A nonlocal optical potential with a Gaussian nonlocality for proton elastic scattering off light 1p-shell nuclei


In a recent work we used the nonlocal optical model of Perey and Buck (Nucl Phys A 32:353, 1962) to fit the angular distribution data corresponding to neutron elastic scattering off light nuclei from \(^6\hbox {Li}\) to \(^{18}\hbox {O}\) over the 9–35 MeV energy range. Although such nuclei posses diffuse edges that complicate the scattering process, the model resulted in improved angular distribution fits compared to those obtained using local optical models. In this work we extend the treatment to the case of proton elastic scattering off light 1p-shell nuclei, but consider the wider 10–70 MeV energy range. No single global set of nonlocal parameters adequately described the measured data across the entire energy range. Instead, we obtained two global sets of fixed nonlocal parameters; one corresponds to the 10–39 MeV range, the other is for the higher 40–70 MeV incident energies. Each set resulted in angular distribution fits which are in very good agreement with experimental data even in the large-angle scattering region, which is usually endowed by nonlocal effects. The fits were improved even further by expressing the imaginary volume and imaginary surface depths as linear functions of energy and the \((N-Z)/A\) asymmetry term. This indicates that there is still need for energy-dependent parameters even when nonlocality is explicitly included in the potential. We also used the model to predict elastic angular distributions for proton scattering off nuclei not included in the fitting procedure. The theoretical predictions showed very good agreement with experiment. As a further test of the nonlocal model, we calculated total reaction cross sections for proton scattering off light 1p-shell nuclei. Our predictions are in fair overall agreements with the experimental data.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This work did not involve any experimental measurements. We present a nonlocal optical model for proton elastic scattering off light 1p-shell nuclei. The global parameters of our model are presented in this work.]


  1. 1.

    H. Feshbach, Ann. Phys. (NY) 5, 357 (1958)

    ADS  Google Scholar 

  2. 2.

    H. Feshbach, Ann. Phys. (NY) 19, 287 (1962)

    ADS  Google Scholar 

  3. 3.

    F.G. Perey, B. Buck, Nucl. Phys. A 32, 353 (1962)

    Google Scholar 

  4. 4.

    K. Amos, L. Canton, G. Pisent, J.P. Svenne, D. van der Knijff, Nucl. Phys. A 728, 65 (2003)

    ADS  Google Scholar 

  5. 5.

    E. Cereda, M. Pignanelli, S. Micheletti, H.V. von Geramb, M.N. Harakeh, R. De Leo, G. D’Erasmo, A. Pantaleo, Phys. Rev. C 26, 1941 (1982)

    ADS  Google Scholar 

  6. 6.

    P. Fraser, K. Amos, S. Karataglidis, L. Canton, G. Pisent, J. Svenne, Eur. Phys. J. A 35, 69 (2008)

    ADS  Google Scholar 

  7. 7.

    G.H. Rawitscher, D. Lukaszek, R.S. Mackintosh, S.G. Cooper, Phys. Rev. C 49, 1621 (1994)

    ADS  Google Scholar 

  8. 8.

    W.S. Al-Rayashi, M.I. Jaghoub, Phys. Rev. C 93, 064311 (2016)

    ADS  Google Scholar 

  9. 9.

    S.B. Masadeh, M.I. Jaghoub, Phys. Rev. C 100, 014603 (2019)

    ADS  Google Scholar 

  10. 10.

    A. Bonaccorso, R.J. Charity, Phys. Rev. C 89, 024619 (2014)

    ADS  Google Scholar 

  11. 11.

    M.I. Jaghoub, M.F. Hassan, G.H. Rawitscher, Phys. Rev. C 84, 034618 (2011)

    ADS  Google Scholar 

  12. 12.

    M.I. Jaghoub, Phys. Rev. C 85, 024606 (2012)

    ADS  Google Scholar 

  13. 13.

    R.A. Zureikat, M.I. Jaghoub, Nucl. Phys. A 916, 183 (2013)

    ADS  Google Scholar 

  14. 14.

    I.N. Ghabar, M.I. Jaghoub, Phys. Rev. C 91, 064308 (2015)

    ADS  Google Scholar 

  15. 15.

    M.I. Jaghoub, Phys. Rev. A 74, 032702 (2006)

    ADS  Google Scholar 

  16. 16.

