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

Haiddar Al-Mustafa; Anees Belal

doi:doi:10.11648/j.ns.20200501.12

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

Haiddar Al-Mustafa, Anees Belal

Published in Nuclear Science (Volume 5, Issue 1)

Received: 2 February 2020 Accepted: 9 March 2020 Published: 30 April 2020

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Abstract

A dispersive optical model analysis of the alpha particles scattering by titanium element nucleus and its natural isotopes has been applied for a new scattering potential within the energy range (1-100) MeV which has contained the range of the Coulomb barrier, and for constant input values of the parameters of this potential. This potential is extent of the mean field potential and is called by (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 have been compared with these resulting from global parameterizations of the alpha particles scattering 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 and polarization resulted only from the Coulomb spin-orbit term that has been appeared characteristically for selected energy and for selected center-of-mass scattering angle within the energy range (1-100) MeV, showed the excellent agreement with available experimental data and better than these resulted from global parameterizations of the alpha particles scattering potential.

Published in	Nuclear Science (Volume 5, Issue 1)
DOI	10.11648/j.ns.20200501.12
Page(s)	8-15
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), Alpha Particles Scattering, (Coulomb-Nuclear) Interference Potential (CNIP), Hatree-Fock potential (HF), Dispersion Relations (DR), Cross Section, Polarization, Coulomb Barrier

References

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[6]	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).
[7]	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.
[8]	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.
[9]	Al-Mustafa, H., & Belal. A. (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.
[10]	Al-Mustafa, H., & Belal. A. (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.
[11]	Al-Mustafa, H., & Belal. A. (2019). A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes, Nuclear Science, Science PG, 4 (4): 44-51, DOI: 10.11648/j.ns.20190404.12.
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[16]	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.
[17]	Vonach, H, Haight, R. C., & Winkler, G. (1983). (Alpha, n) and Total Alpha-Reaction Cross Sections for Ti-48 and V-51. Physics Review, Part C, Nuclear Physics, volume 28, page 2278. (JANIS 4.0- Local- Incident alpha data / EXFOR / (Ti48) / (, NON) / (C0318.004) (8pts)).
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Haiddar Al-Mustafa, Anees Belal. (2020). A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nuclear Science, 5(1), 8-15. https://doi.org/10.11648/j.ns.20200501.12

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ACS Style

Haiddar Al-Mustafa; Anees Belal. A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl. Sci. 2020, 5(1), 8-15. doi: 10.11648/j.ns.20200501.12

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AMA Style

Haiddar Al-Mustafa, Anees Belal. A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl Sci. 2020;5(1):8-15. doi: 10.11648/j.ns.20200501.12

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@article{10.11648/j.ns.20200501.12,
  author = {Haiddar Al-Mustafa and Anees Belal},
  title = {A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes},
  journal = {Nuclear Science},
  volume = {5},
  number = {1},
  pages = {8-15},
  doi = {10.11648/j.ns.20200501.12},
  url = {https://doi.org/10.11648/j.ns.20200501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20200501.12},
  abstract = {A dispersive optical model analysis of the alpha particles scattering by titanium element nucleus and its natural isotopes has been applied for a new scattering potential within the energy range (1-100) MeV which has contained the range of the Coulomb barrier, and for constant input values of the parameters of this potential. This potential is extent of the mean field potential and is called by (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 have been compared with these resulting from global parameterizations of the alpha particles scattering 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 and polarization resulted only from the Coulomb spin-orbit term that has been appeared characteristically for selected energy and for selected center-of-mass scattering angle within the energy range (1-100) MeV, showed the excellent agreement with available experimental data and better than these resulted from global parameterizations of the alpha particles scattering potential.},
 year = {2020}
}

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TY  - JOUR
T1  - A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes
AU  - Haiddar Al-Mustafa
AU  - Anees Belal
Y1  - 2020/04/30
PY  - 2020
N1  - https://doi.org/10.11648/j.ns.20200501.12
DO  - 10.11648/j.ns.20200501.12
T2  - Nuclear Science
JF  - Nuclear Science
JO  - Nuclear Science
SP  - 8
EP  - 15
PB  - Science Publishing Group
SN  - 2640-4346
UR  - https://doi.org/10.11648/j.ns.20200501.12
AB  - A dispersive optical model analysis of the alpha particles scattering by titanium element nucleus and its natural isotopes has been applied for a new scattering potential within the energy range (1-100) MeV which has contained the range of the Coulomb barrier, and for constant input values of the parameters of this potential. This potential is extent of the mean field potential and is called by (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 have been compared with these resulting from global parameterizations of the alpha particles scattering 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 and polarization resulted only from the Coulomb spin-orbit term that has been appeared characteristically for selected energy and for selected center-of-mass scattering angle within the energy range (1-100) MeV, showed the excellent agreement with available experimental data and better than these resulted from global parameterizations of the alpha particles scattering potential.
VL  - 5
IS  - 1
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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APA Style

Haiddar Al-Mustafa, Anees Belal. (2020). A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nuclear Science, 5(1), 8-15. https://doi.org/10.11648/j.ns.20200501.12

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ACS Style

Haiddar Al-Mustafa; Anees Belal. A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl. Sci. 2020, 5(1), 8-15. doi: 10.11648/j.ns.20200501.12

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AMA Style

Haiddar Al-Mustafa, Anees Belal. A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl Sci. 2020;5(1):8-15. doi: 10.11648/j.ns.20200501.12

Copy | Download

@article{10.11648/j.ns.20200501.12,
  author = {Haiddar Al-Mustafa and Anees Belal},
  title = {A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes},
  journal = {Nuclear Science},
  volume = {5},
  number = {1},
  pages = {8-15},
  doi = {10.11648/j.ns.20200501.12},
  url = {https://doi.org/10.11648/j.ns.20200501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20200501.12},
  abstract = {A dispersive optical model analysis of the alpha particles scattering by titanium element nucleus and its natural isotopes has been applied for a new scattering potential within the energy range (1-100) MeV which has contained the range of the Coulomb barrier, and for constant input values of the parameters of this potential. This potential is extent of the mean field potential and is called by (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 have been compared with these resulting from global parameterizations of the alpha particles scattering 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 and polarization resulted only from the Coulomb spin-orbit term that has been appeared characteristically for selected energy and for selected center-of-mass scattering angle within the energy range (1-100) MeV, showed the excellent agreement with available experimental data and better than these resulted from global parameterizations of the alpha particles scattering potential.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes
AU  - Haiddar Al-Mustafa
AU  - Anees Belal
Y1  - 2020/04/30
PY  - 2020
N1  - https://doi.org/10.11648/j.ns.20200501.12
DO  - 10.11648/j.ns.20200501.12
T2  - Nuclear Science
JF  - Nuclear Science
JO  - Nuclear Science
SP  - 8
EP  - 15
PB  - Science Publishing Group
SN  - 2640-4346
UR  - https://doi.org/10.11648/j.ns.20200501.12
AB  - A dispersive optical model analysis of the alpha particles scattering by titanium element nucleus and its natural isotopes has been applied for a new scattering potential within the energy range (1-100) MeV which has contained the range of the Coulomb barrier, and for constant input values of the parameters of this potential. This potential is extent of the mean field potential and is called by (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 have been compared with these resulting from global parameterizations of the alpha particles scattering 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 and polarization resulted only from the Coulomb spin-orbit term that has been appeared characteristically for selected energy and for selected center-of-mass scattering angle within the energy range (1-100) MeV, showed the excellent agreement with available experimental data and better than these resulted from global parameterizations of the alpha particles scattering potential.
VL  - 5
IS  - 1
ER  -

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