PHOTON CROSS SECTIONS FOR ENDF/B-VI*

Transcription

1 CONF TI PHOTON CROSS SECTIONS FOR ENDF/B-VI* D. K. Trubey Radiation Shielding Information Center Oak Ridge National Laboratory P.O. Box 2008 Oak Ridge, TN M. J. Berger and J. H. Hubbell Center for Radiation Research National Institute of Standards and Technology Gaithersburg, MD to be presented to Advances in Nuclear Computation and Radiation Shielding American Nuclear Society Topical Meeting April 9-13, 1989 Santa Fe, New Mexico "The submitted manuscript ha* been authored by a contractor of the U.S. Government under contract DE- AC05-84OR2H00. Accordingly, the U.S. Gc ernment retains a nonexclusive royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes." DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus 1, moduct, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade'name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. MASTER * Research sponsored by the Office of Fusion Energy, U.S. Department of Energy, under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc. OF TH!«i -v "T!5 UNLIMITED

2 PHOTON CROSS SECTIONS FOR ENDF/B-VI D. K. Trubey Radiation Shielding Information Center Oak Ridge National Laboratory P.O. Box 2008 Oak Ridge, TN M. J. Berger and J. H. Hubbell Center for Radiation Research National Institute of Standards and Technology Gaithersburg, MD ABSTRACT The PHOTX library of the National Institute of Standards and Technology will be used as the basis of File 23 (photon cross sections) for ENDF/B-VI. The PHOTX library is based on an experimental data base consisting of data points from 512 literature sources for 82 elements. An important difference from earlier compilations is that renormalization of photo-effect cross sections is not performed. INTRODUCTION The photon cross sections in the ENDF/B-V library are from the DLC-99/HUGO 3 library available from the Radiation Shielding Information Center ai Oak Ridge National Laboratory. This library was developed in A new computer-readable library, called DLC-136/PHOTX, 2 was recently developed at the National Institute of Standards and Technology (NIST), and it is planned to make this the basis of the data for ENDF/B-VI. It is planned to revise only ENDF file 23 (cross sections) and carry over file 27 (coherent scattering form factors and incoherent scattering functions) from ENDF/B-V. The PHOTX library is an extensive database of cross sections for all elements over a wide range of energies. The data include 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 nucleus and in the field of the atomic electrons. For use in transport applications, the free-elect ion Compton cross sections are also included. EXPERIMENTAL DATA BASE The National Bureau of Standards (now NIST) has for over three decades, starting with the work of Grodstein 3 ' 4 under the direction of Fano, supplied photon cross-section and

3 attenuation coefficient data in the x-ray and gamma-ray energy region to diverse medical, industrial, and scientific communities. These tables, including the 1969 widely circulated report 5 NSRDS-NBS 29, are based on evaluations of experimental and theoretical data from the literature, supplemented by some interpolative and original developments at NBS to fill in existing gaps in the available information. As a result of these tables, the NBS became a national and international clearing-house for information on photon cross-section data and applications. This activity was identified and supported by the NBS Office of Standard Reference Data commencing in 1963 as the NBS "X-Ray Attenuation Coefficient Information Center" and continues presently as one of the functions of the NIST "Photon and Charged-Particle Data Center." As recently described by Saloman, Hubbell, and Berger, 6 this Data Center abstracts from the literature and maintains a computerized data base of experimental photon total attenuation coefficients. This collection has been periodically indexed 7 ' 8 and now consists of data points from 512 independent literature sources, spanning the photon energy range 10 ev to 13.5 GeV for 82 elements. Figure 1 summarizes the chronology of production of these papers, starting in 1907, with the decade still incomplete. The measurement techniques which have contributed to this data base vary greatly, depending on the photon energy region and the absorber substance. COMPARISONS OF SCOFIELD THEORETICAL PHOTOEFFECT DATA WITH THE EXPERIMENTAL DATA BASE AND WITH THE 1982 HENKE ET AL. RECOMMENDED VALUES For low-energy x-rays, the total attenuation coefficient, or total interaction cross section, is dominated by the atomic photoeffect, particularly for medium and high-z elements. The NBS present compilations rely on the theoretical photoeffect cross sections calculated by Scofield 9 ' 10 using a relativistic Hartree-Slater model. Scofield 9 provided numerical factors for all subshells for Z 2 to 54 to renormalize his results to the Hartree-Fock model. Although this renormalization was implemented and used in two NBS compilations, 1 lilj recent computerized numerical and graphical comparisons 13 " 15 with the experimental data base tend to favor the use of the Scofield theoretical data without this renormalization. Graphs from references 14 and 15 are shown in Figures 2 and 3 for 0, Si, Xe, and U, including, below 10 kev. the photoabsorption cross sections recommended by Henke et a/. 1G In Figure 4 the percent differences for Si between measurement and the theoretical compilation in the region 1 to 100 kev are shown. This discrepancy for Si is one of the subjects of study of an International Union of Crystallagraphy task group 17 and is conjectured to l>n attributable to use of the theoretical coherent (Rayleigh) scattering for compositing the total attenuation coefficient, whereas the much-reduced thermal diffu.se scattering cross section may be more appropriate for this particular substance. Figure 4 also indicates a gap in Si measurements in the NBS data base extending from 0.6 to 6.0 kev including the K-edge energy 1.84 kev. This gap will be largely filled in by new Si measurements from 0.75 to 2.24 kev by N. K. Del Grande. 18 In Figure 3 the discrepancy between the Scofield U data 100 to 500 ev and the measured and Henke data can be attributed, according to N. K. Del Grande, to a 40% error in

