NBSIR 87-3597

XCOM: Photon Cross Sections on A

Personal Computer

M. J. Berger and J. H. Hubbell

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Gaithersburg, MD 20899

July 1987

Prepared for: U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Office of Standard Reference Data

Gaithersburg, MD 20899

Department of Energy

Office of Health and Environmental Research

Washington, DC 20545

NBSIR 87-3597

XCOM: PHOTON CROSS SECTIONS ON A

PERSONAL COMPUTER

M. J. Berger and J. H. Hubbell

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Gaithersburg, MD 20899

July 1987

Prepared for: U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Office of Standard Reference Data

Gaithersburg, MD 20899

Department of Energy

Office of Health and Environmental Research

Washington, DC 20545

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

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 scattering 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 absorption there is a small difference (omission of a renormalization correction)

which is discussed below.

2
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 Comptonscattering 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 BetheHeitler 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 HartreeSlater 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

<r PAIR (E), where E is the photon energy,

E' the threshold energy for pair production, and crPAI R(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

3
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 360 kB 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 the execution of XCOM by a factor of twenty or better.

The XCOM program is distributed on two 5.25-inch 360 kB 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 XC0M.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 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.

4
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
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 CaW04.

Substances consisting of molecules with only a single species of atoms

can be designated as either 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 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 = 10~ 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

6
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 designations of the absorption edges (K, LI, L2 , L3 , Ml, 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 Si02 , 0.129 B2 03 , 0.038 Na2 0, 0.022 Al2 03 , and 0.004 K2 0

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

.

7
5.8 Additional Output Arrays

The cross section tables described in Section 5.7 are directly comparable 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 constituents 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 interpolation 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)

.

8
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,0,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

(1982).

12. Hubbell, J.H., Veigele, W.J., Briggs, E.A.

,

Brown, R.T.

,

Cromer, D.T.

,

and Howerton, R.J., Atomic Form Factors, Incoherent Scattering Functions,

and Photon Scattering Cross Sections, J. Phys. Chem. Ref. Data 4, 471-538

(1975); erratum in 6, 615-616 (1977).

9
13. Hubbell, J.H. and Overbo, Relativistic Atomic Form Factors and Photon

Coherent Scattering Cross Sections, J. Phys. Chem. Ref. Data £,

69-105, (1979).

14. Scofield, J.H., Theoretical Photolonlzatlon Cross Sections from 1 to

1500 keV, Lawrence Livermore National Laboratory Rep. UCRL-51326 (1973).

15. Pratt, R.H. , Atomic Photoelectric Effect at High Energies, Phys. Rev.

117 . 1017-1028 (1960).

16. Saloman, E.B. and Hubbell, J.H., Critical Analysis of Soft X-ray Cross

Section Data, Nucl. Instr. Meth. A255 . 38-42 (1987).

17. E.B. Saloman and J .H. Hubbell , X-ray Attenuation Coefficients (Total Cross

Sections) : Comparison of the Experimental Data Base with Recommended Values

of Henke and the Theoretical Values of Scofield for Energies between

0.1-100 keV, National Bureau of Standards Report NBSIR 86-3431 (1986).

10
APPENDIX A

C:\xOXCOM

Program XCOM (Version 1.2)

M. J. Berger, 9 MAY 1987

Enter name of substance > Lead

Options for characterization of substance:

1. Elemental substance, specified by atomic number

2. Elemental substance, specified by chemical symbol

3. Compound, specified by chemical formula

4. Mixture of elements and/or compounds

Enter desired option (1,2,3 or 4) -->1

Enter atomic number of element --> 82

Options for output quantities:

1. Cross sections in barns/atom

2. Cross sections in barns/atom, and

attenuation coefficients in cm2/g

3. Partial interaction coefficients and

attenuation coefficients in cm2/g

Enter desired option (1, 2 or 3) -->2

Options for energy list for output data:

1. Standard energy grid only

2. Standard grid plus additional energies

3 . Additional energies only

Enter option desired (1,2 or 3) -->2

Modes of entering additional energies:

1. Entry from keyboard

2 . Entry from prepared input file

Enter option desired (1 or 2) -->1

How many additional energies are wanted? -->3

Enter first energy (in MeV) -->1.33

Enter next energy (in MeV) --> 1.17

Enter next energy (in MeV) --> 0.66

Options for entry of Database files:

1. Read files from floppy-disk drive A

2. Read files from floppy-disk drive B

3. Read files from CURRENT directory on hard disk

Enter desired option (1,2, or 3) . If necessary

A-l
APPENDIX A (Continued)

insert Database Disk into floppy-disk drive

before pressing "enter" -->3

Specify file on which output (cross section table)

is to be stored. Specification can include drive and

path. If necessary, insert floppy disk into selected

drive before pressing "enter" --> OUT. 082

Cross-section table with headings has been stored on file OUT. 082

Options for further output:

1. No more output

2. Selected arrays stored on disk

Select option 1 or 2 -->1

Calculation is finished.

C : \xc>FF

A-2
APPENDIX B

C : \xc>XCOM

Program XCOM (Version 1.2)

M. J. Berger, 9 MAY 1987

Enter name of substance > Calcium Tungstate

Options for characterization of substance:

1. Elemental substance, specified by atomic number

2. Elemental substance, specified by chemical symbol

3. Compound, specified by chemical formula

4. Mixture of elements and/or compounds

Enter desired option (1,2,3 or 4) -->3

Enter chemical formula for compound --> CaW04

Options for energy list for output data:

1. Standard energy grid only

2. Standard grid plus additional energies

3 . Additional energies only

Enter option desired (1,2 or 3) -->1

Options for entry of Database files:

1. Read files from floppy-disk drive A

2. Read files from floppy-disk drive B

3. Read files from CURRENT directory on hard disk

Enter desired option (1,2, or 3). If necessary

insert Database Disk into floppy-disk drive

before pressing "enter" -->1

Specify file on which output (cross section table)

is to be stored. Specification can include drive and

path. If necessary, insert floppy disk into selected

drive before pressing "enter" --> B:0UT.CT1

Cross-section table with headings has been stored on file B:0UT.CT1

Options for further output:

1 . No more output

2. Selected arrays stored on disk

Select option 1 or 2 -->2

Specify file on which selected arrays are to be stored.

Specification can include drive and path.

