NUCLEAR SCIENCE AND ENGINEERING: 153, 33–40 ~2006!

Photonuclear Physics in Radiation Transport—III: Actinide Cross Sections and Spectra M.-L. Giacri-Mauborgne and D. Ridikas* Commissariat à l’Energie Atomique, Saclay, DSM0DAPNIA0SPhN, F-91191 Gif-sur-Yvette, France

and M. B. Chadwick, P. G. Young, and W. B. Wilson University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Received March 7, 2005 Accepted July 25, 2005

Abstract – This paper describes model calculations and nuclear data evaluations of photonuclear reactions on actinides such as 235 U, 238 U, 237 Np, and 239 Pu for incident photon energies from the reaction threshold up to 20 MeV. The calculations are done using the GNASH code, including the giant-dipole resonance for photoabsorption. The emission of secondary particles is computed using a preequilibrium theory, together with an open-ended sequence of the compound nucleus decay using the HauserFeschbach theory. The accuracy of the calculated and evaluated cross sections is assessed through extensive comparison with measured cross sections. This work also summarizes evaluation methods used to create actinide photonuclear files for the forthcoming ENDF/B-VII database, which will facilitate radiation transport studies related to photonuclear reactions in a number of technologies including production of photoneutrons and photofission fragments in electron accelerators, shielding studies, and nondestructive detection of nuclear material in particular.

I. INTRODUCTION

ELBE at Dresden ~Germany! are based on photonuclear reactions. In these and other similar cases, neutrons are produced primarily through the photonuclear process and can pose a serious concern for radiation protection, shielding, and decommissioning. Photonuclear processes can also play a significant role in the detection of nuclear materials, and this has motivated the present work on actinides. Here, both prompt and delayed photoneutrons can provide one with the unique signature of the presence of fissile nuclei in massive cargo containers. Therefore, new simulation capabilities are urgently needed to help develop this technology. This is important in order to design and optimize the electron accelerator, conversion targets, and neutron detectors. Equally, simulations are essential for interpreting new measurements. In this respect, nuclear physics research to produce consistent photonuclear cross-section databases is still needed, and the forthcoming ENDF0BVII release will include most of the new evaluations on photonuclear reactions.

Evaluated nuclear data files, such as the U.S. ENDF0 B-VI cross-section library, have not historically included evaluated photonuclear cross-section data, and additionally, radiation transport codes have not been developed to utilize such data except for some earlier studies.1,2 Recently, this work has built upon a visible growth in photonuclear data and transport efforts.3– 6 Although photoneutrons typically provide only a small additional neutron source in technologies involving proton accelerators and nuclear reactors, photoneutrons and photofission are of significant importance in applications based on electron accelerators and bremsstrahlung targets. For example, intense neutron sources for physics experiments such as ORELA at Oak Ridge National Laboratory, GELINA at Geel ~Belgium!, and more recently *E-mail: [email protected] 33

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This paper follows the previous work 3 in which the description of photonuclear cross sections and particle spectra for isotopes of C, O, Al, Si, Ca, Fe, Cu, Ta, W, and Pb up to 150 MeV using the GNASH code is provided. In this study, our results are presented for 235 U, 238 U, 237 Np, and 239 Pu with photon energies from threshold up to 20 MeV, and where GNASH calculations are undertaken for the first time for photonuclear reactions on actinides.

II. PHOTONUCLEAR REACTIONS

Photonuclear cross sections for absorption, neutron emission, and fission have been measured around the giant dipole resonance ~GDR! region at many laboratories. Work in Russia,7 at Lawrence Livermore National Laboratory 8,9 ~LLNL!, and at Saclay 10 has been particularly important. For these data to be useful in simulation codes, nuclear data evaluation work and nuclear modeling are required. Such work helps to resolve inconsistencies in measured cross sections from different laboratories. In addition, nuclear modeling will provide predictions on the emitted neutron energy and angular spectra, which are needed for transport simulations using a complete set of evaluated cross sections. Such spectra have rarely been measured for monoenergetic photon sources. Some cross sections we are interested in, such as those on 235 U, 238 U, and 239 Pu, have already been evaluated by the group at the Institute of Physics and Power Engineering ~IPPE!, Obninsk, Russia, in the frame of the International Atomic Energy Agency ~IAEA! collaboration project.4 Although the photoneutron and photofission cross sections in the IPPE evaluations appear to be of good quality, we are reevaluating these data to take advantage of our ability to predict accurate prompt neutron spectra, which should be consistently determined with the separate reaction channels. This includes both prompt neutron spectra from ~g,1n! and ~g,2n! processes, as well as prompt fission neutron spectra calculated using the Madland-Nix model. We also are interested in delayed neutron emission spectra, which are not available in the IAEA project. In addition, for 237 Np, no evaluations have been done to date.

