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Response of multi-step compound pre-equilibrium reaction cross sections for the (p, n) reactions to forms of optical model parameters

  • Felix S. Olise
  • Oludaisi I. Oladunjoye
  • Afis Ajala
  • Sunday D. Olorunfunmi
  • Hezekiah B. Olaniyi
Article

Abstract

In furtherance to improving agreement between calculated and experimental nuclear data, the nuclear reaction code GAMME was used to calculate the multi-step compound (MSC) nucleus double differential cross sections (DDCs) for proton-induced neutron emission reactions using the Feshbach-Kerman-Koonin (FKK) formalism. The cross sections were obtained for reactor structural materials involving 52Cr(p, n)52Mn, 56Fe(p, n)56Co, and 60Ni(p, n)60Cu reactions at 22.2 MeV incident energy using the zero-range reaction mechanism. Effective residual interaction strength was 28 MeV, and different optical potential parameters were used for the entrance and exit channels of the proton-neutron interactions. The calculated DDCs were fitted to experimental data at the same backward angle of 150°, where the MSC processes dominate. The calculated and experimental data agree well in the region of pre-equilibrium (MSC) reaction dominance against a weaker fit at the lower emission energies. We attribute underestimations to contributions from the other reaction channels and disagreement at higher outgoing energies to reactions to collectively excited states. Contrary to the FKK multi-step direct calculations, contributions from the higher stages to the DDCs are significant. Different sets of parameters resulted in varying levels of agreement of calculated and experimental data for the considered nuclei.

Keywords

Proton-neutron interaction Multi-step compound theory Optical model parameters Structural materials Nuclear reactor facilities 