If necessary, insert floppy disk into selected drive

before pressing "enter" --> B:0UT.CT2

Options for array to be stored on on disk:

0. Quit

1. Energy list

B-l
APPENDIX B (Continued)

2. Coherent scattering cross section

3. Incoherent scattering cross section

4. Photoelectric absorption cross section

5. Pair prod, cross section (atomic nucleus)

6. Pair prod, cross section (atomic electrons)

7. Total attenuation coeff.(or cross section)

8. Attenuation coeff.(or cross section)

without contribution from coherent scattering

Select option -->1

Make next selection or quit.

Options for array to be stored on on disk:

0. Quit

1. Energy list

2 . Coherent scattering cross section

3. Incoherent scattering cross section

4. Photoelectric absorption cross section

5. Pair prod, cross section (atomic nucleus)

6. Pair prod, cross section (atomic electrons)

7. Total attenuation coeff . (or cross section)

8. Attenuation coeff . (or cross section)

without contribution from coherent scattering

Select option -->7

Make next selection or quit.

Options for array to be stored on on disk:

0. Quit

1. Energy list

2. Coherent scattering cross section

3. Incoherent scattering cross section

4. Photoelectric absorption cross section

5. Pair prod, cross section (atomic nucleus)

6. Pair prod, cross section (atomic electrons)

7. Total attenuation coeff. (or cross section)

8. Attenuation coeff. (or cross section)

without contribution from coherent scattering

Select option -->0

Selected cross section arrays have been stored on file B:0UT.CT2

Calculation is finished.

C : \xc>FF

B-2
APPENDIX C

C : \xc>XCOM

Program XCOM (Version 1.2)

M. J. Berger, 9 MAY 1987

Enter name of substance > Pyrex Glass

Options for characterization of substance:

1. Elemental substance, specified by atomic number

2. Elemental substance, specified by chemical symbol

3. Compound, specified by chemical formula

4. Mixture of elements and/or compounds

Enter desired option (1,2,3 or 4) -->4

How many components in mixture? Enter number -->5

Enter chemical symbol or

Enter fraction by weight

Enter chemical symbol or

Enter fraction by weight

Enter chemical symbol or Enter fraction by weight

Enter chemical symbol or Enter fraction by weight

Enter chemical symbol or Enter fraction by weight

formula for component l--> Si02

for component l--> 0.807

formula for component 2--> B203

for component 2--> 0.129

formula for component 3--> Na20

for component 3--> 0.038

formula for component 4--> A1203

for component 4--> 0.022

formula for component 5--> K20

for component 5--> 0.004

Component Fraction

by Weight

1 0.807000 Si02

2 0.129000 B203

3 0.038000 Na20

4 0.022000 A1203

5 0.004000 K20

Sum = 1.000000

Options for accepting or rejecting composition data:

1. Accept, but let program normalize fractions

by weight so that their sum is unity

2. Reject, and enter different set of fractions

Enter desired option (1 or 2) -->1

C-l
APPENDIX C (Continued)

Options for energy list for output data:

1. Standard energy grid only

2. Standard grid plus additional energies

3. Additional energies only

Enter option desired (1,2 or 3) -->3

Modes of entering additional energies:

1. Entry from keyboard

2. Entry from prepared input file

Enter option desired (1 or 2) -->1

How many additional energies are wanted? -->5

Enter

Enter

Enter

Enter

Enter

first energy (in MeV)

next energy (in MeV)

next energy (in MeV)

next energy (in MeV)

next energy (in MeV)

-->0.0804

--> 0.2790

--> 0.6616

--> 1.3685

--> 2.7541

Options for entry of Database files:

1. Read files from floppy-disk drive A

2. Read files from floppy-disk drive B

3. Read files from CURRENT directory on hard disk

Enter desired option (1,2, or 3). If necessary

insert Database Disk into floppy- disk drive

before pressing "enter” -->3

Specify file on which output (cross section table)

is to be stored. Specification can include drive and

path. If necessary, insert floppy disk into selected

drive before pressing "enter" --> out.pyr

Cross-section table with headings has been stored on file out.pyr

Options for further output:

1. No more output

2. Selected arrays stored on disk

Select option 1 or 2 -->1

Calculation is finished.

C : \xc>ff

C-2
Table 1 Lead

Constituents (Atomic Number : Fraction by Weight)

82:1.00000

Cross Sections and Attenuation Coefficients

(Note that 1 b(arn) = 10** (-24) cm2)

PHOTON SCATTERING PHOTO- PAIR PRODUCTION

ENERGY COHERENT INCOHER. ELECTRIC IN IN

ABSORPTION NUCLEAR ELECTRON

FIELD FIELD

(MeV) (b/atom) (b/atom) (b/atom) (b/atom) (b/atom)