III. NUCLEAR REACTION MODELING WITH GNASH

A model of photonuclear reactions must account for a number of different nuclear reaction mechanisms involved in the initial photonuclear excitation process, and the subsequent decay of the excited nucleus by particle emission. At low energies, say, below 30 MeV, the GDR is the dominant excitation mechanism, where a collective bulk oscillation of the neutrons against the protons

occurs. The initial nuclear excitation can be described by particle-hole excitations ~1p1h!. Therefore, it is natural to use a preequilibrium theory to describe the processes of preequilibrium emission, and damping equilibrium, during the evolution of the reaction. We have recently adapted the GNASH calculation code to model photofission reactions. The extensions were minimal: We had already developed a ~nonactinide! photonuclear modeling capability,3 and we have extensive experience in using GNASH to model neutron-induced reactions on actinides. Our earlier neutron-induced analysis for isotopes of uranium, plutonium, and neptunium had led to a set of input parameters describing fission barriers within a double-humped parabolic model, fission transition states and level densities, and transmission coefficients, which could be directly used in the present photofission studies. Using these parameters one could expect an accurate prediction of the measured ~g,1n!, ~g,2n!, and ~g, fission! data. Note that the neutron capture channel had to be suppressed in the case of photonuclear reactions. In addition, in some cases we made adjustments to the fission barrier parameters to further optimize agreement between calculation and experiment, but the adjustments needed were modest. This builds confidence in the overall nuclear reaction mechanism we apply. To validate emission spectra evaluation, we test the theoretical predictions of partial exclusive reaction channels @e.g., ~g,1n!, ~g,2n!, ~g, fission!# against experimental results. These measurements can indirectly test the calculated particle spectra since the energy dependence of the calculated particle emission spectra strongly influences the exclusive reaction channels populated in terms of energy balance. For more details about the calculation and validation method and data processing, we refer the reader to Refs. 3 and 5.

IV. TOTAL PHOTOABSORPTION CROSS SECTION

The GNASH calculations are the most accurate if the total absorption cross section is chosen to be close to the experimental data. It is well known that the photoabsorption cross section for actinides in the GDR region can be parameterized by the sum of two Lorentzians: sGDR ~E ! ⫽ s1

~EG1 ! 2 ~E 2 ⫺ E12 ! 2 ⫹ ~EG1 ! 2

⫹ s2

~EG2 ! 2 ~E 2 ⫺ E22 ! 2 ⫹ ~EG2 ! 2

.

~1!

In practice, all parameters in Eq. ~1! such as si , Ei , and Gi are determined by fitting the experimental data. The most valuable data for photoabsorption on actinides come NUCLEAR SCIENCE AND ENGINEERING

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from direct photon absorption experiments. On the other hand, for heavy nuclei, the compilations of total photoneutron cross section such as by Dietrich and Berman 6 can be used to approximate the photoabsorption cross sections since the contributions from photoproton reactions ~and other reactions producing complex charged particles! are suppressed by the Coulomb barrier. Unfortunately, some of the experimental data often show discrepancies. In these cases, we employ the precompiled values for Gi and Ei , available from the RIPL-2 library of the IAEA Nuclear Data Section. For the parameters si , we use the classical dipole sum rule, corrected by Fuller’s systematics,11 namely, * sabs dE ⯝ 72~N{Z!0A~mb{MeV!. This should be applicable in the region of GDR with the following condition in the case of a prolate spheroid nucleus: s2 G2 0s1 G1 ⯝ 2 ~Ref. 12!. In Fig. 1, we compare the integrated values of the photoabsorption cross section for some of the actinides. In all cases the integral is taken up to 20 MeV. One notes that the measurements from Veyssière et al.10 ~squares! never agree with the measurements from Berman et al.9 and Caldwell et al.8 ~circles!. On the other hand, the calculations based on RIPL-2 ~interconnected diamonds! agree within 5% with the IAEA evaluations ~triangles! except for 232 Th.