4 measurements at higher energy by Roof 19 which in turn affected the normalization of the measurements by Cukier et a/ to 442 ev shown here as open triangles. INCOHERENT (COMPTON) AND COHERENT (RAYLEIGH) SCATTERING Although for many computational purposes incoherent scattering can be described by the free-electron Klein-Nishina formula, present compilations, including NBS, include electron binding effects in terms of the incoherent scattering function S(x, Z). This function is applied as a multiplicative correction to the Klein-Nishina differential expression prior to integration. The momentum transfer variable x for incoherent scattering, according to Grodstein 4 is 2ksm(0/2)y/l + (k 2 +2k)sin l (6/2) [I + 2fcsin(0/2)J where k is the incident photo energy in me 1 units and 8 is the photon deflection angle. Comparisons of S(x,Z) measurements with theoretical non-relativistic S(x,Z) values 21 compiled and extrapolated from calculations by Cromer et a/., 22 ' 23 are shown for Al, Cu, and Pb in Figures 5-7. Integrated incoherent scattering cross sections are shown in Figure 8 as a function of Z, including also values based on the Thomas-Fermi (TF) and the low-z configurationinteraction calculations by Brown. 24 At 1 kev the atomic shell-filling effects are evident. Coherent scattering is sometimes neglected in transport calculations and other applications, but can contribute as much as 10% to the total attenuation coefficient just below absorption edges, and sometimes well-above edges, such as in Si as mentioned earlier. Present compilations obtain this cross section by modifying the classical Thomson scattering differential expression by multiplying by the square of the atomic form factor F(x, Z). The momentum transfer variable for F(x, Z) is simpler than for S(x, Z), in this case z coh =2fcsm(0/2) (2) since the deflected photon energy loss is negligible. Figure 9 shows F(x, Z) for H and H2 as compiled and extrapolated in reference 21 from various sources. Figure 10 shows a comparison for Be between measurements and the Brown 24 ' 25 configuration-interaction and Thomas-Fermi theoretical results. Figure 11 compares F(x, Z) measurements of Mg at different temperatures with the Cromer 2 "' 2 ' theoretical values listed in reference 21.

