A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes

Haiddar Al-Mustafa; Anees Belal

doi:doi:10.11648/j.ns.20190404.12

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A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes

Haiddar Al-Mustafa, Anees Belal

Published in Nuclear Science (Volume 4, Issue 4)

Received: 10 November 2019 Accepted: 2 December 2019 Published: 10 December 2019

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Abstract

A dispersive optical model analysis of the proton scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100MeV and for constant input values of the parameters of this mean field. This mean field is called (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section, polarization for selected energy showed the excellent agreement with available experimental data and with these resulted from global parameterization of the optical model potential.

Published in	Nuclear Science (Volume 4, Issue 4)
DOI	10.11648/j.ns.20190404.12
Page(s)	44-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Dispersive Optical Model Analysis (DOMA), (Coulomb-Nuclear) Interference Potential (CNIP), Dispersion Relations (DR), Mean Field, Fermi Energy, Cross Section, Polarization

References

[1]	Hodgson, P. E. (1990). The unification of the nuclear optical potential, Contemporary Physics, 31: 5, 295-308, DOI: 10.1080/00107519008213780.
[2]	Koning, A. J., & Delaroche, J. P. (2003). Nucl. Phys. A713, 231.
[3]	Mahaux, C., & Sartor, R. (1991). Dispersion Relation Approach to the Mean Field and Spectral Functions of Nucleons in 40Ca, Nuclear Physics, A528, pp. 253-297, Elsevier Science Publishers B. V. (North-Holland).
[4]	Mahaux, C., & Satchler, G. R. (1993). Temporal Nonlocality of Nuclear and Atomic Mean Fields, Nuclear Physics, A560, pp. 5-22, Elsevier Science Publishers B. V. (North-Holland).
[5]	IAEA, (2006). Handbook for Calculations of Nuclear Reaction Data, RIPL-2, IAEA in Austria, (Final report of a coordinated research project, IAEA-TECDOC-1506), pp. 47-69.
[6]	Melkanoff, M. A, Saxon, D. S, Jnodvik, J. S., & Cantor, D. G. (1961). A Fortran Program for Elastic Scattering Analyses with the Nuclear Optical Model, University of California Press Berkeley and Los Angeles, Retrieved August 24, 2009 [EBook #29784], online at www.gutenberg.org, p. 111.
[7]	Belal. A., & Al-Mustafa, H. (2019). Program Design for Analyzing the Optical Model of the (Coulomb - Nuclear) Interference Potential, Journal of AL Baath University, Homs- Syria, 41 (18), 71-102.
[8]	Belal. A., & Al-Mustafa, H. (2019). Program Design for Analyzing the Dispersive Optical Model of the (Coulomb - Nuclear) Interference Potential, Journal of AL Baath University, Homs- Syria, 41 (17), 51-80.
[9]	Bechetti, F. D., & Greenlees, G. W. (1969)- Nucleon-Nucleus Optical Model Potential, Phys. Rev, 182, 1190P.
[10]	Menet, J. H, Gross, E, Malanify, J., & ZUCKER, A. (1972). Phys. Rev. C4, 1114 P.
[11]	Varner, R. L, Thompson. W. J, Mcabee, T. L, Ludwig, E. J., & Clegg, T. B. (1991)- A Global Nucleon Optical Model Potential. PHYSICS REPORTS (Review Section of Physics Letters) 201, NO. 2, pp. 57-119. Elsevier Science Publishers B. V. (North-Holland).
[12]	Audi, G., & Wapstra, A. H. (1993). The Isotopic Mass Data. Nucl. Phys A. 565, 1-65.
[13]	Audi, G., & Wapstra, A. H. (1995). The Isotopic Mass Data. Nucl. Phys A. 595, 409-480.
[14]	Rosman, K. J. R., & Taylor, P. D. P. (1999). The Percent Natural Abundance Data. (1997 report of the IUPAC Subcommittee for Isotopic Abundance Measurements). Pure Appl. Chem., 71, 1593-1607.
[15]	Wieser, M. E. (2006). Atomic Weights of the Elements 2005. Department of Physics and Astronomy, University of Calgary, Calgary, Canada. (2006 IUPAC TECHNICAL REPORT). Pure Appl. Chem., Vol. 78, No. 11, pp. 2051–2066. DOI: 10.1351/pac200678112051.
[16]	Nasr, T. N, Sourkes, A. M, Margaziotis, D. J., & Cox, A. J (1978). Measurements of the Total Reaction Cross Section for Protons on Ti and B Between 20 and 50 MeV. Canadian Journal of Physical, volume 56, Page 56. (JANIS 4.0- Local- Incident proton data / EXFOR / Ti48 / (NON) / 00746.002, (8pts)).
[17]	Menet, J. J, Groos, E. E, Malanify, J. J., & Zucker, A. (1971). Total- Reaction- Cross Section Measurements for 30-60 MeV Protons and The Imaginary Optical Potential. Physical Review, Part C, Nuclear Physics, volume 4, Page 1114. (JANIS 4.0- Local- Incident proton data / EXFOR / Ti50 / (. NON) / 00081.018, (1pts)).