V. GNASH CALCULATION RESULTS

V.A. Photoabsorption and Photonuclear Cross Sections for 235 U

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sured only the total photoabsorption, while Caldwell et al.8 approximate the total photoabsorption cross section by the sum of photoneutron cross sections. At the same time, as we want to test the IAEA evaluations, we choose as input the absorption cross section recommended by the IAEA evaluation,4 which is based on Gurevich et al.’s data. Our goal is to reproduce Varlamov et al.’s data 7 for photofission as was done in the IAEA evaluation. Varlamov et al. did not perform a new measurement but, rather, reevaluated Caldwell et al.’s data, concluding that the fission cross section for this experiment was overestimated. In this case we have followed Varlamov et al.’s recommendation, and therefore, we adopted the IAEA evaluation for the photoabsorption. The results of individual ~g,1n!, ~g,2n!, and ~g, fission! cross sections compared to experimental cross sections are given in Fig. 2. For the fission cross section, the GNASH results are in a very good agreement with Varlamov et al.’s data. Up to 15-MeV agreement is also good for the ~g,1n! reaction and for the ~g,2n! reaction. Above 15 MeV our evaluations underestimate the data for both the ~g,1n! and the ~g,2n! reactions. The same underestimate was found in the IAEA evaluation ~not shown in Fig. 2!, which was based upon the independent work of the IPPE Obninsk group.4 This result in principle validates our computational process in the use of GNASH for evaluation of photonuclear reactions on actinides.

The experimental data exist for photoabsorption on U from two different sources. Gurevich et al.13 mea-

V.B. Photoabsorption and Photonuclear Cross Sections for 238 U Figure 3 presents Gurevich et al.’s experimental absorption cross section together with the Caldwell et al.

Fig. 1. Comparison of integrated photoabsorption cross sections for a number of actinides. Both existing data and different evaluations are presented ~see the legend!. ~Dimensions are in units of mb{MeV.!

Fig. 2. Evaluated photonuclear cross sections for 235 U, namely, ~g, n!, ~g,2n!, and ~g, fission!, as a function of incident photon energy. The evaluations are based on GNASH calculations and compared with experimental data.

235

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Fig. 3. Total photoabsorption cross section for 238 U as a function of incident photon energy. Both evaluations ~lines! and different experimental data sets ~points! are shown ~see legend!.

Fig. 4. Evaluated photonuclear cross sections for 238 U, namely, ~g, n!, ~g,2n!, and ~g, fission!, as a function of incident photon energy. The evaluations are based on GNASH calculations and compared with experimental data.

and Veyssière et al. data. In the first case, the cross section was measured directly, while in the latter two cases, it is the sum of all photonuclear reaction cross sections measured in each experiment. As cross sections disagree, we decided to use the photoabsorption cross section calculated using RIPL-2 parameters as input for GNASH. The absorption cross section we obtain, using RIPL-2 parameters, is presented by a solid line in Fig. 3. Our evaluation is closer to Caldwell et al.’s data, which is also the case for the IAEA evaluation ~dashed curve!, except the region between two peaks. The individual ~g,1n!, ~g,2n!, and ~g, fission! cross sections obtained with GNASH are given in Fig. 4. The agreement with Caldwell et al.’s data is rather good. This is consistent with the fact that the photoabsorption cross section is also closer to Caldwell et al.’s data. Equally as for 235 U, we choose to reproduce Varlamov et al.’s data for the photofission cross section, and the GNASH results are in a very good agreement with the data.

obtain good agreement between the evaluations and the experimental data for the ~g,1n! and ~g,2n! cross sections. Above 15 MeV the fission cross section is slightly underestimated as in the IAEA evaluation ~not shown! and might be linked to a possible underestimate of the total absorption cross section in this energy region. Indeed, the 15-MeV Berman et al. data show some discrepancies, and the photoabsorption cross-section fit may not be accurate. It seems that by improving the total absorption cross section, we could also improve the result of our GNASH

