The nuclear level density parameters of some deformed isotopes of target nuclei (Pb, Bi) used on the accelerator-driven subcritical systems (ADSs) have been calculated taking into consideration different collective excitation modes of observed nuclear spectra near the neutron binding energy. The method used in the present work assumes equidistant spacing of the collective coupled state bands of the considered isotopes. The present calculated results for different collective excitation bands have been compared with the compiled values from the literature for s-wave neutron resonance data, and good agreement was found. 1. Introduction The knowledge of nuclear level densities is a crucial input in various fields/applications such as the creation of consistent theoretical description of excited nucleus properties and the nuclear reaction cross-section calculations for many branches of nuclear physics, nuclear astrophysics, nuclear medicine, and applied areas (medical physics, etc.) [1–14]. The neutron capture cross-sections, required for both design and nuclear model calculations in nuclear science and technologies, are approximately proportional to the corresponding level densities around the neutron resonance region. In nuclear medicine, the cross-section data obtained from nuclear level density approaches are needed to optimize production of radioactive isotopes for therapeutic purposes, for example, biomedical applications such as production of medical radioisotopes and cancer therapy and accelerator-driven incineration/transmutation of the long-lived radioactive nuclear wastes. Recently, the accelerator-driven systems (ADSs), which are used for production of neutrons in spallation neutron source and can act as an intense neutron source in accelerator-driven subcritical reactors, and their neutronics have been studied by many researchers [15–20]. Most of the studies were concerned with specific design concepts and the production of neutrons from spallation reactions. New accelerator-driven technologies make use of spallation neutrons produced in (p,xn) and (n,xn) nuclear reactions on high-Z targets. Through (p,xn) and (n,xn) nuclear reactions, neutrons are produced and moderated by heavy water in the target region and light water in the blanket region. These moderated neutrons are subsequently captured on 3-He, which flows through the blanket system, to produce tritium via the (n,p) reaction. Therefore, new nuclear cross-section data are needed to improve the theoretical predictions of neutron production, shielding requirements, activation, radiation
References
[1]
S. Shaleen, Calculation of nuclear level densities near the drip lines, Ph.D. thesis, Faculty of the College of Arts and Sciences of Ohio University, Physics and Astronomy, 2008.
[2]
H. A. Bethe, “An attempt to calculate the number of energy levels of a heavy nucleus,” Physical Review, vol. 50, no. 4, pp. 332–341, 1936.
[3]
A. Gilbert and A. G. W. Cameron, “A composite nuclear-level density formula with shell corrections,” Canadian Journal of Physics, vol. 43, pp. 1446–1496, 1965.
[4]
T. Von Egidy and D. Bucurescu, “Systematics of nuclear level density parameters,” Physical Review C, vol. 72, no. 4, 2005.
[5]
A. V. Ignatyuk and N. Yu Shubin, “Role of collective effects in the systematics of nuclear level densities,” Soviet Journal of Nuclear Physics, vol. 8, p. 660, 1969.
[6]
H. Ahmadov, I. Zorba, M. Yilmaz, and B. G？nül, “On the level density of even-nuclei in the regions of rare-earth and actinide elements,” Nuclear Physics A, vol. 706, no. 3-4, pp. 313–321, 2002.
[7]
？. Okuducu and H. Ahmadov, “On the estimation of nuclear level density parameters in the region of some large deformed nuclei,” Physics Letters B, vol. 565, no. 1-4, pp. 102–106, 2003.
[8]
？. Okuducu, E. Eser, and S. S？nmezo？lu, “Analysis of the nuclear level-density parameters of some large deformed odd-A and odd-odd nuclei in the region of Rare Earth Elements,” Nuclear Science and Engineering, vol. 154, no. 3, pp. 374–381, 2006.
[9]
？. Okuducu, S. S？nmezo？lu, and E. Eser, “Calculation of nuclear level density parameters of some deformed light nuclei using collective excitation modes,” Physical Review C, vol. 74, no. 3, Article ID 034317, 2006.
[10]
？. Okuducu, N. N. Akti, H. Sara？, M. H. B？lükdemir, and E. Tel, “Calculation of nuclear level density parameters of some light deformed medical radionuclides using collective excitation modes of observed nuclear spectra,” Modern Physics Letters A, vol. 24, no. 33, pp. 2681–2691, 2009.
[11]
？. Okuducu and N. N. Akti, “Nuclear level density parameters of some largely deformed nuclei of medical radionuclides in low-lying collective excitation modes,” Kerntechnik, vol. 75, no. 3, pp. 109–116, 2010.
[12]
？. Okuducu, N. N. Akti, and E. Eser, “The theoretical nuclear level density parameters of some deformed target radioisotopes 181–187？W and 196–204？Hg used on the accelerator-driven systems,” Annals of Nuclear Energy, vol. 38, no. 8, pp. 1769–1774, 2011.
[13]
D. Bucurescu and T. Von Egidy, “Systematics of nuclear level density parameters,” Journal of Physics G, vol. 31, no. 10, pp. S1675–S1680, 2005.
[14]
S. K. Kataria, V. S. Ramamurthy, and S. S. Kapoor, “Semiempirical nuclear level density formula with shell effects,” Physical Review C, vol. 18, no. 1, pp. 549–563, 1978.
[15]
T. Takizuka, T. Nishida, M. Mizumoto, and H. Yoshida, “JAERI R&D on accelerator-based transmutation under OMEGA Program,” in Proceedings of the International Conference on Accelerator-Driven Transmutation Technologies and Applications, pp. 64–73, Las Vegas, Nev, USA, 1994.