References

  1. 1.
    H. Feshbach, A. Kerman, S. Koonin, The statistical theory of multi-step compound and direct reactions. Ann. Phys. 125, 429–476 (1980). doi: 10.1016/0003-4916(80)90140-2 CrossRefGoogle Scholar
  2. 2.
    R. Bonetti, M.B. Chadwick, P.E. Hodgson et al., The Feshback-Kerman-Koonin multistep compound reaction theory. Phys. Rep. 202(4), 171–231 (1991). doi: 10.1016/0370-1573(91)90105-U CrossRefGoogle Scholar
  3. 3.
    R. Bonetti, A.J. Koning, J.M. Akkermans et al., The Feshback-Kerman-Koonin multistep compound reaction theory. Phys. Rep. 247, 1–58 (1994). doi: 10.1016/0370-1573(94)90153-8 CrossRefGoogle Scholar
  4. 4.
    E. Gadioli, P.E. Hodson, Pre-equilibrium nuclear reactions (Oxford University Press, Oxford, 1992). ISBN 0-19-851734-3Google Scholar
  5. 5.
    F.S. Olise, A. Ajala, H.B. Olaniyi, Some calculated (p, α) cross-sections using the alpha particle knock-on and triton pick-up reaction mechanisms: an optimisation of the single-step Feshbach-Kerman-Koonin (FKK) theory. Nucl. Eng. Technol. 48, 482–494 (2016). doi: 10.1016/j.net.2015.11.010 CrossRefGoogle Scholar
  6. 6.
    T. Tamura, T. Udagawa, D.H. Fengl et al., Deep inelastic reactions treated as multi-step direct reaction processes application to (p, p´) reaction. Phys. Lett. B 66(2), 109–112 (1977). doi: 10.1016/0370-2693(77)90151-4 CrossRefGoogle Scholar
  7. 7.
    T. Tamura, T. Udagawa, H. Lenske, Multistep direct reaction analysis of continuum spectra in reactions induced by light ions. Phys. Rev. C 26(2), 379–404 (1982). doi: 10.1103/PhysRevC.26.379 CrossRefGoogle Scholar
  8. 8.
    H. Nishioka, J.J.M. Verbaarschot, H.A. Weidenmüller et al., Statistical theory of precompound reactions: the multi-step compound process. Ann. Phys. 172(1), 67–99 (1986). doi: 10.1016/0003-4916(86)90020-5 CrossRefGoogle Scholar
  9. 9.
    H. Nishioka, H.A. Weidenmüller, S. Yoshida, Statistical theory of precompound reactions: the multi-step direct process. Ann. Phys. 183(1), 166–187 (1988). doi: 10.1016/0003-4916(88)90250-3 CrossRefGoogle Scholar
  10. 10.
    H. Feshbach, in Proceedings of the International Conference on Nuclear Physics (Munich), vol. II, ed. By J. de Boer, H.J. Mang (Amsterdam, North-Holland, 1973), p. 632Google Scholar
  11. 11.
    H.A. Bethe, A continuum theory of the compound nucleus. Phys. Rev. 57, 1125–1144 (1940). doi: 10.1103/PhysRev.57.1125 CrossRefMATHGoogle Scholar
  12. 12.
    O. Bersillon, in Lectures on the Computer Code SCAT-2, Workshop on Applied Nuclear Theory and Nuclear Model Calculations For Nuclear Technology Applications, Trieste, Italy, 15 Feb–18 Mar (1988)Google Scholar
  13. 13.
    H. Feshbach, C.E. Porter, V.F. Weisskopf, Model for nuclear reactions with neutrons. Phys. Rev. 96, 448–464 (1954). doi: 10.1103/PhysRev.96.448 CrossRefMATHGoogle Scholar
  14. 14.
    R.D. Woods, D.C. Saxon, Diffuse surface optical model for nucleon-nuclei scattering. Phys. Rev. 95(2), 577–578 (1954). doi: 10.1103/PhysRev.95.577 CrossRefGoogle Scholar
  15. 15.
    A.M.R. Rahman, Neutron cross-sections for 55Mn in the energy range from 0.2 to 22 MeV. Turk. J. Phys. 36, 343–351 (2012). doi: 10.3906/fiz-1107-3 Google Scholar
  16. 16.
    International Atomic Energy Agency, in Handbook for Calculations of Nuclear Reaction Data, RIPL-2 IAEA, IAEA-Tecdoc-1506, Vienna, vol 47 (2006)Google Scholar
  17. 17.
    B.V. Carlson, in Optical Model Calculations with the Code ECIS95, Workshop on Nuclear Data and Nuclear Reactors: Physics, Design and Safety, Trieste, Italy, 13 Mar–14 April (2000)Google Scholar
  18. 18.
    A.G. Camacho, P.R.S. Gomes, J. Lubian et al., Optical model calculations on the threshold anomaly for the 6Li + 28Si and 7Li + 28Si systems at near-Coulomb-barrier energies. Phys. Rev. C (2010). doi: 10.1103/PhysRevC.82.067601 Google Scholar
  19. 19.
    S. Kunieda, N. Shigyo, K. Ishibashi, Nuclear data evaluations on zirconium, niobium and tungsten for neutron and proton incidence up to 200 MeV. J. Nucl. Sci. Technol. 41(11), 1047–1058 (2004). doi: 10.1080/18811248.2004.9726329 CrossRefGoogle Scholar
  20. 20.
    M.E. Kürkçüoğlu, H. Aytekin, I. Boztosun, Optical model analysis of the 16O + 16O nuclear scattering reaction around ELab = 5 Mev/nucleon. Gazi Univ. J. Sci. 19(2), 105–112 (2006)Google Scholar