1 . 000E-03

1 . 500E-03

2 . 000E-03

2 . 484E-03

4.30E+03

4.13E+03

3.93E+03

3.74E+03

1.23E+00

2.27E+00

3.31E+00

4.27E+00

1.79E+06

8.07E+05

4.38E+05

2.72E+05

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

82 M5 2 . 484E-03

2 . 534E-03

2 . 586E-03

3.74E+03

3.72E+03

3.70E+03

4.27E+00

4.36E+00

4.46E+00

4.76E+05

5.63E+05

6.65E+05

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

82 M4 2 . 586E-03

3 . 000E-03

3 . 066E-03

3 . 70E+03

3.53E+03

3.51E+03

4.46E+00

5.25E+00

5.37E+00

8.39E+05

6.72E+05

6.35E+05

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

82 M3 3 . 066E-03

3 . 301E-03

3 . 554E-03

3.51E+03

3.42E+03

3.32E+03

5.37E+00

5.79E+00

6 . 24E+00

7.35E+05

6.13E+05

5 . 11E+05

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

82 M2 3 . 554E-03

3 . 699E-03

3 . 851E-03

3.32E+03

3.27E+03

3.21E+03

6 . 24E+00

6.49E+00

6.75E+00

5.42E+05

4.93E+05

4.48E+05

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

82 Ml 3 . 851E-03

4 . 000E-03

5 . 000E-03

6 . 000E-03

8 . 000E-03

1 . 000E-02

1 . 304E-02

3.21E+03

3.16E+03

2.82E+03

2.53E+03

2.06E+03

1.71E+03

1 . 32E+03

6.75E+00

7.01E+00

8.65E+00

1.02E+01

1.31E+01

1.56E+01

1.87E+01

4.67E+05

4.27E+05

2.48E+05

1.58E+05

7.66E+04

4 . 32E+04

2.17E+04

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

82 L3 1 . 304E-02

1 . 500E-02

1 . 520E-02

1 . 32E+03

1.14E+03

1.12E+03

1.87E+01

2.04E+01

2.05E+01

5.44E+04

3.72E+04

3.59E+04

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

82 L2 1 . 520E-02

1 . 553E-02

1 . 586E-02

1.12E+03

1.09E+03

1.07E+03

2.05E+01

2.08E+01

2 . 10E+01

5 . 00E+04

4.75E+04

4.51E+04

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

82 LI 1 . 586E-02

2 . 000E-02

3 . 000E-02

4 . 000E-02

5 . 000E-02

6 . 000E-02

8 . 000E-02

1.07E+03

8.04E+02

4 . 74E+02

3.17E+02

2 . 2.5E+02

1.69E+02

1.06E+02

2 . 10E+01

2.37E+01

2.83E+01

3 . 10E+01

3.26E+01

3.35E+01

3.41E+01

5.22E+04

2.89E+04

9.93E+03

4.59E+03

2.51E+03

1.52E+03

6.92E+02

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

TOTAL ATTENUATION

WITH WITHOUT

COHERENT COHERENT

SCATT. SCATT.

(cm2/g) (cm2/g)

5.21E+03 5.20E+03

2.36E+03 2.34E+03

1.29E+03 1.27E+03

8.01E+02 7.90E+02

1.40E+03 1.38E+03

1.65E+03 1.64E+03

1.94E+03 1.93E+03

2.45E+03 2.44E+03

1.96E+03 1.95E+03

1.86E+03 1.85E+03

2.15E+03 2.14E+03

1.79E+03 1.78E+03

1.50E+03 1.49E+03

1.58E+03 1.58E+03

1.44E+03 1.43E+03

1.31E+03 1.30E+03

1.37E+03 1.36E+03

1.25E+03 1.24E+03

7.30E+02 7.22E+02

4.67E+02 4.60E+02

2.29E+02 2.23E+02

1.31E+02 1 . 26E+02

6.70E+01 6.32E+01

1.62E+02 1.58E+02

1.12E+02 1.08E+02

1.08E+02 1.05E+02

1.49E+02 1.45E+02

1.41E+02 1.38E+02

1.34E+02 1.31E+02

1.55E+02 1.52E+02

8 . 64E+01 8.40E+01

3.03E+01 2.89E+01

1.44E+01 1.34E+01

8.04E+00 7.39E+00

5.02E+00 4.53E+00

2.42E+00 2 . 11E+00
Table 1 (Continued)

82 K

Lead

Constituents (Atomic Number : Fraction by Weight)

82:1.00000

Cross Sections and Attenuation Coefficients

(Note that 1 b(arn) - 10**(-24) cm2)

PHOTON SCATTERING PHOTO- PAIR PRODUCTION

ENERGY COHERENT INCOHER. ELECTRIC IN IN

ABSORPTION NUCLEAR ELECTRON

FIELD FIELD

(MeV) (b/atom) (b/atom) (b/atom) (b/atom) (b/atom)

