Dispersive Optical Potential Study for Proton-Nucleus Scattering Using Dispersion Relations

Soad, Marow Abdul Kream; Ali, Akram Mohammed

doi:10.37652/juaps.2024.144273.1160

	Dispersive Optical Potential Study for Proton-Nucleus Scattering Using Dispersion Relations
Journal of University of Anbar for Pure Science
Volume 18, Issue 1, June 2024, Pages 211-218 PDF (586.96 K)
Document Type: Research Paper
DOI: 10.37652/juaps.2024.144273.1160
Authors
marow abdul kream soad^* ¹; Akram Mohammed Ali²
¹Department of Physics, College of Science, University of Anbar, Ramadi, Iraq;
²Department of Physics, College of Science, University of Anbar, Baghdad, Iraq;
Abstract
Abstract: Usually in nucleon-nucleon reactions, optical potential is used to study the nuclear structures resulting from these reactions. As this potential during the reaction is subject to dispersion by the nuclei surface as well as the total size of the nucleus, it is very important to calculate the dispersive behaviour. We present an analytical and numerical expressions used to evaluate the dispersive contribution to the real potential of the imaginary part and surface contribution and applied to 9B+14C at energy 60 MeV. For both imaginary volume and surface potentials, solutions to the nuclear optical model dispersion relation have been obtained. For the volume imaginary term, a typical Brown-Rho shape has been considered with the parameters (n=2,m=2,4), and for the surface contribution, a Brown-Rho shape multiplied by the decreasing exponential. For exponent with any even value appearing in these forms, the analytical solutions are valid. The energy representation of the real and imaginary parts of the OMP is carried out by these approaches. Keywords: dispersion relation, imaginary potential, volume and surface, Brown-Rho function.
Keywords
dispersion relation; imaginary potential; volume and surface; Brown-Rho function

References
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Dispersive Optical Potential Study for Proton-Nucleus Scattering Using Dispersion Relations

[1]C. Mahaux, H. Ngo, and G. R. Satchler," Causality and the threshold anomaly of the nucleus-nucleus potential", (1986), Nucl. Phys. A 449, 354.

[3]J. P. Delaroche, Y. Wang, and J. Rapaport, "Neutron−⁹⁰Zr mean field from a dispersive optical model analysis",(1989) Phys. Rev. C 39, 391.

[4] C. Mahaux and R. Sartor, "Variational moment approach to the single-particle properties of protons in²⁰⁸Pb",

[5] C. H. Johnson, D. J. Horen, and C. Mahaux, "Unified description of the neutron−²⁰⁸Pb mean field between -20 and +165 MeV from the dispersion relation constraint", (1987), Phys. Rev. C 36, 2252.

[6] C. Mahaux and R. Sartor,” Single-particle potential and quasiparticle properties of protons in ²⁰⁸Pb” Nucl. Phys. A, 481 (3), (1988). 381-406

[9] Feshbach, "Unified theory of nuclear reactions",, Ann. of Phys. Volume 5, Issue 4, December 1958, Pages 357-390.

[10] Koning, A. J., & Delaroche, J. P. ,"Local and global nucleon optical models from 1 keV to 200 MeV",(2003). Nucl. Phys. A, 713, 231.

[18] Lijuan Hao, Weili Sun, and E. Sh. Soukhovitskiı, "A global dispersive coupled-channel potential for the A = 24–122 mass range up to 200 MeV",(2008) J. Phys. G: Nucl. Part. Phys. 35, 095103 .

[20] C. Mahaux , H. Ngo, "Effective masses, occupation probabilities and quasiparticle strengths in ²⁰⁸Pb",(1984), Nucl. Phys. A 431, 486.

[21] J. P. Delaroche, Y. Wang, J. Rapaport,” Neutron−⁹⁰Zr mean field from a dispersive optical model analysis”, Phys. Rev. C 39,391 (1989).

[22] Brown GE, Rho M.,” Scaling effective Lagrangian in a dense medium”, Phys. Rev. Lett. 66:2720–23 (1991).

[25] R. Capote, A. Molina, J.M. Quesada," A general numerical solution of dispersion relations for the nuclear optical model",J. Phys. G: Nucl. Part. Phys. 27, B15(2001).

[26] M.M. Nagadi, C.R. Howell, W. Tornow, et al., "Dispersive optical-model and coupled-channels descriptions of neutron scattering from ²⁷Al and ⁵⁹Co up to 80MeV", Phys. Rev. C 68,044610(2003).