5 Integrated coherent scattering cross sections are shown in Figure 12 as a function of Z for incident (and deflected) photon energies of 1, 10, 100, and 1000 kev. The Thomas-Fermi statistical model, used in earlier compilations, 3 " 5 is seen to be a good approximation except for the lowest Z elements. Although the non-relativistic S(x, Z) tabulations in reference 21 are still the recommended set for present compilations, two further sets of F(x,Z) have become available. 28>2f ' However, comparisons of the fully relativistic F(x, Z) of Hubbell and 0verb0, 28 extending the work of Doyle and Turner 30 and Cromer et a/. 31 with measurements suggest that the non-relativistic values in reference 21, due to compensating errors, are more realistic. The modified relativistic form factors by Schaupp et a/., 29 should be better, but have not been extensively checked against measurements. PAIR AND TRIPLET PRODUCTION The total attenuation coefficient above 10 MeV is dominated by the photon interaction process in which 2mc 2 of the photon's energy is converted, in the field of an atomic nucleus, into an electron-positron pair. The balance of the incident photon's energy, except for the negligible nuclear recoil energy, is imparted as kinetic energy to the created pair particles. A similar process, but less probable by 1/Z and with a higher threshold energy of 4mr, takes place in the field of the atomic electrons. In this case the recoil energy of the target electron is significant, and the process is called "triplet production." Pair production theory was extensively reviewed by Motz, Olsen, and Koch 32 in 1969, and more recently by Hubbell. Gimm, and 0verb0. 33 Nuclear physics interest in the giant dipole resonance (GDR) has motivated extensive high-precision total attenuation coefficient measurements, from which the atomic cross sections, mostly pair production, must be subtracted, in the photon energy region 5 to 30 MeV The GDR can be seen as a 5% "bump" in the total cross section. Such measurements by Sherman et a/., 34 for Al and Bi are shown in Figures 11 and 12. In these graphs, the Storm and Israel 35 pair production data were taken from NBS Report S6S1 (1966) by Hubbell and Berger 36 and NSRDS-NBS 29 (1969) 5 which for high-z elements are now surmised to be, as seen here, as much as 4% low in the GDR region. Gurevich ei al. 37 obtained similar results for Ta and W. Reference 33 gives some notion of the input information required for the calculation of pair production cross sections. The calculation starts with the basic unscreened (bare nucleus) Bethe-Heitler Born approximation cross section accurately calculable using rapidly converging series expansions derived by Maximon. 32 Coulomb, radiative, and screening effects are then folded into the computations as described in detail in reference 33. Unfortunately, our theoretical knowledge of all these effects is least reliable in the region where the total attenuation coefficient is perturbed by the GDR. For these nuclear-field pair production computations, which require atomic form factors F(x, Z) as input data for the screening, the relativistic F(x, Z) values compiled by Hubbell and 0verb0 28 resulted in the best agreement with measurements, and were used generating the tables in reference 33. For computing screening for triplet cross sections, the nonrelativistic 5(x, Z) values from reference 21 were used in reference 33.

6 UNCERTAINTIES Estimating uncertainties in a hazardous enterprise, and sometimes additional knowledge of the processes, both theoretical and experimental, tends to increase these estimates, as discrepancies become more apparent. Previous NBS uncertainty estimates in the soft x- ray region are now seen to be too optimistic. We now believe that the present estimated maximum uncertainties in the total attenuation coefficient are: Energv range ev kev kev kev kev MeV 10 MeV-100 GeV Solid (%) Gas (%) based on discussions of the above and other data now available CONCLUSIONS The PHOTX database was constructed through the combination of incoherent and coherent scattering cross sections from Ref. 21 and 28, photoelectric absorption from Scofield, 9 and pair production cross sections from Ref. 33. For scattering and pair production, the same cross sections are used as in other recent tabulations in Ref. 33, and 11-12, whereas for photoelectric absorption, there is a small difference (omission of a renormalization correction) which is discussed below. The incoherent (Compton) scattering cross sections in Ref. 21 were obtained from a combination of the Klein-Nishina formula and non-relativistic Hartree-Fock incoherent scattering functions. Radiative and double Compton-scattering corrections were also included. The coherent (Rayleigh) scattering cross sections in Ref. 28 were calculated from a combination of the Thompson formula and relativistic Hartree-Fock atomic form factors. The photoelectric cross sections were obtained by Scofield 9 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 semiempirical formula from Ref. 5 connects Scofield's values at 1.5 MeV to the asymptotic high-energy limit calculated by Pratt 39. Cross sections for pair production given in Ref. 33 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 9 presented correction factors for individual atomic subshells, with which the photo-effect cross sections can be renornmlized 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 rcnormalization to the cross sections given in his tables. The renorrnalization was used, however, in the tabulations