    M.I. Jaghoub, G.H. Rawitscher, Nucl. Phys. A 877, 59 (2012)

    ADS  Google Scholar 

  17. 17.

    M. Al Jaghoub, Eur. Phys. J. A 11, 175 (2001)

    ADS  Google Scholar 

  18. 18.

    M.I. Jaghoub, Eur. Phys. J. A 13, 349 (2002)

    ADS  Google Scholar 

  19. 19.

    M.I. Jaghoub, Eur. Phys. J. A 15, 443 (2006)

    ADS  Google Scholar 

  20. 20.

    M.I. Jaghoub, Eur. Phys. J. A 28, 253 (2006)

    ADS  Google Scholar 

  21. 21.

    O. Bayrak, A. Soylu, I. Boztosun, Chin. Phys. Lett. 28, 040304 (2011)

    ADS  Google Scholar 

  22. 22.

    Y.B. Ateş, U.S. Okorie, A.N. Ikot, E. Olğar, Phys. Scr. 94, 115705 (2019)

    ADS  Google Scholar 

  23. 23.

    Y. Tian, D.-Y. Pang, Z.-Y. Ma, Int. J. Mod. Phys. E 24, 1550006 (2015)

    ADS  Google Scholar 

  24. 24.

    A.E. Lovell, P.-L. Bacq, P. Capel, F.M. Nunes, L.J. Titus, Phys. Rev. C 96, 051601(R) (2017)

    ADS  Google Scholar 

  25. 25.

    M.I. Jaghoub, A.E. Lovell, F.M. Nunes, Phys. Rev. C 98, 024609 (2018)

    ADS  Google Scholar 

  26. 26.

    T. Aqel, M.I. Jaghoub, Nucl. Phys. A 989, 145 (2019)

    ADS  Google Scholar 

  27. 27.

    L. Titus, A. Ross, F. Nunes, Comput. Phys. Commun. 207, 499 (2016)

    ADS  Google Scholar 

  28. 28.

    I.J. Thompson, Comput. Phys. Rep. 7, 167 (1988)

    ADS  Google Scholar 

  29. 29.

    N. Otuka, E. Dupont, V. Semkova, B. Pritychenko, A.I. Blokhin, M. Aikawa, S. Babykina, M. Bossant, G. Chen, S. Dunaeva, R.A. Forrest, T. Fukahori, N. Furutachi, S. Ganesan, Z. Ge, O.O. Gritzay, M. Herman, S. Hlavač, K. Katō, B. Lalremruata, Y.O. Lee, A. Makinaga, K. Matsumoto, M. Mikhaylyukova, G. Pikulina, V.G. Pronyaev, A. Saxena, O. Schwerer, S.P. Simakov, N. Soppera, R. Suzuki, S. Takács, X. Tao, S. Taova, F. Tárkányi, V.V. Varlamov, J. Wang, S.C. Yang, V. Zerkin, Y. Zhuang, Towards a more complete and accurate experimental nuclear reaction data library (EXFOR): international collaboration between Nuclear Reaction Data Centres (NRDC). Nucl. Data Sheets 120, 272 (2014)

    ADS  Google Scholar 

  30. 30.

    H.J. Votava, T.B. Clegg, E.J. Ludwig, W.J. Thompson, Nucl. Phys. A 204, 3 (1973)

    Google Scholar 

  31. 31.

    I.E. Dayton, G. Schrank, Phys. Rev. 101, 4 (1956)

    Google Scholar 

  32. 32.

    N.M. Clarke, E.J. Burge, D.A. Smith, J.C. Dore, Nucl. Phys. A 157, 1 (1970)

    Google Scholar 

  33. 33.

    M. Harada, Y. Watanabe, A. Yamamoto, S. Yoshioka, K. Sato, T. Nakashima, H. Ijiri, H. Yoshida, Y. Uozumi, N. Koori, S. Meigo, O. Iwamoto, T. Fukahori, S. Chiba, J. Nucl. Sci. Technol. 36, 4 (1999)

    Google Scholar 

  34. 34.