V.C. Photoabsorption and Photonuclear Cross Sections for 239 Pu The experimental data together with the IAEA evaluation for photoabsorption on 239 Pu are presented in Fig. 5. The Gurevich et al. results 13 and IAEA evaluations 4 are inconsistent for the energies around 11 MeV, namely, at the position of the first fission peak. Note that the absorption cross section from Berman et al.9 is the sum of the ~g,1n!, ~g,2n!, and ~g, fission! cross sections. Again, we choose to use the RIPL-2 parameters to calculate the absorption cross section as input for GNASH. This cross section is represented by the solid line in Fig. 5. The individual ~g,1n!, ~g,2n!, and ~g, fission! cross sections calculated with GNASH are given in Fig. 6. We

Fig. 5. Total photoabsorption cross section for 239 Pu as a function of incident photon energy. Both evaluations ~lines! and different experimental data sets ~points! are shown ~see legend!. NUCLEAR SCIENCE AND ENGINEERING

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Fig. 6. Evaluated photonuclear cross sections for 239 Pu, namely, ~g, n!, ~g,2n!, and ~g, fission!, as a function of incident photon energy. The evaluations are based on GNASH calculations and compared with experimental data.

Fig. 7. Total photoabsorption cross section for 237 Np as a function of incident photon energy. Both evaluations ~lines! and different experimental data sets ~points! are shown ~see legend!.

evaluations for partial channels. Therefore, a future precise total absorption cross-section measurement would be most valuable.

section, our evaluation lies between the two sets of experimental values, as was the case for the absorption cross section in this energy range. For photofission as shown in Fig. 9, we have the same situation as for photoabsorption: The data from the two experiments are inconsistent. Our evaluation corresponds to the compromise we made on the absorption. This means our evaluation is in good agreement with Caldwell et al.’s data for the first peak. At the second fission peak, the evaluation is between the two sets of the experimental data.

V.D. Photoabsorption and Photonuclear Cross Sections for 237 Np Neptunium-237 was not evaluated in the IAEA work. In this case we found two different mono-energetic photon experiments in which the measurements of photonuclear cross sections were made. One was performed by Berman et al.9 and the other one was made by Veyssière et al.10 Unfortunately, the absorption cross section, which is needed as input for the GNASH calculations, exhibits discrepancies between the two experiments as shown in Fig. 7. For this reason as in previous cases, we decided to use a photoabsorption cross section based on a model that employs theoretical parameters from the RIPL-2 library. The absorption cross section we obtained is presented by the solid line in Fig. 7. These values are used as input for the GNASH calculations. Our evaluation for the first peak is close to Caldwell et al.’s data, whereas for the second peak it is between the two sets of experimental data ~see Fig. 7!. We remind the reader that another independent check indicates that the calculations based on the RIPL-2 photoabsorption parameters are not contradictory with respect to the data in the mass region around 237, which was already indicated in Fig. 1. Once the absorption cross section is chosen, we can use GNASH to evaluate the photoneutron and photofission cross sections. Both experiments agree on the ~g,1n! reaction cross section ~see Fig. 8!, and they are well reproduced with GNASH. For the ~g,2n! reaction cross NUCLEAR SCIENCE AND ENGINEERING

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Fig. 8. Evaluated photoneutron cross sections from GNASH calculations for 237 Np as a function of incident photon energy. Different data sets are also presented for a direct comparison.

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TABLE I Integrated Photofission Cross Sections for 237 Np, Based on Experimental Data and GNASH Evaluation Together with Calculated Corresponding Photofission Yields* Integrated Calculation0 Calculation0 Cross GNASH Data Section Photofission Photofission ~mb{MeV! Yield Yield Use of data 7 Use of data 9 GNASH, this work

2540 2010 2300

1.13 0.88 1.00

1.20 0.93 1.06

*The photofission yield data were obtained with the 30MeV end-point bremsstrahlung spectra.15 Fig. 9. Evaluated photofission cross section from GNASH calculations for 237 Np as a function of incident photon energy. Different data sets are also presented for a direct comparison.