8 . 800E-02

8 . 800E-02

1 . 000E-01

1 . 500E-01

2 . 000E-01

3 . 000E-01

4 . 000E-01

5 . 000E-01

6 . 000E-01

6 . 600E-01

8 . 000E-01

1 . 000E+00

1 . 022E+00

1 . 170E+00

1 . 250E+00

1 . 330E+00

1 . 500E+00

2 . 000E+00

2 . 044E+00

3 . 000E+00

4 . 000E+00

5 . 000E+00

6 . 000E+00

7 . 000E+00

8 . 000E+00

9 . 000E+00

1 . 000E+01

1 . 100E+01

1 . 200E+01

1 . 300E+01

1 . 400E+01

1 . 500E+01

1 . 600E+01

1 . 800E+01

2 . 000E+01

2 . 200E+01

2 . 400E+01

2 . 600E+01

2 . 800E+01

3 . 000E+01

4 . 000E+01

5 . 000E+01

6 . 000E+01

9.06E+01

9.06E+01

7.32E+01

3.61E+01

2.15E+01

1.03E+01

6.01E+00

3.93E+00

2 . 77E+00

2.31E+00

1 . 59E+00

1.03E+00

9.86E-01

7.56E-01

6.64E-01

5.88E-01

4.64E-01

2.62E-01

2.51E-01

1.17E-01

6.60E-02

4.23E-02

2 . 94E-02

2.16E-02

1 . 65E-02

1.31E-02

1 . 06E-02

8.75E-03

7.35E-03

6.27E-03

5.40E-03

4 . 71E-03

4.14E-03

3.27E-03

2.65E-03

2.19E-03

1.84E-03

1.57E-03

1 . 35E-03

1.18E-03

6.62E-04

4.24E-04

2 . 94E-04

3.42E+01

3.42E+01

3.40E+01

3 . 26E+01

3.09E+01

2.76E+01

2.51E+01

2.32E+01

2 . 15E+01

2 . 07E+01

1.90E+01

1.72E+01

1.70E+01

1.59E+01

1 . 54E+01

1.49E+01

1 . 40E+01

1 . 20E+01

1 . 18E+01

9.44E+00

7.88E+00

6 . 81E+00

6.02E+00

5.41E+00

4.92E+00

4.53E+00

4.19E+00

3.91E+00

3 . 67E+00

3.46E+00

3.27E+00

3 . 10E+00

2.96E+00

2 . 70E+00

2.49E+00

2.31E+00

2 . 16E+00

2 . 03E+00

1.92E+00

1 . 81E+00

1.44E+00

1 . 20E+00

1 . 04E+00

5.32E+02

2.52E+03

1.80E+03

6 . 24E+02

2.91E+02

1.01E+02

4.88E+01

2 . 84E+01

1.86E+01

1 . 50E+01

9.88E+00

6 . 23E+00

5.96E+00

4.56E+00

4.02E+00

3.58E+00

2.86E+00

1.73E+00

1 . 67E+00

9.05E-01

5.93E-01

4.34E-01

3.40E-01

2.79E-01

2.35E-01

2.04E-01

1.79E-01

1 . 60E-01

1.44E-01

1 . 31E-01

1.20E-01

1.11E-01

1.03E-01

9.03E-02

8.03E-02

7.22E-02

6.56E-02

6 . 01E-02

5.55E-02

5.15E-02

3 . 79E-02

2.99E-02

2.47E-02

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0 . 00E-01

0.00E-01

0.00E-01

0.00E-01

0 . 00E-01

0.00E-01

4.51E-02

1.30E-01

2.57E-01

6.22E-01

1.87E+00

1 . 99E+00

4 . 10E+00

5.89E+00

7.39E+00

8.68E+00

9.82E+00

1.08E+01

1.18E+01

1.26E+01

1 . 34E+01

1.42E+01

1.49E+01

1.55E+01

1.61E+01

1.67E+01

1 . 77E+01

1.86E+01

1 . 94E+01

2 . 02E+01

2.08E+01

2.15E+01

2.20E+01

2.44E+01

2.62E+01

2.75E+01

0 . 00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0 . 00E-01

0.00E-01

0 . 00E-01

0.00E-01

0.00E-01

0 . Q0E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0.00E-01

0 . 00E-01

3.30E-03

1.34E-02

2.67E-02

4. 10E-02

5.51E-02

6 . 88E-02

8 . 19E-02

9 . 43E-02

1.06E-01

1 . 17E-01

1.27E-01

1.37E-01

1.46E-01

1.55E-01

1.71E-01

1.86E-01

2.00E-01

2.12E-01

2 . 23E-01

2.34E-01

2.44E-01

2.84E-01

3 . 14E-01

3 . 37E-01

TOTAL ATTENUATION

WITH WITHOUT

COHERENT COHERENT

SCATT. SCATT.

(cm2/g) (cm2/g)

1.91E+00 1.65E+00

7.68E+00 7..42E+00

5.55E+00 5.34E+00

2.01E+00 1.91E+00

9.99E-01 9.36E-01

4.03E-01 3.73E-01

2.32E-01 2 . 15E-01

1.61E-01 1.50E-01

1.25E-01 1.17E-01

1.11E-01 1.04E-01

8.87E-02 8.41E-02

7 . 10E-02 6 . 80E-02

6.96E-02 6 . 68E-02

6.19E-02 5.97E-02

5.88E-02 5.68E-02

5.62E-02 5 . 45E-02

5.22E-02 5.09E-02

4.61E-02 4.53E-02

4.58E-02 4.50E-02

4.23E-02 4.20E-02

4.20E-02 4 . 18E-02

4.27E-02 4.26E-02

4 . 39E-02 4.38E-02

4.53E-02 4.52E-02

4.67E-02 4.67E-02

4.82E-02 4.82E-02

4.97E-02 4.97E-02

5.12E-02 5.11E-02

5.26E-02 5.26E-02

5 . 40E-02 5.40E-02

5.53E-02 5.53E-02

5.66E-02 5 . 66E-02

5.78E-02 5.78E-02

6.00E-02 6 . 00E-02

6.21E-02 6 . 20E-02

6.39E-02 6.39E-02

6.57E-02 6.57E-02

6.73E-02 6.73E-02

6.88E-02 6.88E-02

7.02E-02 7.02E-02

7 . 61E-02 7.61E-02

8.06E-02 8.06E-02

8.41E-02 8.41E-02
Table 1 (Continued)

Lead

Constituents (Atomic Number : Fraction by Weight)

82:1.00000

Cross Sections and Attenuation Coefficients

(Note that 1 b(arn) = 10**(-24) cm2)

SCATTERING PHOTO- PAIR PRODUCTION

COHERENT INCOHER. ELECTRIC IN IN

ABSORPTION NUCLEAR ELECTRON

FIELD FIELD

(b/atom) (b/atom) (b/atom) (b/atom) (b/atom)

PHOTON

ENERGY

(MeV)

8 . 000E+01

1.000E+02

1 . 500E+02

2 . 000E+02

3 . 000E+02

4 . 000E+02

5 . 000E+02

6 . 000E+02

8 . 000E+02

1.000E+03

1 . 500E+03

2 . 000E+03

3 . 000E+03

4.000E+03

5 . 000E+03

6 . 000E+03

8 . 000E+03

1 . 000E+04

1 . 500E+04

2 . 000E+04

3 . 000E+04

4 . 000E+04

5 . 000E+04

6 . 000E+04

8 . 000E+04

1.000E+05

1 . 65E-04

1.06E-04

4.71E-05

2.65E-05

1.18E-05

6.62E-06

4.24E-06

2.94E-06

1.66E-06

1.06E-06

4.71E-07

2.65E-07

1.18E-07

6.62E-08

4.24E-08

2.94E-08

1.66E-08

1.06E-08

4.71E-09

2.65E-09

1.18E-09

6.62E-10

4.24E-10

2.94E-10

1.66E-10

1.06E-10

8.18E-01

6 . 79E-01

4.83E-01

3.79E-01

2.69E-0I

2 . 10E-01

1.74E-01

1.49E-01

1.16E-01

9.58E-02

6.69E-02

5.18E-02

3 . 60E-02

2.78E-02

2.27E-02

1.93E-02

1.48E-02

1.21E-02

8 . 38E-03

6.44E-03

4.44E-03

3.41E-03

2.78E-03

2.35E-03

1.80E-03

1.46E-03

1.84E-02

1 . 46E-02

9.66E-03

7.21E-03

4.79E-03

3.58E-03

2 . 86E-03

2.38E-03

1.79E-03

1.43E-03

9.51E-04

7.13E-04

4.75E-04

3.56E-04

2.85E-04

2.38E-04

1.78E-04

1.42E-04

9.50E-05

7.12E-05

4 . 75E-05

3.56E-05

2.85E-05

2.37E-05

1.78E-05

1 . 42E-05

2.95E+01

3.09E+01

3.32E+01

3.45E+01

3.60E+01

3.69E+01

3 . 75E+01

3.79E+01

3 . 84E+01

3.88E+01

3.93E+01

3.96E+01

3.99E+01

4.00E+01

4.01E+01

4.02E+01

4.03E+01

4.03E+01

4.04E+01

4.05E+01

4.05E+01

4.05E+01

4.O5E+01

4.06E+01

4.06E+01

4.06E+01

3.73E-01

3.98E-01

4.40E-01

4.65E-01

4.96E-01

5.15E-01

5.27E-01

5.36E-01

5.49E-01

5.57E-01

5.69E-01

5.76E-01

5.84E-01

5 . 88E-01

5 . 91E-01

5.93E-01

5.95E-01

5.97E-01

5.99E-01

6.00E-01

6.01E-01

6 . 02E-01

6.03E-01

6.03E-01

6.03E-01

6 . 03E-01

TOTAL ATTENUATION

WITH WITHOUT

COHERENT COHERENT

SCATT. SCATT.