  21. 21.
    G.M. Perey, F.G. Perey, Compilation of phenomenological optical-model parameters 1954–1975. Atom. Data Nucl. Data Tables 17, 1–101 (1976). doi: 10.1016/0092-640X(76)90007-3 CrossRefGoogle Scholar
  22. 22.
    P.A. Moldauer, Optical model of low energy neutron interactions with spherical nuclei. Nucl. Phys. 47, 65–92 (1963). doi: 10.1016/0029-5582(63)90854-X CrossRefGoogle Scholar
  23. 23.
    C. Mahaux, R. Sartor, The p-40Ca and n-40Ca mean fields from the iterative moment approach. Nucl. Phys. A 484(2), 205–263 (1988). doi: 10.1016/0375-9474(88)90071-1 CrossRefGoogle Scholar
  24. 24.
    C. Mahaux, R. Sartor, Single-particle potential and quasiparticle properties of protons in 208Pb. Nucl. Phys. A 481, 381–406 (1988). doi: 10.1016/0375-9474(88)90335-1 CrossRefGoogle Scholar
  25. 25.
    M. Jamion, C. Mahaux, Real part of the neutron and proton optical potentials at 11 MeV for mass numbers 40 ≤ A ≤ 76. Phys. Rev. C 34, 2084–2096 (1986). doi: 10.1103/PhysRevC.34.2084 CrossRefGoogle Scholar
  26. 26.
    J. Rapaport, An optical model analysis of neutron scattering. Phys. Rev. 87(2), 25–75 (1982). doi: 10.1016/0370-1573(82)90105-3 Google Scholar
  27. 27.
    D. Wilmore, J. Hodgson, Neutron scattering and reactions on 59Co from 1–20 MeV. J. Phys. G: Nucl. Phys. 11(9), 1007–1023 (1985). doi: 10.1088/0305-4616/11/9/010 CrossRefGoogle Scholar
  28. 28.
    K. Yabana, Y. Ogawa, Y. Suzuki, Break-up effect on the elastic scattering and the optical potential of 11Li. Phys. Rev. C 45, 2909–2918 (1992). doi: 10.1103/PhysRevC.45.2909 CrossRefGoogle Scholar
  29. 29.
    M.N. Islam, N. Siddiqua, A.K.M. Harunar-Rashid, Neutron cross sections for 56Fe and 238U, from 0.2 to 22 MeV energy. J. Phys. G: Nucl. Part. Phys. (1994). doi: 10.1088/0954-3899/20/9/016 Google Scholar
  30. 30.
    R. Bonetti, M.B. Chadwick, GAMME Code, Oxford University Report, OUNP-91-16 (1991)Google Scholar
  31. 31.
    N.S. Biryukov, B.V. Zhuravlev, A.P. Rudenko et al., Spin-dependence parameter from neutron angular distributions in (p, n) reactions. Sov. J. Nucl. Phys. (1979). doi: 10.1134/S1063776111060124 Google Scholar
  32. 32.
    P. Demetriou, P. Kanjanarat, P.E. Hodgson, FKK analysis of 14 MeV neutrons-induced reactions. J. Phys. G: Nucl. Part. Phys. 20, 1779–1788 (1994). doi: 10.1088/0954-3899/20/11/007 CrossRefGoogle Scholar
  33. 33.
    H.B. Olaniyi, P. Demetriou, P.E. Hodgson, Analysis of (p, α) reaction using the pre-equilibrium multi-step direct Feshbach-Kerman-Koonin theory. J. Phys. G: Nucl. Part. Phys. 21, 361–375 (1995). doi: 10.1088/0954-3899/21/3/011 CrossRefGoogle Scholar
  34. 34.
    G.F. Bertsch, H. Esbensen, The (p, n) reaction and the nucleon–nucleon force. Rep. Prog. Phys. 50, 607–654 (1987). doi: 10.1088/0034-4885/50/6/001 CrossRefGoogle Scholar
  35. 35.
    P. Obložinsky, Particle-hole state densities for statistical multi-step compound reactions. Nucl. Phys. A 453(1), 127–140 (1986). doi: 10.1007/978-94-009-4636-1_14 CrossRefGoogle Scholar
  36. 36.
    A. Gilbert, A.G.W. Cameron, A composite nuclear-level density formula with shell corrections. Can. J. Phys. 43(8), 1446–1496 (1965). doi: 10.1139/p65-139 CrossRefGoogle Scholar
  37. 37.
    F.D. Becchetti, G.W. Greenlees, Nucleon-nucleus optical-model parameters, A > 40, E > 50 MeV. Phys. Rev. 182(4), 1190–1209 (1969). doi: 10.1103/PhysRev.182.1190 CrossRefGoogle Scholar
  38. 38.
    D. Wilmore, P.E. Hodgson, The calculation of neutron cross-sections from optical potentials. Nucl. Phys. 55, 673–694 (1964). doi: 10.1016/0029-5582(64)90184-1 CrossRefGoogle Scholar
  39. 39.
    D.M. Patterson, R.R. Doering, A. Galonsky, An energy-dependent lane-model nucleon-nucleus optical potential. Nucl. Phys. A 263, 261–275 (1976). doi: 10.1016/0375-9474(76)90172-X CrossRefGoogle Scholar

Copyright information

© Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Chinese Nuclear Society, Science Press China and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Felix S. Olise
    • 1
  • Oludaisi I. Oladunjoye
    • 1
  • Afis Ajala
    • 1
  • Sunday D. Olorunfunmi
    • 1
  • Hezekiah B. Olaniyi
    • 1
  1. 1.Department of Physics and Engineering PhysicsObafemi Awolowo UniversityIle-IfeNigeria

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