    T. Fujisawa, N. Kishida, T. Kubo, T. Wada, Y. Toba, T. Hasegawa, M. Sekiguchi, N. Ueda, M. Yasue, F. Soga, H. Kamitsubo, M. Nakamura, K. Hatanaka, Y. Wakuta, T. Tanaka, A. Nagao, J. Phys. Soc. Jpn. 50, 10 (1981)

    Google Scholar 

  35. 35.

    E. Fabrici, S. Micheletti, M. Pignanelli, F.G. Resmini, R. De Leo, G. D’Erasmo, A. Pantaleo, Phys. Rev. C 21, 3 (1980)

    Google Scholar 

  36. 36.

    S. Kobayashi, S. Motonaga, Y. Chiba, K. Katori, A. Stricker, T. Fujisawa, T. Wada, J. Phys. Soc. Jpn. 29, 1 (1970)

    ADS  Google Scholar 

  37. 37.

    A.C.L. Barnard, J.B. Swint, T.B. Clegg, Nucl. Phys. 86, 1 (1966)

    Google Scholar 

  38. 38.

    A.N. Zhu, Chen Quan, Cheng Ye-HAO, Shen Dong-Jun, Guo Gang, Chin. Phys. Lett. 20, 4 (2003)

    Google Scholar 

  39. 39.

    M. Ieiri, H. Sakaguchi, M. Nakamura, H. Sakamoto, H. Ogawa, M. Yosol, T. Ichihara, N. Isshiki, Y. Takeuchi, H. Togawa, T. Tsutsumi, S. Hirata, T. Nakano, S. Kobayashi, Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrom. Detect. Assoc. Equip. 257, 2 (1987)

    Google Scholar 

  40. 40.

    V.I. Grantsev, V.I. Konfederatenko, V.A. Kornilov, O.F. Nemets, R.G. Ofengenden, B.A. Rudenko, M.V. Sokolov, B.G. Struzhko, Ukrainskii Fizicheskii Zhurnal 28, 4 (1983)

    Google Scholar 

  41. 41.

    Itaru Nonaka, Yoshio Saji, Arata Suzuki, Hisashi Yamaguchi, Robert Eisberg, Yoshihide Ishisaki, Ken Kikuchi, Kazuhisa Matsuda, Takashi Mikumo, Yutaka Nakajima, J. Phys. Soc. Jpn. 17, 12 (1962)

    Google Scholar 

  42. 42.

    S. Kato, K. Okada, M. Kondo, A. Shimizu, K. Hosono, T. Saito, N. Matsuoka, S. Nagamachi, K. Nisimura, N. Tamura, K. Imai, K. Egawa, M. Nakamura, T. Noro, H. Shimizu, K. Ogino, Y. Kadota, Nucl. Instrum. Methods 169, 3 (1980)

    Google Scholar 

  43. 43.

    M. Girod, Nguyen Van Sen, J.P. Longequeue, Tsan Ung Chan, J. Phys. 31, 2 (1970)

    Google Scholar 

  44. 44.

    S. Kobayashi, J. Phys. Soc. Jpn. 15, 7 (1960)

    ADS  Google Scholar 

  45. 45.

    G.M. Crawley. Thesis/Dissertation (Inelastic Proton Scattering in the 2S-1D Shell). Princeton University (1965)

  46. 46.

    J.M. Cameron, J.R. Richardson, W.T.H. Vanoers, J.W. Verba, Phys. Rev. 167, 4 (1968)

    Google Scholar 

  47. 47.

    J.A. Fannon, E.J. Burge, D.A. Smith, N.K. Ganguly, Nucl. Phys. A 97, 2 (1967)

    Google Scholar 

  48. 48.

    F.E. Bertrand, R.W. Peelle, Phys. Rev. C 8, 3 (1973)

    Google Scholar 

  49. 49.

    H. Sakaguchi, PhD Thesis (Systematic Study on the Elastic Scattering of 65 MeV Polarized Protons). Kyoto University (1982)

  50. 50.

    O. Karban, P.D. Greaves, V. Hnizdo, J. Lowe, N. Berovic, H. Wojciechowski, G.W. Greenlees, Nucl. Phys. A 132, 3 (1969)

    Google Scholar 

  51. 51.

    E. Fabrici, S. Micheletti, M. Pignanelli, F.G. Resmini, R. De Leo, G. D’Erasmo, A. Pantaleo, J.L. Escudie, A. Tarrats, Phys. Rev. C 21, 3 (1980)

    Google Scholar 

  52. 52.