(cm2/g) (cm2/g)

8.93E-02 8.93E-02

9.31E-02 9.31E-02

9.91E-02 9.91E-02

1.03E-01 1.03E-01

1.07E-01 1.07E-01

1.09E-01 1.09E-01

1.11E-01 1.11E-01

1.12E-01 1.12E-01

1.14E-01 1.14E-01

1.15E-01 1.15E-01

1.16E-01 1.16E-01

1.17E-01 1.17E-01

1.18E-01 1.18E-01

1.18E-01 1.18E-01

1.18E-01 1.18E-01

1.19E-01 1.19E-01

1.19E-01 1.19E-01

1.19E-01 1.19E-01

1.19E-01 1.19E-01

1.19E-01 1.19E-01

1.20E-01 1.20E-01

1.20E-0I 1.20E-01

1.20E-01 1.20E-01

1.20E-01 1.20E-01

1.20E-01 1.20E-01

1.20E-01 1.20E-01
Calcium Tungstate

Table 2

Constituents (Atomic Number : Fraction by Weight)

8:0.22227 20:0.13920 74:0.63853

Partial Interaction Coefficients and Total Attenuation Coefficients

PHOTON SCATTERING PHOTO- PAIR PRODUCTION TOTAL ATTENUATION

ENERGY COHERENT INCOHER. ELECTRIC IN IN WITH WITHOUT

ABSORPTION NUCLEAR ELECTRON COHERENT COHERENT

FIELD FIELD SCATT. SCATT.

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

1 . 000E-03 8 . 14E+00 6.74E-03 4.04E+03 0.00E-01 0.00E-01 4.05E+03 4.04E+03

1 . 500E-03 7.76E+00 1.20E-02 1.62E+03 0.00E-01 0.00E-01 1.63E+03 1.62E+03

1 . 809E-03 7 . 51E+00 1.53E-02 1.05E+03 0.00E-01 0.00E-01 1.06E+03 1.05E+03

74 M5 1 . 809E-03 7.51E+00 1.53E-02 1.18E+03 0.00E-01 0.00E-01 1.19E+03 1.18E+03

1 . 840E-03 7.49E+00 1.56E-02 1.57E+03 0.00E-01 0.00E-01 1.57E+03 1.57E+03

1 . 872E-03 7.46E+00 1.60E-02 2.14E+03 0.00E-01 0.00E-01 2.15E+03 2.14E+03

74 M4 1 . 872E-03 7 . 46E+00 1.60E-02 2 . 31E+03 0.00E-01 0.00E-01 2.31E+03 2 . 31E+03

2 . 000E-03 7.35E+00 1.74E-02 2.76E+03 0.00E-01 0.00E-01 2.77E+03 2.76E+03

2 . 281E-03 7.12E+00 2.04E-02 1.98E+03 0.00E-01 0.00E-01 1.99E+03 1.98E+03

74 M3 2 . 281E-03 7.12E+00 2.04E-02 2.27E+03 0.00E-01 0.00E-01 2.28E+03 2.27E+03

2.423E-03 7.00E+00 2.19E-02 1.96E+03 0.00E-01 0.00E-01 1.96E+03 1.96E+03

2 . 575E-03 6.89E+00 2.35E-02 1.69E+03 0.00E-01 0.00E-01 1.69E+03 1.69E+03

74 M2 2 . 575E-03 6.89E+00 2.35E-02 1.78E+03 0.00E-01 0 . 00E-01 1.79E+03 1.78E+03

2 . 694E-03 6.79E+00 2.48E-02 1.60E+03 0.00E-01 0.00E-01 1.61E+03 1.60E+03

2 . 820E-03 6.69E+00 2.61E-02 1 . 44E+03 0.00E-01 0.00E-01 1.45E+03 1.44E+03

74 Ml 2 . 820E-03 6.69E+00 2.61E-02 1.50E+03 0.00E-01 0.00E-01 1.50E+03 1.50E+03

3 . 000E-03 6 . 54E+00 2.80E-02 1.29E+03 0.00E-01 0.00E-01 1.30E+03 1.29E+03

4 . 000E-03 5.80E+00 3.77E-02 6.42E+02 0.00E-01 0.00E-01 6.48E+02 6.43E+02

4 . 038E-03 5 . 78E+00 3.80E-02 6.28E+02 0.00E-01 0.00E-01 6.33E+02 6.28E+02

20 K 4 . 038E-03 5.78E+00 3.80E-02 7.53E+02 0.00E-01 0.00E-01 7.59E+02 7 . 53E+02

5 . 000E-03 5.15E+00 4.62E-02 4.43E+02 0.00E-01 0.00E-01 4.48E+02 4.43E+02

6 . 000E-03 4.59E+00 5.35E-02 2.78E+02 0.00E-01 0.00E-01 2.82E+02 2.78E+02

8 . 000E-03 3.69E+00 6.50E-02 1.32E+02 0.00E-01 0.00E-01 1.35E+02 1 . 32E+02

1 . 000E-02 3.02E+00 7 . 36E-02 7 . 31E+01 0.00E-01 0.00E-01 7.62E+01 7.32E+01

1 . 021E-02 2.96E+00 7.44E-02 6.92E+01 0.00E-01 0.00E-01 7.23E+01 6 . 93E+01

74 L3 1 . 021E-02 2.96E+00 7.44E-02 1 . 60E+02 0.00E-01 0.00E-01 1.63E+02 1.60E+02

1 . 085E-02 2.79E+00 7.67E-02 1.35E+02 0.00E-01 0.00E-01 1.38E+02 1 . 35E+02

1 . 154E-02 2.62E+00 7.91E-02 1.15E+02 0.00E-01 0.00E-01 1.17E+02 1.15E+02

74 L2 1 . 154E-02 2.62E+00 7.91E-02 1.55E+02 0.00E-01 0.00E-01 1 . 57E+02 1.55E+02

1 . 182E-02 2.56E+00 7.99E-02 1.46E+02 0.00E-01 0.00E-01 1.48E+02 1.46E+02

1 . 210E-02 2.49E+00 8.08E-02 1.38E+02 0.00E-01 0.00E-01 1.40E+02 1.38E+02

74 LI 1 . 210E-02 2.49E+00 8.08E-02 1.58E+02 0.00E-01 0.00E-01 1.60E+02 1 . 58E+02

1 . 500E-02 1.95E+00 8.87E-02 9.12E+01 0 . 00E-01 0.00E-01 9.32E+01 9.13E+01

2 . 000E-02 1.38E+00 9.89E-02 4.25E+01 0.00E-01 0.00E-01 4.40E+01 4.26E+01

3 . 000E-02 8.09E-01 1.11E-01 1.42E+01 0.00E-01 0.00E-01 1.52E+01 1.44E+01
Table 2 (Continued)

74 K

Calcium Tungstate

Constituents (Atomic Number : Fraction by Weight)

8:0.22227 20:0.13920 74:0.63853

Partial Interaction Coefficients and Total Attenuation Coefficients

PHOTON SCATTERING PHOTO- PAIR PRODUCTION TOTAL ATTENUATION

ENERGY COHERENT INCOHER. ELECTRIC IN IN WITH WITHOUT

ABSORPTION NUCLEAR ELECTRON COHERENT COHERENT

FIELD FIELD SCATT. SCATT

.