Finally, we note that recently Soldatov and Smirenkin extracted photofission cross sections using a bremsstrahlung photon flux up to 11 MeV ~Ref. 14!. To solve the deconvolution problem, they measured the ratio of fissions in 237 Np with respect to fissions in 238 U. Their results are represented by the open circles in Fig. 9, and they are in a good agreement with our GNASH evaluations. Additional interesting information could be extracted from the work of Kase et al.,15 in which the authors measured the experimental transmutation yield for 237 Np with bremsstrahlung photons. Kase et al. compared their results with a calculated transmutation yield using photofission cross sections from Caldwell et al. and Veyssière et al. Kase et al. argued that they obtain the best agreement ~within 10%! by using the Veyssière et al. cross sections. The difference of calculation with the Caldwell et al. cross sections and measured transmutation is ;20%. We have done the same calculation with the 30-MeV end-point bremsstrahlung photons, and the results are presented in Table I. The calculated values are the integral of the photofission cross section multiplied by the 30-MeV end-point bremsstrahlung flux. Briefly, our evaluation is in good agreement with Kase et al.’s data. The 6% difference may be linked to the extrapolation of the fission cross section beyond 20 MeV, which involves significant uncertainties. The relative photofission yields have also been measured by Huizenga et al.,16 who obtained the photofission ratio between a number of actinides and 238 U at 12-, 17-, and 20-MeV end-point bremsstrahlung energies. The Huizenga et al. results are compared with our evaluation for 237 Np in Table II. Here we used the IAEA evaluation for 238 U to calculate the ratio. We have very good agreement at 12 MeV. For higher energies our eval-

uation somewhat underestimates the experiment. This happens in the energy region where the monoenergetic photon data are in disagreement. In addition, between 18 and 20 MeV, no such data are available. This may explain the differences shown in Table II. V.E. From GNASH Results to ENDF Files The GNASH model simulations described here have been the basis for creating new ENDF evaluated nuclear data files for the forthcoming ENDF0B-VII U.S. library release, anticipated in early 2006. The GNASH calculations predict the cross sections for ~g,1n!, ~g,2n!, and ~g, fission! including the angle-energy correlated emission spectra for the secondary particles ~neutrons, protons, etc.!. These calculated spectra were used in the ENDF evaluations we have generated since measured data for monochromatic photons do not exist for actinides. Regarding the cross sections ~g,1n!, ~g,2n!, and ~g, fission!, we have based our evaluations mainly on experimental data, and for certain evaluations we adopted the values used in the IAEA evaluations as summarized in Table III since these cross-section evaluations were already based on the available measured data. Regarding the prompt fission neutron multiplicities, we generally

TABLE II Relative Photofission Yields of 237 Np to 238 U with End-Point Bremsstrahlung Spectra of 12, 17, and 20 MeV* Energy ~MeV! 12

17

20

Experimental data 2.53 6 0.16 2.39 6 0.10 2.40 6 0.11 GNASH, this work 2.54 2.24 2.11 *The data are from Ref. 16. NUCLEAR SCIENCE AND ENGINEERING

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TABLE III A Summary of the Procedures from Evaluations to ENDF Formatting for Six Actinides Used to Create Photonuclear Files for the Forthcoming Release of the ENDF0B-VII Database Target

Cross Sections

Prompt Nubar

Delayed Nubar

Prompt x Spectra a

235 U

Taken from Blohkin evaluation; based on experimental data of Caldwell et al., 1980, and evaluation of Varlamov, 1999

Taken from Blohkin evaluation; based on experimental data of Caldwell et al., 1980

n ⫹ 234 U ENDF0B-VI evaluation, shifted by Sn and normalized to experimental data of Caldwell and Dowdy, 1975 ~Ref. 18!

Taken from Blohkin evaluation; Maxwellian distributions

238

Taken from Blohkin evaluation; based on experimental data of Caldwell et al., 1980, and Veyssière et al., 1973

Taken from Blohkin evaluation; based on experimental data of Caldwell et al., 1980

n ⫹ 237 U ENDF0B-VI evaluation, shifted by Sn and normalized to experimental data of Caldwell and Dowdy, 1975 ~Ref. 18!

