Born Approximation for Polarization Observables at the Scattering of Protons by 40Ca Nuclei

  • O. V. Babak Institute for Nuclear Research, Nat. Acad. of Sci. of Ukraine
  • Yu. A. Berezhnoy Karazin Kharkov National University
  • V. P. Mikhailyuk Institute for Nuclear Research, Nat. Acad. of Sci. of Ukraine
Keywords: optical model, Born approximation, intermediate energies, elastic scattering, polarization observables


A development of the optical model for the description of the hadron-nucleus scattering is proposed. When describing the behavior of polarization observables for the elastic proton scattering on 40Ca nuclei in the energy interval from 200 to 800 MeV, the Born approximation is used. Analytical expressions for the scattering amplitudes, as well as for the differential cross-sections and polarization observables, are obtained. The comparison of the scattering observables calculated in the 1st and 2nd Born approximations is made. It is shown that the observables calculated in this approach are in a reasonable agreement with the available experimental data.


H. Feshbach, C.E. Porter, V.F. Weisskopf. The formation of a compound nucleus in neutron reactions. Phys. Rev. 90, 166 (1953).

H. Feshbach, C.E. Porter, V.F. Weisskopf. Model for nuclear reactions with neutrons. Phys. Rev. 96, 448 (1954).

H. Feshbach. Unified theory of nuclear reactions. Ann. Phys. 5, 357 (1958).

P.E. Hodgson, Nuclear Reactions and Nuclear Structure, (Clarendon Press, 1971). [ISBN-10: 0198512619].

H. Feshbach. A unified theory of nuclear reactions. Ann. Phys. (New York) 281, 519 (2000).

R.D. Woods, D.S. Saxon. Diffuse surface optical model for nucleon-nuclei scattering. Phys. Rev. 95, 577 (1954).

W.T.H. van Oers. Optical-model analysis of p+40Ca elastic scattering from 10-180 MeV Phys. Rev. C 3, 1550 (1971).

A. Nadasen, P. Schwandt, P.P. Singh, W.W. Jacobs, A.D. Bacher, P.T. Debevec, M.D.Kaitchuck, J.T. Meek. Elastic scattering of 80-180 MeV protons and the proton-nucleus optical potential. Phys. Rev. C 23, 1023 (1981).

P. Schwandt, H.O. Meyer, W.W. Jacobs, A.D. Bacher, S.E. Vigdor, M.D. Kaitchuck, T.R. Donoghue. Analyzing power of proton-nucleus elastic scattering between 80 and 180 MeV. Phys. Rev. C 26, 55 (1982).

H. Seifert, J.J. Kelly, A.E. Feldman, B.S. Flanders, M.A. Khandaker, Q. Chen, A.D. Bacher, G.P.A. Berg, E.J. Stephenson, P. Karen, B.E. Norum, P. Welch,

A. Scott. Effective interaction for 16O(p,p') and 40Ca(p,p') at Ep = 200 MeV. Phys. Rev. C 47, 1615 (1993).

J.J. Kelly, P. Boberg, A.E. Feldman, B.S. Flanders, M.A. Khandaker, S.D. Hyman, H. Seifert, P. Karen, B.E. Norum, P. Welch, S. Nanda, A. Saha. Effective interaction for 40Ca(p,p') at Ep = 318 MeV. Phys. Rev. C 44, 2602 (1991).

D. Frekers, S.S.M. Wong, R.E. Azuma, T.E. Drake, J.D. King, R. Abegg, K.P. Jackson, C.A. Miller, S. Yen, W.P. Alford, R.L. Helmer, C. Broude, S. Mattsson,

E. Rost. Elastic and inelastic scattering of 362 MeV polarized protons from 40Ca Phys. Rev. C 35, 2236 (1987).

D.A. Hutcheon, W.C. Olsen, H.S. Sherif, R. Dymarz, J.M. Cameron, J. Johansson, P. Kitching, P.R. Liljestrand, W.J. McDonald, C.A. Miller, G.C. Neilson, D.M. Sheppard, D.K. McDaniels, J.R. Tinsley, P. Schwandt, L.W. Swenson, C.E. Stronach. The elastic scattering of intermediate energy protons from 40Ca and 208Pb. Nucl. Phys. A 483, 1 (1988).

A. Nadasen, S. Balaji, J. Brace, K.A.G. Rao, P.G. Roos, P. Schwandt, J.T. Ndefru. Nucleon elastic scattering potentials: Energy and isospin dependence. Phys. Rev. C 66, 064605 (2002).

A.J. Koning, J.P. Delaroche. Local and global nucleon optical models from 1 keV to 200 MeV. Nucl. Phys. A 713, 213 (2003).

G. Igo, G.S. Adams, T.S. Bauer, G. Pauletta, C.A. Whitten, Jr., A. Wriekat, G.W. Hoffmann, G.S. Blanpied, W.R. Coker, C. Harvey, R.P. Liljestrand, L. Ray, J.E. Spencer, H.A. Thiessen, C. Glashausser, N.M. Hintz, M.A. Oothoudt, H. Nann, K.K. Seth, B.E.Wood, D.K.McDaniels, M. Gazzaly. Elastic differential cross-sections and analyzing powers for p+40,42,44,48Ca at 0.8 GeV. Phys. Lett. B 81, 151 (1979).

L. Ray, G.W. Hoffmann, M. Barlett, J. McGill, J. Amann, G. Adams, G. Pauletta, M. Gazzaly, G.S. Blanpied. Proton elastic scattering from 40,42,44,48Ca at 800 MeV. Phys. Rev. C 23, 828 (1981).