7 in Refs. 33, and Recent reviews 13 ' 14 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 purpose of interpolation with respect to photon energy, the methods used by the XCOM program 40 are recommended. 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 (l E'/E) 3 T, P {E), where E is the photon energy, E 1 the threshold energy for pair production, and H p (E) is the cross section. The fitting is done separately for pair production in the field of the atomic nucleus (E' = MeV) and in the field of the atomic electrons (E' = 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 utting 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. It is anticipated that newer evaluations may become available prior to the selection of the final data to be placed in ENDF/B-VI. If so, the values from PHOTX will be suitably modified. ACKNOWLEDGEMENTS Special thanks are due to Dr. Ed Saloman for providing much of the material, particularly the graphical material, for this paper. This work was supported by the NBS Office of Standard Reference. Data, and by the U.S. Department of Energy (OHER). REFERENCES R. W. Roussin, J. R. Knight, J. H. Hubbell, and R. J. Howerton, Description of the DLC-99/HUGO Package of Photon Interaction Data in ENDF/B- V Format, Oak Ridce National Laboratory Report ORNL/RSIC-46 (1983). Radiation Shielding Information Center Data Library DLC-136/PHOTX, Photov Interaction Cross Section Library, (contributed by the National Institute of Stn.ndn.rdK and Technology). G. R. White (Grodstein), X-Ray Attenuation Coefficients from 10 kev to 100 MeV, Report 1003, National Bureau of Standards (1952). G. White Grodstein, X-Ray Attenuation Coefficients from 10 kev to 100 MeV, Circular 583, National Bureau of Standards (1957).

8 5. J. H. Hubbell, Photon Cross Sections, Attenuation Coefficients, and Energy Absorption Coefficients from 10 kev to 100 GeV, Report NSRDS-NBS 29, National Bureau of Standards (1969). 6. E. B. Saloman, J. H. Hubbell, and M. J. Berger, SPIE, 911, 100 (1988). 7. J. H. Hubbell, Atomic Data, 3, 241 (1971). 8. J. H. Hubbell, H. M. Gerstenberg, and E. B. Saloman, Bibliography of Photon Total Cross Section (Attenuation Coefficient) Measurements 10 ev to IS.5 GeV, NBSIR (1986). 9. J. H. Scofield, Theoretical Photoionization Cross Sections from 1 to 1500 kev, Lawrence Livermore National Laboratory Report UCRL (1973). 10. J. H. Scofield, private communication of additional calculation for energies 0.1 to 1.0 kev (1985). 11. J. H. Hubbell, Rad. Res., 70, 58 (1977). 12. J. H. Hubbell, Int. J. Appl. Radiat. Isotopes, 33, 1269 (1982). 13. E. B. Saloman and J. H. Hubbell, Nucl. Instr. Meth., A255, 38 (1987). 14. E. B. Saloman and J. H. Hubbell, X-Ray Attenuation Coefficients (Total Cross Sections): Comparison of the Experimental Data Base with the Recommended Values of Henke and the Theoretical Values of Scofield for Energies Between kev, NBS Internal Report NBSIR (1986). 15. E. B. Saloman, J. H. Hubbell, and J. H. Scofield, Atomic Data and Nucl. Data Tables, 38, 1 (1988). 16. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, and B. K. Fujikawa, Atomic Data and Nucl. Data Tables, 27, 1 (1982). 17. D. C. Creagh and J. H. Hubbell, Ada Cryst. A, 43, 102 (1987). 18. N. K. Del Grande, private communication (1988). 19. R. B. Roof, Phys. Rev., 113, 820 (1959). 20. M. Cukier, P. Dhez, and F. Wuilleumier, Phys. Lett. A, 48, 307 (1974). 21. J. H. Hubbell et al., J. Phys. Chem. Ref Data, 4, 471 (1975): errata in 6, 615 (1977); see also eq. (26) erratum in S. C. Roy, L. Kissel, and R. H. Pratt, Phys. Rev. A, 27, 285 (1983). 22. D. T. Cromer and J. B. Mann, J. Chem. Phys., 47, 1892 (1967). 23. D. T. Cromer, /. Chem. Phys., 50, 4857 (1969). 24. R. T. Brown, Phys. Rev. A, 1, 1342 (1970); A, 2, 614 (1970); A, 5, 2141 (1972); A, S (1974). 25. R. T. Brown, Phys. J. Chem. Phys., 55, 353 (1971). 26. D. T. Cromer and J. B. Mann, Ada Cryst. A, 24, Part 2, 321 (1968). 27. D. T. Cromer, private communication to W. J. Veigele extending calculations up to 80 A" 1 (1971). 28. J. H. Hubbell and I. 0verb0, /. Phys. Chem. Ref. Data, 8, 69 (1979). 29. D. Schaupp, M. Schumacher, F. Smend, P. Rullhusen, and J. H. Hubbell, J. Phys. Chem. Ref. Data, 12, 467 (1983). 30. P. A. Doyle and P. S. Turner, Ada Cryst. A, 24(Part 3), 390 (1968).

