies, which items separated by blank spaces.  
   
  5.6.  Database Input Data 
   
       The  program  will  prompt  the   user  as to the  location of the file 
  containing the database files.  The user can request that these data be read 
  from  a  floppy  disk drives (A or B),  or from the current directory in the 
  hard disk.  Even  when the program is run from the  special directory on the 
  hard disk,  the data can still come from drives A or B.  If the data  are to
  come from  the  hard  disk,  they  must have been  previously  stored in the
  special directory, i.e.,  the current directory  from which the XCOM run was
  started. 
   
  5.7.  Output Table 
   
       The  user  is  asked  by a prompt where the file with the cross section 
  table is to be stored.  The file specification can include the letter of the 
  drive,  the subdirectory,  and the file name.  If the current directory on a 
  hard  disk is to be used,  only the file name need be supplied.  If the user 
  wants  to  see the output table only on the monitor screen,  the output file 
  should  be designated as "CON".  If the user wants neither to inspect nor to 
  save  the  output table (because only the output arrays discussed in section 
  5.8 are wanted), the output file should be designated as "NUL".  
   
       On the top of each page of the table the name of the substance is given, 
  followed  by a listing of the atomic numbers and fractions by weight of  the 
  atomic  constituents.  The  main body of the  table is supplied  with enough 
  headings  to be  self-explanatory.  This left-most column gives the designa-
  tions of  the  absorption  edges  (K, L1, L2, L3, M1, M2,..) as  well as the
  atomic number Z  of the  pertinent  atomic constituent.  Data  for  energies
  immediately below and above each edge, are given on two lines separated by a 
  blank  line.  It should be noted that the standard energy grid automatically 
  includes  at  least one  other  energy between any two successive absorption 
  edges.  For  materials  of low atomic number,  there are no absorption edges 
  above 1 keV, and the column indicating the names of edges is absent.  
   
       Typical output tables are shown in Table 1 (for an element,  lead),  in 
  Table  2 (for a compound,  calcium tungstate) and in Table 3 (for a mixture, 
  pyrex glass:  0.807 SiO2, 0.129 B2O3, 0.038 Na2O, 0.022 Al2O3, and 0.004 K2O 
  by  weight).  On  the top of each page,  the name of the substance is given, 
  followed  by  a listing of the atomic numbers and fractions by weight of the 
  atomic constituents.  Fig. 1 shows some of the results from Table 2, namely, 
  the  total  mass attenuation coefficient plotted as a function of the photon 
  energy.

                         5.8 Additional Output Arrays 
   
       The cross section tables described  in Section 5.7 are directly compar-
  able in format  to printed  tables found  in the  literature,  and  are most
  convenient for visual inspection of the data.  If these  data are to be used
  in subsequent  computer  calculations,  the appropriate cross section arrays
  must be extracted for the tables.  XCOM provides an option which facilitates
  this task.
       After  the  production  of the  cross  section table  is completed, the
  program prompts the  user to indicate whether  additional output in the form
  of arrays of selected quantities is  desired.  If the answer is affirmative,
  a selection menu is presented.  The arrays which can be  selected correspond
  to the columns in the  cross section table.  After each selection, this menu
  is presented again.
       The user  is also  asked to  provide the name  of the file in which the
  additional arrays are to be stored. At the beginning of this file, preceding
  the arrays, the following information  is stored.  The first record consists
  of the name of the substance.  The second record gives  the number of atomic
  constituents,  the  third  contains a  list of atomic numbers of the consti-
  tuents and the fourth a list of fractions by weight.
       The fifth  record gives the number of  sub-arrays into which each array
  is divided, and the sixth contains the lengths of all successive sub-arrays.
  Each  sub-array  contains   data  for  all  energies  between  two  adjacent
  absorption edges.  This partitioning  facilitates the setting up of interpo-
  lation schemes in which interpolation  across  absorption edges is  avoided. 
       Subsequent records  contain, for  each of the  quantities  selected, an
  identifier (such as "energy list," "total attenuation coefficient") followed
  by one or more sub-arrays.  
   
       Even though the arrangement of the file, as described above, may appear
  somewhat complicated,  it can easily  be understood  by comparison  with the
  corresponding  output table.  A typical set of output arrays,  consisting of
  photon  energies  and  total   mass  attenuation  coefficients  for  calcium
  tungstate,  is given  Table 4.   These arrays  are the same  as the  data in
  columns 2 and 7 in Table 2, and were used to produce the plot in Fig. 1.   
   
                              Acknowledgement.   
   
       This work  was supported by the  NBS Office of Standard Reference Data,
  and by the U.S. Department of Energy (OHER). 

                                References 
   
   1.  Hubbell, J.H. and Berger, M.J., Sections 4.1 and 4.2 in Jaeger, R.G. 
       (ed.): Engineering Compendium on Radiation Shielding (IAEA, Vienna), 
       Vol. 1, Ch. 4, pp. 167-202, Springer, Berlin (1968). 
   
   2.  Hubbell, J.H., Photon Cross Sections, Attenuation Coefficients and Energy
       Absorption Coefficients  from 10 keV to 100 GeV, Natl. Stand. Ref. Data
       Ser. 29 (1969). 
   
   3.  McMaster, W.H., Del  Grande,  N.K.,Mallett,  J.H,  and  Hubbell,  J.H. 
       Compilation of  X-ray Cross  Sections, Lawrence  Livermore Lab., Report
       UCRL-50174, (1969). 
   
   4.  Storm, E. and Israel, H.I., Photon Cross Sections from 1 keV to 100 MeV 
       for Elements Z=1 to Z=100, Nucl. Data Tables A7, 565-681 (1970). 
   
   5.  Veigele, W.J., Photon Cross Sections from 0.1 keV to 1 MeV for Elements 
       Z=1 to Z=94, Atomic Data 5, 51-111 (1973). 
   
   6.  Hubbell, J.H., Photon Mass Attenuation and Mass Energy-Absorption 
       Coefficients for H,C,N,O,Ar and Seven Mixtures from 0.1 keV to 20 MeV, 
       Radiat. Res. 70, 58-81 (1977).
   
   7.  Leroux, J, and Thinh, T.P., Revised Tables of X-ray Mass Attenuation 
       Coefficients, Corporation Scientifique Classique, Quebec (1977). 
   
   8.  Hubbell, J.H.,  Gimm., H.A.,  and Overbo,  I., Pair,  Triplet and Total
       Atomic  Cross Sections (and Mass Attenuation Coefficients) for 1 MeV-100
       GeV Photons in Elements Z=1 to 100, J. Phys. Chem. Ref. Data 9, 1023-1147
       (1980). 
   
   9.  Plechaty, E.F., Cullen, D.E., and Howerton, R.J., Tables and Graphs of 
       Photon-Interaction Cross Sections from 0.1 keV to 100 MeV Derived from 
       the LLL Evaluated-Nuclear-Data Library, Report UCRL-50400, Vol. 6, 
       Rev. 3 (1981). 
   
  10.  Henke, B.L., Lee, P., Tanaka, T.J., Shimabukuro, R.L. and Fujikawa, B.K.,
       Low Energy X-ray Interaction Coefficients:  Photoabsorption, Scattering
       and Reflection, Atomic Data and Nuclear Data Tables, 27,1-144 (1982). 
   
  11.  Hubbell, J.H., Photon Mass Attenuation and Energy Absorption Coefficients
       from 1 keV to 20 MeV, Int. J. Appl. Radiation & Isotopes, 33, 1269-1290
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