R.W. Fergerson, M.L. Barlett, G.W. Hoffmann, J.A. Marshall, E.C. Milner, G. Pauletta, L. Ray, J.F. Amann, K.W. Jones, J.B. McClelland, M. Gazzaly, G.J. Igo. Spin-rotation parameter Q for 800 MeV proton elastic scattering from 16O,40Ca, and 208Pb Phys. Rev. C 33, 239 (1986).

B. Aas, E. Bleszynski, M. Bleszynski, M. Hajisaeid, G.J. Igo, F. Irom, G. Pauletta, A. Rahbar, A.T.M. Wang, C.F. Amann, T.A. Carey, W.D. Cornelius, J.B. McClelland, M. Barlett, G.W. Hoffmann, M. Gazzaly. Proton polarization observables for the elastic and inelastic scattering of 500 MeV protons from 40Ca and 208Pb. Nucl. Phys. A 446, 675 (1986).

G.W. Hoffmann, M.L. Barlett, G. Pauletta, L. Ray, J.F. Amann, K. Ones, J.B. McClelland, R.W. Fergerson, M.M. Gazzaly, B.C. Clark, R.L. Mercer. Large angle p+40Ca elastic scattering at 497.5 MeV. Phys. Rev. C 37, 1307 (1988).

E. Bleszynski, B. Aas, D. Adams, M. Bleszynski, G.J. Igo, T. Jaroszewicz, A. Ling, D. Lopiano, F. Sperisen, M.G. Moshi, C.A. Whitten, Jr., C.A. Whitten, K. Jones, J.B. McClelland. Energy dependence of relativistic effects in the elastic scattering of polarized protons from 16O and 40Ca. Phys. Rev. C 37, 1527 (1988).

L.G. Arnold, B.C. Clark, E.D. Cooper, H.S. Sherif, D.A. Hutcheon, P. Kitching, J.M. Cameron, R.P. Liljestrand, R.N. MacDonald, W.J. McDonald, C.A. Miller,

G.C. Neilson, W.C. Olsen, D.M. Sheppard, G.M. Stinson, D.K. McDaniels, J.R. Tinsley, R.L. Mercer, L.W. Swenson, P. Schwandt, C.E. Stronach. Energy dependence of the p-40Ca optical potential: A Dirac equation perspective. Phys. Rev. C 25, 936 (1982).

J.A. McNeil, L. Ray, S.J. Wallace. Impulse approximation NN amplitudes for proton-nucleus interactions. Phys. Rev. C 27, 2123 (1983).

B.C. Clark, S. Hama, R.L. Mercer, L. Ray, G.W. Hoffmann, B.D. Serot. Dirac-equation impulse approximation for intermediate-energy nucleon-nucleus scattering. Phys. Rev. Lett. 50, 1644 (1983).

N. Ottenstein, S.J.Wallace, J.A. Tjon. Elastic scattering of protons by 16O, 40Ca, and 208Pb at 200, 500, and 800 MeV: Relativistic and nonrelativistic analyses based on the impulse approximation. Phys. Rev. C 38, 2272 (1988).

N. Ottenstein, S.J. Wallace, J.A. Tjon.Elastic scattering of protons by 16O, 40Ca, and 208Pb at 200, 500, and 800 MeV: Effects of vacuum polarization and Pauli-blocking corrections. Phys. Rev. C 38, 2289 (1988).

S. Hama, B.C. Clark, E.D. Cooper, H.S. Sherif, R.L. Mercer. Global Dirac optical potentials for elastic proton scattering from heavy nuclei. Phys. Rev. C 41, 2737 (1990).

R.D. Amado, J. Piekarewicz, D.A. Sparrow, J.A. McNeil. Intermediate-energy-proton scattering, the Dirac equation, and nuclear structure. Phys. Rev. C 28, 2180 (1983).

J.J. Kelly, S.J. Wallace. Comparison between relativistic and nonrelativistic models of the nucleon-nucleon effective interaction. I. Normal-parity isoscalar transitions. Phys. Rev. C 49, 1315 (1994).

Yu.A. Berezhnoy, V.P. Mikhailyuk. Polarization of protons in the optical model. Chinese Phys. C 41, 024102 (2017).

L. Wolfenstein. Polarization of fast nucleons. Annu. Rev. Nucl. Sci. 6, 43 (1956).

A. Dar, B. Kozlowsky. Polarization in meson-baryon elastic scattering at high energies. Phys. Lett. 20, 314 (1966).

S. Varma. Polarization in elastic scattering at low energies. Nucl. Phys. A 97, 282 (1967).

Yu.A. Berezhnoy, V.P. Mikhailyuk, V.V. Pilipenko. Intermediate energy multiple scattering of particles by light a-cluster nuclei. Int. J. Mod. Phys. E 24, 1530004 (2015).

D.A. Goldberg, S.M. Smith. Criteria for the elimination of discrete ambiguities in nuclear optical potentials. Phys. Rev. Lett. 29, 500 (1972).

D.A. Goldberg, S.M. Smith, H.G. Pugh, P.Q. Boos, N.S. Wall. Scattering of 139-MeV alpha particles by 58Ni and 208Pb. Phys. Rev. 7, 1938 (1973).

G.D. Alkhazov, S.L. Belostotsky, A.A. Vorobyov. Scattering of 1 GeV protons on nuclei. Phys. Rep. 42, 89 (1978).

L. Ray, G.W. Hoffmann, W.R. Coker. Nonrelativistic and relativistic descriptions of proton-nucleus scattering. Phys. Rep. 212, 223 (1992).

How to Cite
Babak, O., Berezhnoy, Y., & Mikhailyuk, V. (2020). Born Approximation for Polarization Observables at the Scattering of Protons by 40Ca Nuclei. Ukrainian Journal of Physics, 65(5), 369.
Fields and elementary particles