9 31. D. T. Cramer and J. T. Waber, Section 2.2 of International Tables for X-Ray Crystallography, Vol. IV, Ibers and Hamilton, eds., Kynoch Press (1974), p J. W. Motz, H. A. Olsen, and H. W. Koch, Rev. Mod. Phys., 41, 581 (1969). 33. J. H. Hubbell, H. A. Gimm, and I. 0verb0, J. Phys. Chem. Ref. Data 9, 1023 (1980). 34. N. K. Sherman, C. K. Ross, and K. H. Lokan, Phys. Rev. C, 21, 2328 (1980). 35. E. Storm and H. I. Israel, Nucl. Data Tables A, 7, 565 (1970). 36. J. H. Hubbell and M. J. Berger, Photon Attenuation and Energy Absorption Coefficients. Tabulations and Discussion (Second Edition), NBS Report 8681 (1966); published as Sections 4.1 and 4.2 in the IAEA Engineering Compendium on Radiation Shielding, Vol. 1, R. G. Jaeger, ed., Springer (1968), p G. M. Gurevich, L. E. Lazareva, V. M. Mazur, S. Yu. Merkulov, and G. V. Solodukhov, Nucl Phys. A, 336, 97 (1980). 38. L. C. Maximon, NBS J. Res. B, 72, 79 (1968). 39. R. H. Pratt, Atomic Photoelectric Effect at High Energies, Phys. Rev., 117, (1960). 40. M. J. Berger and J. H. Hubbell, XCOM: Photon Cross Sections on a Personal Computer. National Bureau of Standards Report NBSIR (1987).

10 NUMBER OF REFERENCES IN DATA BASE BY DECADE REFERENCES Figure 1 fitomic NUMBER 8 OXYGEN ENERGY IEV) * - 55flBi * - 77SFI1 * - 78ME1-78C01 * - 750fll DE HE1-70DE1-33ME1 * - 28KU1 a = 31DE1-640G1 o - 76B01-66BE1-79BH01-85SR01 Figure 2

11 RTOMIC NUMBER 92 URRN1UM * - 74CU1-81DE1 x - 730E1 ENERGY (EV) Figure 3 RTOMIC NUMBER SILICON H lcr ENERGY (EV) Figure 4

12 1.2 ' 1 S(*. Z) SU.Z) z hfv (42!_ 01 I»OJ*»V CM MOll A 210».V [«4 A. 01] IT.3 livid f»oi).4 0 / 1 I x, tin(0/2)/l(a) C 2(0 UV 64 l/i 01) CALC.: PRESENT <CKOMEKI I Figure 5 Figure 6 i St», Z) 8 \ 1] r T I T '«M } 2 P b - - ^ 260 LrV [64 Ax 00 O 662»«v [66 Ou 0(1 20 < Figure 7 Figure S

13 A a a A 10 F(x. (Hi) I0 1 FU.H1. PlRENNE. F(«.K-FS I. STEWART T AL.. ANO «'* EXTRAPOLATION W~ «. Fl«.iHjl.BENTLEY-STEWART. ANO "* EXTRAPOLATION *. sin(8/2)/x(a) 30 (A) Figure 9 Figure Mg MEAS * 1 90* 296' 8.04 k«v [62 BrOl] CALX.: PRESENT (CROMER) THOMAS - FERMI CROMER-VEIGELE * BROWN. BETHE-LEV1NGER Figure 11 Figure 12