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

4 . 000E-02 5.32E-01 1.17E-01 6.48E+00 0.00E-01 0 . 00E-01 7 . 12E+00 6.59E+00

5 . 000E-02 3.76E-01 1.19E-01 3.49E+00 0.00E-01 0.00E-01 3.99E+00 3.61E+00

6 . 000E-02 2.81E-01 1.20E-01 2 . 10E+00 0.00E-01 0.00E-01 2 . 50E+00 2 . 22E+00

6 . 953E-02 2.22E-01 1.20E-01 1 . 39E+00 0.00E-01 0.00E-01 1 . 74E+00 1.51E+00

6 . 953E-02 2.22E-01 1.20E-01 6 . 94E+00 0.00E-01 0.00E-01 7.28E+00 7 . 06E+00

8 . 000E-02 1.76E-01 1.20E-01 4.78E+00 0.00E-01 0.00E-01 5.07E+00 4.90E+00

1 . 000E-01 1.21E-01 1.17E-01 2.67E+00 0.00E-01 0.00E-01 2 . 90E+00 2.78E+00

1 . 500E-01 5.90E-02 1 . 10E-01 8.94E-01 0.00E-01 0.00E-01 1.06E+00 1 . 00E+00

2 . 000E-01 3.51E-02 1.02E-01 4.10E-01 0.00E-01 0.00E-01 5.48E-01 5.12E-01

3 . 000E-01 1.67E-02 9.07E-02 1.39E-01 0.00E-01 0.00E-01 2.46E-01 2.29E-01

4. 000E-01 9.68E-03 8 . 20E-02 6.61E-02 0.00E-01 0.00E-01 1.58E-01 1.48E-01

5 . 000E-01 6.31E-03 7.52E-02 3.82E-02 0.00E-01 0.00E-01 1.20E-01 1.13E-01

6 . 000E-01 4.44E-03 6.98E-02 2.48E-02 0.00E-01 0.00E-01 9.91E-02 9.46E-02

8 . 000E-01 2.54E-03 6.16E-02 1.31E-02 0.00E-01 0.00E-01 7.72E-02 7.46E-02

1.000E+00 1.64E-03 5.55E-02 8.21E-03 0.00E-01 0.00E-01 6.53E-02 6.37E-02

1 . 022E+00 1.57E-03 5.49E-02 7.86E-03 0.00E-01 0.00E-01 6.43E-02 6.27E-02

1 . 250E+00 1.06E-03 4.96E-02 5.30E-03 2.18E-04 0.00E-01 5.62E-02 5.52E-02

1 . 500E+00 7.36E-04 4.52E-02 3.78E-03 1.03E-03 0.00E-01 5.07E-02 5.00E-02

2 . 000E+00 4.16E-04 3.86E-02 2.29E-03 3.24E-03 0.00E-01 4.45E-02 4.41E-02

2 . 044E+00 3.98E-04 3.81E-02 2.21E-03 3.44E-03 0.00E-01 4.41E-02 4.37E-02

3 . 000E+00 1.85E-04 3.04E-02 1.20E-03 7.51E-03 1.06E-05 3.93E-02 3.91E-02

4 . 000E+00 1.04E-04 2.53E-02 7.88E-04 1.11E-02 4.33E-05 3.74E-02 3.73E-02

5 . 000E+00 6.69E-05 2.19E-02 5.79E-04 1.42E-02 8.62E-05 3.68E-02 3.67E-02

6 . 000E+00 4.65E-05 1.93E-02 4.55E-04 1.68E-02 1.32E-04 3.68E-02 3.67E-02

7 . 000E+00 3.41E-05 1.74E-02 3.73E-04 1.91E-02 1.78E-04 3.71E-02 3.71E-02

8 . 000E+00 2.61E-05 1.58E-02 3.15E-04 2.12E-02 2.23E-04 3.76E-02 3.76E-02

9 . 000E+00 2.07E-05 1.45E-02 2.73E-04 2.31E-02 2.65E-04 3.82E-02 3.82E-02

1 . 000E+01 1.67E-05 1.35E-02 2.40E-04 2.49E-02 3.05E-04 3.89E-02 3.89E-02

1.100E+01 1.38E-05 1.26E-02 2.14E-04 2.65E-02 3.44E-04 3.96E-02 3.96E-02

1 . 200E+01 1.16E-05 1.18E-02 1.93E-04 2.80E-02 3.80E-04 4.04E-02 4.03E-02

1 . 300E+01 9.90E-06 1.11E-02 1.76E-04 2.94E-02 4.14E-04 4.11E-02 4.11E-02

1.400E+01 8.54E-06 1.05E-02 1.62E-04 3.07E-02 4.46E-04 4.18E-02 4.18E-02

1 . 500E+01 7.44E-06 9.98E-03 1.49E-04 3.19E-02 4.76E-04 4.25E-02 4.25E-02

1 . 600E+01 6.54E-06 9.50E-03 1.39E-04 3.30E-02 5.06E-04 4.32E-02 4.32E-02

1 . 800E+01 5.17E-06 8.68E-03 1.22E-04 3.51E-02 5.60E-04 4.44E-02 4.44E-02

2 . 000E+01 4.18E-06 8 . 01E-03 1.08E-04 3.69E-02 6.09E-04 4.56E-02 4.56E-02

2 . 200E+01 3.46E-06 7.44E-03 9.73E-05 3.85E-02 6.54E-04 4.67E-02 4.67E-02

2 . 400E+01 2.91E-06 6.95E-03 8.85E-05 4.00E-02 6.95E-04 4.78E-02 4.78E-02

2 . 600E+01 2.48E-06 6.53E-03 8.11E-05 4.14E-02 7.33E-04 4.87E-02 4.87E-02

2 . 800E+01 2.13E-06 6.16E-03 7.48E-05 4.27E-02 7.69E-04 4.97E-02 4.97E-02

3 . 000E+01 1.86E-06 5.83E-03 6.95E-05 4.38E-02 8.02E-04 5.05E-02 5.05E-02

4 . 000E+01 1.05E-06 4.63E-03 5 . 11E-05 4.86E-02 9.39E-04 5.42E-02 5.42E-02

5 . 000E+01 6.70E-07 3.87E-03 4.04E-05 5.21E-02 1.04E-03 5.71E-02 5.71E-02
Table 2 (Continued)