    E. Khan, Y. Blumenfeld, Nguyen Van Giai, T. Suomijarvi, N. Alamanos, F. Auger, G. Colo, N. Frascaria, A. Gillibert, T. Glasmacher, M. Godwin, K.W. Kemper, V. Lapoux, I. Lhenry, F. Marechal, D.J. Morrissey, A. Musumarra, N.A. Orr, S. Ottini-Hustache, P. Piattelli, E.C. Pollacco, P. RousselChomaz, J.C. Roynette, D. Santonocito, J.E. Sauvestre, J.A. Scarpaci, C. Volpe, Phys. Lett. B 490, 1 (2000)

    MathSciNet  Google Scholar 

  53. 53.

    A.J. Koning, J.P. Delaroche, Nucl. Phys. A 713, 231 (2003)

    ADS  Google Scholar 

  54. 54.

    B.A. Watson, P.P. Singh, R.E. Segel, Phys. Rev. 182, 4 (1969)

    Google Scholar 

  55. 55.

    M.S. Hussein, E. Farrelly-Pessoa, H.R. Schelin, R.A. Douglas, Nucl. Phys. A 458, 3 (1986)

    Google Scholar 

  56. 56.

    L.F. Hansen, S.M. Grimes, J.L. Kammerdiener, V.A. Madsen, Phys. Rev. C 7, 6 (1973)

    Google Scholar 

  57. 57.

    H.F. Lutz, D.W. Heikkinen, W. Bartolini, Nucl. Phys. A 198, 1 (1972)

    Google Scholar 

  58. 58.

    C.J. Joachain, Quantum Scattering Theory (North-Holland Publishing Company, Amsterdam, 1975), p. 502

    Google Scholar 

  59. 59.

    D.G. Montague, R.K. Cole, M. Makino, C.N. Waddell, Nucl. Phys. A 199, 3 (1973)

    Google Scholar 

  60. 60.

    I. Slaus, D.J. Margaziotis, R.F. Carlson, W.T.H. VanOers, J.R. Richardson, Phys. Rev. C 12, 3 (1975)

    Google Scholar 

  61. 61.

    J.F. Dicello, G. Igo, Phys. Rev. C 2, 2 (1970)

    Google Scholar 

  62. 62.

    R.F. Carlson, A.J. Cox, J.R. Nimmo, N.E. Davison, S.A. Elbakr, J.L. Horton, A. Houdayer, A.M. Sourkes, W.T.H. VanOers, D.J. Margaziotis, Phys. Rev. C 12, 4 (1975)

    Google Scholar 

  63. 63.

    J.J. Menet, E.E. Gross, J.J. Malanify, A. Zucker, Phys. Rev. C 4, 4 (1971)

    Google Scholar 

  64. 64.

    E.J. Burge, Nucl. Phys. 13, 4 (1959)

    Google Scholar 

  65. 65.

    J.J. Menet, E.E. Gross, J.J. Malanify, A. Zucker, Phys. Rev. Lett. 22, 21 (1969)

    Google Scholar 

  66. 66.

    R.F. Carlson, A. Auce, R. Johansson, G. Tibell, B.C. Clark, L.K. Kerr, S. Hama, Nucl. Phys. A 653, 4 (1999)

    Google Scholar 

  67. 67.

    R.F. Carlson, A.J. Cox, J.R. Nimmo, N.E. Davison, S.A. Elbakr, J.L. Horton, A. Houdayer, A.M. Sourkes, W.T.H. VanOers, D.J. Margaziotis, Phys. Rev. C 12, 4 (1975)

    Google Scholar 

  68. 68.

    J. Stevens, H.F. Lutz, S.F. Eccles, Nucl. Phys. 76, 129 (1966)

    Google Scholar 

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We thank the Deanship of Scientific Research at the University of Jordan for funding this work and our previous work of Ref. [26].

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Communicated by Pierre Capel

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Aqel, T., Jaghoub, M.I. A nonlocal optical potential with a Gaussian nonlocality for proton elastic scattering off light 1p-shell nuclei. Eur. Phys. J. A 56, 216 (2020). https://doi.org/10.1140/epja/s10050-020-00226-5

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