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

Haiddar Al-Mustafa; Anees Belal

doi:doi:10.11648/j.ns.20200501.11

| Peer-Reviewed |

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

Haiddar Al-Mustafa, Anees Belal

Received: 26 December 2019 Accepted: 6 March 2020 Published: 30 April 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper, a dispersive optical model analysis of the neutrons 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 100 MeV and for constant input values of the parameters of this mean field and the varied input values of Hatree-Fock approximation parameters of the nonlocal potential. 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, total reaction, elastic) cross sections within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), elastic differential cross section and polarization 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 parameterization of the optical model potential, and thus more reliable for calculation the cross sections of unknown interactions of elements nuclei and their isotopes such neutrons scattering by titanium element nucleus and its natural isotopes.

DOI	10.11648/j.ns.20200501.11
Published in	Nuclear Science (Volume 5, Issue 1, March 2020)
Page(s)	1-7
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), Neutrons Scattering, Hatree-fock Potential, 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]	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.
[5]	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.
[6]	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.
[7]	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.
[8]	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.
[9]	Bechetti, F. D., & Greenlees, G. W. (1969)- Nucleon-Nucleus Optical Model Potential, Phys. Rev, 182, 1190P.
[10]	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).
[11]	Audi, G., & Wapstra, A. H. (1993). The Isotopic Mass Data. Nucl. Phys A. 565, 1-65.
[12]	Audi, G., & Wapstra, A. H. (1995). The Isotopic Mass Data. Nucl. Phys A. 595, 409-480.
[13]	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.
[14]	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.
[15]	Dyumin, A. L, Kaminker, D. M, Popova, G. N., & Smolin, V. A, (1973). Total Neutron Cross Sections of Titanium, Chromium and Copper Isotopes. Bull Russian Academy of Sciences-Physics, volume 36, Page 771. (JANIS 4.0- Local- Incident neutron data / EXFOR / (Ti46, Ti47, Ti48, Ti49, Ti50) / (, TOT) / (40149.002, 40149.003, 40149.004, 40149.005 and 40149.006) (1pts, 1pts, 1pts, 1pts and 1pts)).

Cite This Article

Plain Text BibTeX RIS

APA Style

Haiddar Al-Mustafa, Anees Belal. (2020). A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nuclear Science, 5(1), 1-7. https://doi.org/10.11648/j.ns.20200501.11

Copy | Download

ACS Style

Haiddar Al-Mustafa; Anees Belal. A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl. Sci. 2020, 5(1), 1-7. doi: 10.11648/j.ns.20200501.11

Copy | Download

AMA Style

Haiddar Al-Mustafa, Anees Belal. A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl Sci. 2020;5(1):1-7. doi: 10.11648/j.ns.20200501.11

Copy | Download

@article{10.11648/j.ns.20200501.11,
  author = {Haiddar Al-Mustafa and Anees Belal},
  title = {A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes},
  journal = {Nuclear Science},
  volume = {5},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.ns.20200501.11},
  url = {https://doi.org/10.11648/j.ns.20200501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20200501.11},
  abstract = {In this paper, a dispersive optical model analysis of the neutrons 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 100 MeV and for constant input values of the parameters of this mean field and the varied input values of Hatree-Fock approximation parameters of the nonlocal potential. 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, total reaction, elastic) cross sections within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), elastic differential cross section and polarization 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 parameterization of the optical model potential, and thus more reliable for calculation the cross sections of unknown interactions of elements nuclei and their isotopes such neutrons scattering by titanium element nucleus and its natural isotopes.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - A Dispersive Optical Model Analysis of the Neutrons 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.20200501.11
DO  - 10.11648/j.ns.20200501.11
T2  - Nuclear Science
JF  - Nuclear Science
JO  - Nuclear Science
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2640-4346
UR  - https://doi.org/10.11648/j.ns.20200501.11
AB  - In this paper, a dispersive optical model analysis of the neutrons 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 100 MeV and for constant input values of the parameters of this mean field and the varied input values of Hatree-Fock approximation parameters of the nonlocal potential. 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, total reaction, elastic) cross sections within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), elastic differential cross section and polarization 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 parameterization of the optical model potential, and thus more reliable for calculation the cross sections of unknown interactions of elements nuclei and their isotopes such neutrons scattering by titanium element nucleus and its natural isotopes.
VL  - 5
IS  - 1
ER  -

Copy | Download

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Haiddar Al-Mustafa, Anees Belal. (2020). A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nuclear Science, 5(1), 1-7. https://doi.org/10.11648/j.ns.20200501.11

Copy | Download

ACS Style

Haiddar Al-Mustafa; Anees Belal. A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl. Sci. 2020, 5(1), 1-7. doi: 10.11648/j.ns.20200501.11

Copy | Download

AMA Style

Haiddar Al-Mustafa, Anees Belal. A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes. Nucl Sci. 2020;5(1):1-7. doi: 10.11648/j.ns.20200501.11

Copy | Download

@article{10.11648/j.ns.20200501.11,
  author = {Haiddar Al-Mustafa and Anees Belal},
  title = {A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes},
  journal = {Nuclear Science},
  volume = {5},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.ns.20200501.11},
  url = {https://doi.org/10.11648/j.ns.20200501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20200501.11},
  abstract = {In this paper, a dispersive optical model analysis of the neutrons 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 100 MeV and for constant input values of the parameters of this mean field and the varied input values of Hatree-Fock approximation parameters of the nonlocal potential. 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, total reaction, elastic) cross sections within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), elastic differential cross section and polarization 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 parameterization of the optical model potential, and thus more reliable for calculation the cross sections of unknown interactions of elements nuclei and their isotopes such neutrons scattering by titanium element nucleus and its natural isotopes.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - A Dispersive Optical Model Analysis of the Neutrons 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.20200501.11
DO  - 10.11648/j.ns.20200501.11
T2  - Nuclear Science
JF  - Nuclear Science
JO  - Nuclear Science
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2640-4346
UR  - https://doi.org/10.11648/j.ns.20200501.11
AB  - In this paper, a dispersive optical model analysis of the neutrons 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 100 MeV and for constant input values of the parameters of this mean field and the varied input values of Hatree-Fock approximation parameters of the nonlocal potential. 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, total reaction, elastic) cross sections within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), elastic differential cross section and polarization 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 parameterization of the optical model potential, and thus more reliable for calculation the cross sections of unknown interactions of elements nuclei and their isotopes such neutrons scattering by titanium element nucleus and its natural isotopes.
VL  - 5
IS  - 1
ER  -

Copy | Download