[16]
A. Boudard, F. Borne, F. Brochard et al., “Spallation study with proton beams around 1？GeV: neutron production,” Nuclear Physics A, vol. 663-664, no. 1-2, 2000.
[17]
C. H. M. Broeders and I. Broeders, “Neutron physics analyses of accelerator-driven subcritical assemblies,” Nuclear Engineering and Design, vol. 202, no. 2-3, pp. 209–218, 2000.
[18]
H. Yapici, G. Gen？, and N. Dem？r, “Neutronic limits in infinite target mediums driven by high energetic protons,” Annals of Nuclear Energy, vol. 34, no. 5, pp. 374–384, 2007.
[19]
I. Demirkol, E. Tel, A. Araso？lu et al., “The neutron production cross sections for Pb, Bi, and Au targets and neutron multiplicity for nuclear spoliation reaction induced by 20- to 1600？MeV protons,” Nuclear Science and Engineering, vol. 147, no. 1, pp. 83–91, 2004.
[20]
A. Kaplan, E. Tel, E. G. Aydin, A. Aydin, and M. Yilmaz, “Spallation neutron emission spectra in medium and heavy target nuclei by a proton beam up to 140？MeV energy,” Applied Radiation and Isotopes, vol. 67, no. 4, pp. 570–576, 2009.
[21]
E. G. Aydin, E. Tel, A. Kaplan, and A. Aydin, “Equilibrium and pre-equilibrium calculations of neutron production in medium-heavy targets irradiated by protons up to 100？MeV,” Annals of Nuclear Energy, vol. 35, no. 12, pp. 2306–2312, 2008.
[22]
C. Rubbia and J. A. Rubio, “A Tentative Programme Towards a Full Scale Energy Amplifier,” CERN/LHC/96-11 (EET), Geneva, Switzerland, 1996.
[23]
E. Tel, H. M. ？ahin, A. Kaplan, A. Aydin, and T. Altinok, “Investigation of the properties of the nuclei used on the new generation reactor technology systems,” Annals of Nuclear Energy, vol. 35, no. 2, pp. 220–227, 2008.
[24]
I. Demirkol, A. Araso？lu, and E. Tel, “Neutron multiplicity with 1.0 and 1.2？GeV proton-induced spallation reactions on thin targets,” Chinese Journal of Physics, vol. 46, no. 2, pp. 124–134, 2008.
[25]
S. Hilaire, “Energy dependence of the level density parameter,” Physics Letters B, vol. 583, no. 3-4, pp. 264–268, 2004.
[26]
S. E. Woosley, Theory and Applications of Moments Methods in Many-Fermion Systems, Plenum, New York, NY, USA, 1980.
[27]
P. L. Huang, S. M. Grimes, and T. N. Massey, “Level densities for nuclei with 20≤A≤41,” Physical Review C, vol. 62, no. 2, pp. 240021–2400212, 2000.
[28]
T. Newton, “Shell effects on the spacing of nuclear levels,” Canadian Journal of Physics, vol. 34, pp. 804–829, 1956.
[29]
T. Ericson, “Level density of degenerate Fermi systems,” Nuclear Physics, vol. 8, no. C, pp. 265–283, 1958.
[30]
A. Bohr and B. Mottelson, Nuclear Structure, Vol. II, Benjamin, New York, NY, USA, 1969.
[31]
G. Puddu, P. F. Bortignon, and R. A. Broglia, “Nuclear level densities including thermal and quantal fluctuations,” Physical Review C, vol. 42, no. 5, pp. R1830–R1833, 1990.
[32]
B. J. Dalton, S. M. Grimes, J. P. Vary, and S. A Williams, Theory and Applications of Moments Methods in Many-Fermion Systems, Plenum, New York, NY, USA, 1980.
[33]
H. Baba, “A shell-model nuclear level density,” Nuclear Physics A, vol. 159, no. 2, pp. 625–641, 1970.
[34]
G. Rohr, “New perspectives on the level density of compound resonances,” Zeitschrift für Physik A, vol. 318, no. 3, pp. 299–308, 1984.
[35]
Nuclear Structure and Decay Data, National Nuclear Data Center. Brookhaven National Laboratory. ENSDF (Evaluated Nuclear Structure Data File), Upton, NY, USA, 2001.
[36]
A. V. Ignatyuk, K. K. Istekov, and G. N. Smirenkin, “Collective effects in level density, and the probability of fission,” Soviet Journal of Nuclear Physics, vol. 29, pp. 450–454, 1979.
[37]
J. Rainwater, “Nuclear energy level argument for a spheroidal nuclear model,” Physical Review, vol. 79, no. 3, pp. 432–434, 1950.
[38]
A. Bohr, “On the quantization of angular momenta in heavy nuclei,” Physical Review, vol. 81, no. 1, pp. 134–138, 1951.
[39]
A. S. Davydov and G. F. Filippov, “Rotational states in even atomic nuclei,” Nuclear Physics, vol. 8, no. C, pp. 237–249, 1958.
[40]
A. S. Davydov and A. A. Chaban, “Rotation-vibration interaction in non-axial even nuclei,” Nuclear Physics, vol. 20, no. C, pp. 499–508, 1960.
[41]
J. P. Davidson, Collective Models of the Nucleus, Academic Press, New York, NY, USA, 1968.
[42]
S. F. Mughabgahab and C. L. Dunford, “New approach for the determination of the nuclear level density parameters,” in Proceedings of the International Conference on Physics of Nuclear Science and Technology, American Nuclear Society, Long Island, NY, USA, October 1998, Report BNL-NCS-65712, Brookhaven National Laboratory.