Calcium Tungstate

Constituents (Atomic Number : Fraction by Weight)

8:0.22227 20:0.13920 74:0.63853

Partial Interaction Coefficients and Total Attenuation

SCATTERING PHOTO

COHERENT INC0HER. ELECTRIC

ABSORPTION

(cm2/g) (cm2/g) (cm2/g)

PAIR PRODUCTION

IN IN

NUCLEAR ELECTRON

FIELD FIELD

(cm2/g) (cm2/g)

PHOTON

ENERGY

(MeV)

6 . 000E+01

8 . 000E+01

1 . 000E+02

1 . 500E+02

2 . 000E+02

3 . 000E+02

4 . 000E+02

5 . 000E+02

6 . 000E+02

8 . 000E+02

1 . 000E+03

1 . 500E+03

2 . 000E+03

3 . 000E+03

4 . 000E+03

5 . 000E+03

6 . 000E+03

8 . 000E+03

1 . 000E+04

1 . 500E+04

2 . 000E+04

3 . 000E+04

4 . 000E+04

5 . 000E+04

6 . 000E+04

8 . 000E+04

1 . 000E+05

4.65E-07

2 . 61E-07

1.67E-07

7.44E-08

4.18E-08

1.86E-08

1.05E-08

6.70E-09

4.65E-09

2.61E-09

1.67E-09

7.44E-10

4.18E-10

1.86E-10

1.05E-10

6.70E-11

4.65E-11

2.61E-11

1.67E-11

7.44E-12

4.18E-12

1 . 86E-12

1.05E-12

6.70E-13

4. 65E-13

2.61E-13

1.67E-13

3.33E-03

2.63E-03

2.18E-03

1.55E-03

1.22E-03

8.63E-04

6.76E-04

5.60E-04

4.79E-04

3.74E-04

3.08E-04

2.15E-04

1.66E-04

1.16E-04

8.93E-05

7.30E-05

6.19E-05

4.77E-05

3.90E-05

2.69E-05

2.07E-05

1.43E-05

1 . 10E-05

8.92E-06

7.54E-06

5.78E-06

4.70E-06

3.34E-05

2 . 48E-05

1.97E-05

1.31E-05

9.76E-06

6.48E-06

4.85E-06

3.87E-06

3.23E-06

2.42E-06

1.93E-06

1 . 29E-06

9.65E-07

6.43E-07

4.82E-07

3.86E-07

3.21E-07

2.41E-07

1 . 93E-07

1.29E-07

9.64E-08

6.43E-08

4.82E-08

3.86E-08

3.21E-08

2.41E-08

1.93E-08

5.49E-02

5.89E-02

6.18E-02

6.63E-02

6.90E-02

7.22E-02

7.40E-02

7.52E-02

7.60E-02

7.72E-02

7.79E-02

7.90E-02

7 . 95E-02

8.02E-02

8.05E-02

8.07E-02

8.09E-02

8 . 11E-02

8.12E-02

8 . 14E-02

8.15E-02

8.15E-02

8.16E-02

8.16E-02

8.16E-02

8.17E-02

8.17E-02

1.13E-03

1 . 25E-03

1.34E-03

1.50E-03

1.60E-03

1.72E-03

1.79E-03

1.84E-03

1.88E-03

1.93E-03

1 . 97E-03

2.02E-03

2.05E-03

2.08E-03

2.10E-03

2 . 11E-03

2.12E-03

2.13E-03

2.14E-03

2 . 15E-03

2.15E-03

2.16E-03

2.16E-03

2.16E-03

2 . 16E-03

2 . 16E-03

2.16E-03

Coefficients

TOTAL ATTENUATION

WITH WITHOUT

COHERENT COHERENT

SCATT. SCATT.

(cm2/g) (cm2/g)

5 . 94E-02 5 . 94E-02

6.28E-02 6 . 28E-02

6.53E-02 6.53E-02

6 . 94E-02 6.94E-02

7.19E-02 7.19E-02

7.48E-02 7 . 48E-02

7.65E-02 7.65E-02

7.76E-02 7.76E-02

7.84E-02 7.84E-02

7 . 95E-02 7.95E-02

8.02E-02 8.02E-02

8.12E-02 8.12E-02

8.18E-02 8.18E-02

8 . 24E-02 8 . 24E-02

8.27E-02 8.27E-02

8.29E-02 8.29E-02

8.30E-02 8 . 30E-02

8 . 32E-02 8 . 32E-02

8.34E-02 8.34E-02

8.35E-02 8.35E-02

8 . 36E-02 8 . 36E-02

8.37E-02 8.37E-02

8.37E-02 8.37E-02

8.38E-02 8.38E-02

8.38E-02 8.38E-02

8.38E-02 8.38E-02

8.38E-02 8.38E-02
Table 3

Pyrex Glass

Constituents (Atomic Number : Fraction by Weight)

5:0.04006 8:0.53956 11:0.02819 13:0.01164 14:0.37722 19:0.00332

Partial Interaction Coefficients and Total Attenuation Coefficients

PHOTON SCATTERING PHOTO

ENERGY COHERENT INCOHER. ELECTRIC

ABSORPTION

(MeV) (cm2/g) (cm2/g) (cm2/g)

PAIR PRODUCTION TOTAL ATTENUATION

IN IN WITH WITHOUT

NUCLEAR ELECTRON COHERENT COHERENT

FIELD FIELD SCATT. SCATT.