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APA Style

Haiddar Al-Mustafa, Anees Belal. (2019). A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nuclear Science, 4(4), 44-51. https://doi.org/10.11648/j.ns.20190404.12

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ACS Style

Haiddar Al-Mustafa; Anees Belal. A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl. Sci. 2019, 4(4), 44-51. doi: 10.11648/j.ns.20190404.12

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AMA Style

Haiddar Al-Mustafa, Anees Belal. A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl Sci. 2019;4(4):44-51. doi: 10.11648/j.ns.20190404.12

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@article{10.11648/j.ns.20190404.12,
  author = {Haiddar Al-Mustafa and Anees Belal},
  title = {A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes},
  journal = {Nuclear Science},
  volume = {4},
  number = {4},
  pages = {44-51},
  doi = {10.11648/j.ns.20190404.12},
  url = {https://doi.org/10.11648/j.ns.20190404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20190404.12},
  abstract = {A dispersive optical model analysis of the proton scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100MeV and for constant input values of the parameters of this mean field. This mean field is called (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section, polarization for selected energy showed the excellent agreement with available experimental data and with these resulted from global parameterization of the optical model potential.},
 year = {2019}
}

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TY  - JOUR
T1  - A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes
AU  - Haiddar Al-Mustafa
AU  - Anees Belal
Y1  - 2019/12/10
PY  - 2019
N1  - https://doi.org/10.11648/j.ns.20190404.12
DO  - 10.11648/j.ns.20190404.12
T2  - Nuclear Science
JF  - Nuclear Science
JO  - Nuclear Science
SP  - 44
EP  - 51
PB  - Science Publishing Group
SN  - 2640-4346
UR  - https://doi.org/10.11648/j.ns.20190404.12
AB  - A dispersive optical model analysis of the proton scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100MeV and for constant input values of the parameters of this mean field. This mean field is called (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section, polarization for selected energy showed the excellent agreement with available experimental data and with these resulted from global parameterization of the optical model potential.
VL  - 4
IS  - 4
ER  -

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Author Information

Haiddar Al-Mustafa

Department of Physics, Faculty of Science, Al-Baath University, Homs, Syria
Anees Belal

Department of Physics, Faculty of Science, Al-Baath University, Homs, Syria

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Plain Text BibTeX RIS

APA Style

Haiddar Al-Mustafa, Anees Belal. (2019). A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nuclear Science, 4(4), 44-51. https://doi.org/10.11648/j.ns.20190404.12

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ACS Style

Haiddar Al-Mustafa; Anees Belal. A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl. Sci. 2019, 4(4), 44-51. doi: 10.11648/j.ns.20190404.12

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AMA Style

Haiddar Al-Mustafa, Anees Belal. A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl Sci. 2019;4(4):44-51. doi: 10.11648/j.ns.20190404.12

Copy | Download

@article{10.11648/j.ns.20190404.12,
  author = {Haiddar Al-Mustafa and Anees Belal},
  title = {A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes},
  journal = {Nuclear Science},
  volume = {4},
  number = {4},
  pages = {44-51},
  doi = {10.11648/j.ns.20190404.12},
  url = {https://doi.org/10.11648/j.ns.20190404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20190404.12},
  abstract = {A dispersive optical model analysis of the proton scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100MeV and for constant input values of the parameters of this mean field. This mean field is called (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section, polarization for selected energy showed the excellent agreement with available experimental data and with these resulted from global parameterization of the optical model potential.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes
AU  - Haiddar Al-Mustafa
AU  - Anees Belal
Y1  - 2019/12/10
PY  - 2019
N1  - https://doi.org/10.11648/j.ns.20190404.12
DO  - 10.11648/j.ns.20190404.12
T2  - Nuclear Science
JF  - Nuclear Science
JO  - Nuclear Science
SP  - 44
EP  - 51
PB  - Science Publishing Group
SN  - 2640-4346
UR  - https://doi.org/10.11648/j.ns.20190404.12
AB  - A dispersive optical model analysis of the proton scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100MeV and for constant input values of the parameters of this mean field. This mean field is called (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section, polarization for selected energy showed the excellent agreement with available experimental data and with these resulted from global parameterization of the optical model potential.
VL  - 4
IS  - 4
ER  -

Copy | Download