Taken from Blohkin evaluation; Maxwellian distributions

n ⫹ 238 Pu ENDF0B-VI evaluation, shifted by Sn and normalized to experimental data of Caldwell and Dowdy, 1975 ~Ref. 18!

n ⫹ 238 Pu ENDF0B-VI evaluation, shifted by Sn ; Maxwellian distributions

U

239 Pu

~g, n! GNASH, Based on experimental ~g,2n! GNASH, data of Berman et al., ~g, fission! based on 1986 experimental data of Berman et al., 1986, and Moreas, 1993 ~Ref. 19!, plus GNASH above 10 MeV

240

~g, n! GNASH, ~g,2n! GNASH, ~g, fission! GNASH plus experimental data of Soldatov and Smirenkin, 1994

n ⫹ 239 Pu ENDF0B-VI evaluation, n ⫹ 239 Pu ENDF0B-VI evaluation, shifted by Sn shifted by Sn

~g, n! GNASH, ~g,2n! GNASH, ~g, fission! GNASH plus experimental data of Berman et al., 1986, and Veyssière et al., 1973

Based on experimental data of Berman et al., 1986

Pu

237 Np

241

Am ~g, n! GNASH, ~g,2n! GNASH, ~g, fission! GNASH plus experimental data of Soldatov and Smirenkin, 1994

n ⫹ 239 Pu ENDF0B-VI evaluation, shifted by Sn ~tabulated distributions!

n ⫹ 236 Np ENDF0B-VI evaluation, n ⫹ 236 Np ENDF0B-VI shifted by Sn and normalized to evaluation, shifted by Sn ~Maxwellian distributions! experimental data of Caldwell and Dowdy, 1975 ~Ref. 18!

n ⫹ 241Am ENDF0B-VI n ⫹ 241Am ENDF0B-VI evaluation, n ⫹ 241Am ENDF0B-VI evaluation, shifted by Sn shifted by Sn evaluation, shifted by Sn ~Madland-Nix Law 12 distributions!

a In all cases the energy-angle correlated spectra of neutrons from the ~g, n!, ~g,2n!, ~g,3n! reactions come from the GNASH calculations.

based our data on measurements from LLNL ~Caldwell et al.17 and Berman et al.9 !. Where no measurements exist, we modified information available from neutroninduced reactions on actinides. Prompt neutron energy spectra ~ x! were adopted from neutron evaluations too. Delayed neutron data ~fractions and spectra! were initially based upon information from ENDF neutronNUCLEAR SCIENCE AND ENGINEERING

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induced cross-section evaluations ~e.g., g ⫹ 235 U data were based upon n ⫹ 234 U data but shifted by the appropriate Q value!, and these data were then scaled ~typically by ;20%! to agree with the measured delayed neutron data by Caldwell et al. ~obtained from the bremsstrahlung source!. A summary of the procedures adopted for each isotope is given in Table III.

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VI. CONCLUSIONS

We have developed nuclear reaction modeling capabilities to include photofission reactions on actinides. This is a continuation of the efforts toward evaluations of photonuclear cross sections with GNASH of some of the most important actinides such as 235 U, 238 U, and 239 Pu. These newly evaluated data tables are being represented in the ENDF format to be included in transport codes. In addition, for the first time, we present here the evaluation of photonuclear cross sections on 237 Np, which are based on earlier measurements for neutron production and fission cross sections. Good agreement with integral measurement for the fission cross section was obtained using these new evaluations. Our new evaluations are scheduled to be included in ENDF0B-VII in the near future. GNASH calculations for other actinides such as 241Am and 240 Pu are in progress and will be reported in a later publication. Our future efforts will also include the photofission fragment distributions, delayed neutron yields, and corresponding time spectra. Together with advances in Monte Carlo simulations, this work will provide the necessary tools to enable one to simulate nondestructive photofission detection of sensitive nuclear materials as well as other applications involving photonuclear reactions on actinides. REFERENCES 1. F. X. GALLMEIER, “ Photoneutron Production in MCNP4A,” Proc. Topl. Mtg. Radiation Protection and Shielding, North Falmouth, Massachusetts, April 21–25, 1996, Vol. 2, p. 780, American Nuclear Society ~1996!. 2. P. VERTES and D. RIDIKAS, “Some Test Calculations with the IAEA Photonuclear Data Library,” Nucl. Sci. Technol., 2, 1167 ~2002!. 3. M. B. CHADWICK, P. G. YOUNG, R. E. MacFARLANE, M. C. WHITE, and R. C. LITTLE, “ Photonuclear Physics in Radiation Transport—I: Cross Sections and Spectra,” Nucl. Sci. Eng., 144, 157 ~2003!. 4. M. B. CHADWICK, P. OBLOZINSKY, A. I. BLOKHIN, T. FUKAHORI, Y. HAN, Y.-O. LEE, M. N. MARTINS, S. F. MUGHABGHAB, V. V. VARLAMOV, B. YU, and J. ZHANG, “Handbook on Photonuclear Data for Applications: Cross Sections and Spectra,” IAEA TECHDOC, 1178, International Atomic Energy Agency ~Oct. 2000!.