(cm2/g) (cm2/g) (cm2/g) (cm2/g)

8 . 040E-02 1.45E-02

2 . 790E-01 1.32E-03

6 . 616E-01 2.38E-04

1 . 368E+00 5.56E-05

2 . 754E+00 1.37E-05

1 . 50E-01 2.40E-02

1.08E-01 4.61E-04

7.67E-02 4.24E-05

5.40E-02 9.30E-06

3.64E-02 3.07E-06

0.00E-01 0.00E-01

0.00E-01 0.00E-01

0.00E-01 0.00E-01

6 . 87E-05 0.00E-01

1.32E-03 6.17E-06

1.88E-01 1.74E-01

1.10E-01 1.09E-01

7.69E-02 7.67E-02

5.41E-02 5.40E-02

3.77E-02 3.77E-02
Table 4

Calcium Tungstate

3

8 20 74

0.222271 0.139196 0.638533

11

3 3 3 3 3 4 6 3 3 8 66

ENERGY LIST

1 . 0000E-03 1 . 5000E-03 1 . 8092E-03

1 . 8092E-03 1 . 8401E-03 1 . 8716E-03

1 . 8716E-03 2 . 0000E-03 2.2810E-03

2 . 2810E-03 2.4235E-03 2 . 5749E-03

2 . 5749E-03 2 . 6945E-03 2 . 8196E-03

2 . 8196E-03 3 . 0000E-03 4.0000E-03 4.0381E-03

4 . 0381E-03 5 . 0000E-03 6 . 0000E-03 8.0000E-03 1 . 0000E-02 1 . 0207E-02

1 . 0207E-02 1 . 0855E-02 1 . 1544E-02

1 . 1544E-02 1 . 1819E-02 1 . 2100E-02

1 . 2100E-02 1 . 5000E-02 2 . 0000E-02 3 . 0000E-02 4.0000E-02 5 . 0000E-02

6 . 0000E-02 6 . 9525E-02

6 . 9525E-02 8 . 0000E-02 1 . 0000E-01 1 . 5000E-01 2 . 0000E-01 3 . 0000E-01

4 . 0000E-01 5 . 0000E-01 6 . 0000E-01 8 . 0000E-01 1 . 0000E+00 1 . 0220E+00

1 . 2500E+00 1 . 5000E+00 2 . 0000E+00 2 . 0440E+00 3 . 0000E+00 4 . 0000E+00

5 . 0000E+00 6 . 0000E+00 7 . 0000E+00 8 . 0000E+00 9 . 0000E+00 1 . 0000E+01

1 . 1000E+01 1 . 2000E+01 1 . 3000E+01 1.4000E+01 1 . 5000E+01 1 . 6000E+01

1 . 8000E+01 2 . 0000E+01 2 . 2000E+01 2 . 4000E+01 2 . 6000E+01 2 . 8000E+01

3.0000E+01 4 . 0000E+01 5 . 0000E+01 6 . 0000E+01 8 . 0000E+01 1.0000E+02

1 . 5000E+02 2 . 0000E+02 3 . 0000E+02 4 . 0000E+02 5 . 0000E+02 6 . 0000E+02

8 . 0000E+02 1 . 0000E+03 1 . 5000E+03 2 . 0000E+03 3 . 0000E+03 4.0000E+03

5 . 0000E+03 6 . 0000E+03 8 . 0000E+03 1 . 0000E+04 1 . 5000E+04 2 . 0000E+04

3 . 0000E+04 4.0000E+04 5 . 0000E+04 6 . 0000E+04 8 . 0000E+04 1 . 0000E+05

TOTAL ATTENUATION COEFFICIENT

4 . 0495E+03 1 . 6322E+03 1 . 0575E+03

1 . 1899E+03 1 . 5735E+03 2 . 1483E+03

2 . 3131E+03 2 . 7698E+03 1 . 9900E+03

2 . 2784E+03 1 . 9638E+03 1 . 6929E+03

1 . 7908E+03 1 . 6087E+03 1.4450E+03

1 . 5028E+03 1 . 3000E+03 6.4832E+02 6 . 3335E+02

7 . 5927E+02 4.4777E+02 2 . 8242E+02 1 . 3550E+02 7 . 6199E+01 7 . 2272E+01

1 . 6254E+02 1 . 3812E+02 1 . 1740E+02

1 . 5720E+02 1.4848E+02 1 .4025E+02

1 . 6045E+02 9 . 3237E+01 4. 3974E+01 1 . 5165E+01 7 . 1246E+00 3 . 9886E+00

2 . 5046E+00 1 . 7354E+00

7 . 2791E+00 5 . 0744E+00 2 . 9034E+00 1 . 0632E+00 5.4755E-01 2 . 4607E-01

1 . 5778E-01 1 . 1972E-01 9 . 9070E-02 7 . 7172E-02 6 . 5311E-02 6.4292E-02

5 . 6217E-02 5 . 0699E-02 4.4515E-02 4.4146E-02 3 . 9276E-02 3 . 7398E-02

3 . 6786E-02 3 . 6783E-02 3 . 7104E-02 3 . 7611E-02 3 . 8230E-02 3 . 8907E-02

3 . 9614E-02 4 . 0351E-02 4. 1069E-02 4. 1799E-02 4. 2480E-02 4. 3170E-02

4 . 4424E-02 4 . 5603E-02 4. 6722E-02 4. 7776E-02 4. 8749E-02 4. 9680E-02

5 . 0533E-02 5.4205E-02 5 . 7067E-02 5 . 9353E-02 6 . 2822E-02 6 . 5323E-02

6 . 9396E-02 7 . 1870E-02 7.4778E-02 7 . 6484E-02 7 . 7604E-02 7 . 8402E-02

7 . 9486E-02 8 . 0195E-02 8 . 1200E-02 8 . 1753E-02 8 . 2377E-02 8 . 2695E-02

8 . 2911E-02 8 . 3036E-02 8 . 3232E-02 8 . 3353E-02 8 . 3525E-02 8 . 3623E-02

8 . 3700E-02 8 . 3749E-02 8 . 3795E-02 8 . 3798E-02 8 . 3845E-02 8 . 3847E-02
CALCIUM

TUNGSTATE

irO L ^OL ^0 L [01 0 Ol i ~~ 0 ^ g— 0 L 6/jUjo ‘J.N3I0IJJ300 NOIlVnN311V

Fig. 1. Total Mass attenuation coefficient for calcium tungstate

PHOTON

ENERGY,

MeV
U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. BIBLIOGRAPHIC DATA

REPORT NO.

SHEET (See instructions) NBSIR 87-3597

3. Publication Date JULY 1987

4. TITLE AND SUBTITLE

XCOM: Photon Cross Sections on a Personal Computer

5. AUTHOR(S)

M. J. Berger and J. H. Hubbell

6. PERFORMING ORGANIZATION (If Joint or other than NBS, see Instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

I. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City , State, ZIP)

10. SUPPLEMENTARY NOTES

~| Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

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.

—

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

attenuation coefficient; computer program; pair production; photoelectric

absorption; photons; scattering

13. AVAILABILITY

fXl Unlimited

| | For Official Distribution. Do Not Release to NTIS

f | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

[X] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

28

15. Price

$11.95

USCOMM-DC 6O43-P80