[27] J. S. Bell, E. J. Squires, "A Formal Optical Model" Phys. Rev. Lett., 3, 96 (1959).

Dispersive Optical Potential Study for Proton-Nucleus Scattering Using Dispersion Relations

[1]C. Mahaux, H. Ngo, and G. R. Satchler," Causality and the threshold anomaly of the nucleus-nucleus potential", (1986), Nucl. Phys. A 449, 354.

[3]J. P. Delaroche, Y. Wang, and J. Rapaport, "Neutron−90Zr mean field from a dispersive optical model analysis",(1989) Phys. Rev. C 39, 391.

[4] C. Mahaux and R. Sartor, "Variational moment approach to the single-particle properties of protons in208Pb",

[5] C. H. Johnson, D. J. Horen, and C. Mahaux, "Unified description of the neutron−208Pb mean field between -20 and +165 MeV from the dispersion relation constraint", (1987), Phys. Rev. C 36, 2252.

[6] C. Mahaux and R. Sartor,” Single-particle potential and quasiparticle properties of protons in 208Pb” Nucl. Phys. A, 481 (3), (1988). 381-406

[9] Feshbach, "Unified theory of nuclear reactions",, Ann. of Phys. Volume 5, Issue 4, December 1958, Pages 357-390.

[10] Koning, A. J., & Delaroche, J. P. ,"Local and global nucleon optical models from 1 keV to 200 MeV",(2003). Nucl. Phys. A, 713, 231.

[18] Lijuan Hao, Weili Sun, and E. Sh. Soukhovitskiı, "A global dispersive coupled-channel potential for the A = 24–122 mass range up to 200 MeV",(2008) J. Phys. G: Nucl. Part. Phys. 35, 095103 .

[20] C. Mahaux , H. Ngo, "Effective masses, occupation probabilities and quasiparticle strengths in 208Pb",(1984), Nucl. Phys. A 431, 486.

[21] J. P. Delaroche, Y. Wang, J. Rapaport,” Neutron−90Zr mean field from a dispersive optical model analysis”, Phys. Rev. C 39,391 (1989).

[22] Brown GE, Rho M.,” Scaling effective Lagrangian in a dense medium”, Phys. Rev. Lett. 66:2720–23 (1991).

[25] R. Capote, A. Molina, J.M. Quesada," A general numerical solution of dispersion relations for the nuclear optical model",J. Phys. G: Nucl. Part. Phys. 27, B15(2001).

[26] M.M. Nagadi, C.R. Howell, W. Tornow, et al., "Dispersive optical-model and coupled-channels descriptions of neutron scattering from 27Al and 59Co up to 80MeV", Phys. Rev. C 68,044610(2003).

[27] J. S. Bell, E. J. Squires, "A Formal Optical Model" Phys. Rev. Lett., 3, 96 (1959).

[3]J. P. Delaroche, Y. Wang, and J. Rapaport, "Neutron−⁹⁰Zr mean field from a dispersive optical model analysis",(1989) Phys. Rev. C 39, 391.

[4] C. Mahaux and R. Sartor, "Variational moment approach to the single-particle properties of protons in²⁰⁸Pb",

[5] C. H. Johnson, D. J. Horen, and C. Mahaux, "Unified description of the neutron−²⁰⁸Pb mean field between -20 and +165 MeV from the dispersion relation constraint", (1987), Phys. Rev. C 36, 2252.

[6] C. Mahaux and R. Sartor,” Single-particle potential and quasiparticle properties of protons in ²⁰⁸Pb” Nucl. Phys. A, 481 (3), (1988). 381-406

[20] C. Mahaux , H. Ngo, "Effective masses, occupation probabilities and quasiparticle strengths in ²⁰⁸Pb",(1984), Nucl. Phys. A 431, 486.

[21] J. P. Delaroche, Y. Wang, J. Rapaport,” Neutron−⁹⁰Zr mean field from a dispersive optical model analysis”, Phys. Rev. C 39,391 (1989).

[26] M.M. Nagadi, C.R. Howell, W. Tornow, et al., "Dispersive optical-model and coupled-channels descriptions of neutron scattering from ²⁷Al and ⁵⁹Co up to 80MeV", Phys. Rev. C 68,044610(2003).