7. A. V. VARLAMOV, V. V. VARLAMOV, D. S. RIDENKO, and M. E. STEPANOV, “Atlas of Giant Dipole Resonance Parameters and Graphs of Photonuclear Reaction Cross Sections,” INDC~NDS!-399, International Atomic Energy Agency, International Nuclear Data Committee ~1999!; see also ^http:00cdfe.sinp.msu.ru&. 8. J. T. CALDWELL, E. T. DOWDY, B. L. BERMAN, R. A. ALVAREZ, and P. MEYER, “Giant Resonance for Actinide Nuclei: Photoneutron and Photofission Cross Sections of 235 U, 236 U, 238 U and 232 Th,” Phys. Rev. C, 21, 4, 1215 ~1980!. 9. B. L. BERMAN, J. T. CALDWELL, E. J. DOWDY, S. S. DIETRICH, P. MEYER, and R. A. ALVAREZ, “ Photofission and Photoneutron Cross Sections and Photofission Neutron Multiplicities for 233 U, 234 U, 237 Np and 239 Pu,” Phys. Rev. C, 34, 6, 2201 ~1986!. 10. A. VEYSSIÈRE, R. BERGERE, P. CARLOS, and A. LEPRETRE, “A Study of Photofission and Photoneutron Processes in Giant Dipole Resonance of 232 Th, 238 U and 237 Np,” Nucl. Phys. A, 199, 45 ~1973!. 11. E. G. FULLER, in Proc. Int. Conf. Photonuclear Reactions and Applications, Pacific Grove, California, March 26– 30, 1973, p. 1201 ~1973!. 12. M. DANOS, “On the Long Range Model of the Photonuclear Effect,” Nucl. Phys., 5, 23 ~1958!. 13. G. M. GUREVICH, L. E. LAZAREVA, V. M. MAZUR, SOLODUKHOV, and B. A. TULUPOV, “Giant Resonance in the Total Photoabsorption Cross Section near of Z ⫽ 90 Nuclei,” Nucl. Phys. A, 273, 326 ~1976!. 14. A. S. SOLDATOV and G. N. SMIRENKIN, “Results of Relative Measurement of Photofission Yields and Cross Sections for 233;235 U, 237 Np, 239;241 Pu and 241Am Nuclei in the 5–11 MeV Region,” INDC~CCP!-379, International Atomic Energy Agency, International Nuclear Data Committee ~1994!. 15. T. KASE, A. YAMADERA, T. NAKAMURA, S. SHIBATA, and I. FUJIWARA, “Product Yields of 235U, 238U, 237Np, and 239 Pu by Photofission Reactions with 20-, 30-, and 60MeV Bremsstrahlung,” Nucl. Sci. Eng., 111, 368 ~1992!. 16. J. R. HUIZENGA, J. E. GINDLER, and R. B. DUFFIELD, “Relative Photofission Yields of Several Fissionable Materials,” Phys. Rev., 95, 4, 1009 ~1954!. 17. J. T. CALDWELL, E. J. DOWDY, R. A. ALVAREZ, B. L. BERMAN, and P. MEYER, “Experimental Determination of Photofission Neutron Multiplicities for 235 U, 236 U, 238 U, and 232 Th Using Monoenergetic Photons,” Nucl. Sci. Eng., 73, 153 ~1980!.

5. M. C. WHITE, R. C. LITTLE, M. B. CHADWICK, P. G. YOUNG, and R. E. MacFARLANE, “ Photonuclear Physics in Radiation Transport—II: Implementation,” Nucl. Sci. Eng., 144, 174 ~2003!.

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