The Elastic and Inelastic Electron-Nucleus Scattering Form Factors for Be9 Nucleus
DOI:
https://doi.org/10.21928/uhdjst.v4n2y2020.pp56-62Keywords:
Beryllium Nucleus, Core Polarization Effect, Electron Scattering, Form Factor, Harmonic OscillatorAbstract
The computations of the elastic and inelastic Coulomb form factors for the electron-nucleus scattering of Beryllium nucleus Be9 have performed with Core Polarization (CP) effects including the realistic Michigan sum of Three Range Yukawa (M3Y) Interaction, and the other residual interaction which is Modified Surface Delta Interaction (MSDI). In addition to mean square root charge density and charge radii for the ground state. The perturbation theory was adopted to compute the Core Polarization by using the Harmonic Oscillators (HO) potential to calculate single-particle radial wave functions.
In the comparison between the theoretical calculations of Coulomb form factors by (MSDI) interaction, realistic (M3Y) interaction, and the experimental results that measured before, it noticed that the Coulomb form factors for the (M3Y) interaction gave a reasonable depiction of the measured data.
References
[1] T. W. Donnelly and J. D. Walecka. “Electron scattering and nuclear structure”. Annual Review of Nuclear Science, vol. 25, no. 1, pp. 329-405, 1975.
[2] D. J. Millener, D. I. Sober, H. Crannell, J. T. O’Brien, L. W. Fagg and L. Lapikas. “Inelastic electron scattering from 13C”. Physical Reviews, vol. 39, no. 1, pp.14-46, 1989.
[3] S. Cohen and D. Kurath. “Effective interactions for the 1p shell”. Nuclear Physics, vol. 73, no. 1, pp. 1-24, 1965.
[4] D. Salman, S. A. Al-Ramahi and M. H. Oleiwi. “Inelastic electron-nucleus scattering form factors for 64, 66, 68Zn isotopes”. Vol. 2144. In: AIP Conference Proceedings, p. 030029, 2019.
[5] K. S. Jassim. “Longitudinal form factor for some sd-shell nuclei using large scale model space”. International Journal of Science and Technology, vol. 1, no. 3, pp. 140-143, 2011.
[6] N. F. Mott. “Sir Nevill Mott: 65 Years in Physics”. Vol. 12. World Scientific, Singapore, 1995.
[7] Z. Czyżewski, D. O. N. MacCallum, A. Romig and D. C. Joy. “Calculations of Mott scattering cross section”. Journal of Applied Physics, vol. 68, no. 7, pp. 3066-3072, 1990.
[8] H. Uberall. “Electron Scattering from Complex Nuclei V36A”. Academic Press, New York, London, 2012.
[9] F. A. Majeed. “The effect of core polarization on longitudinal form factors in 10B”. Physica Scripta, vol. 85, no. 6, p. 065201, 2012.
[10] G. Fricke, C. Bernhardt, K. Heilig, L. A. Schaller, L. Schellenberg, E. B. Shera and C. W. Dejager. “Nuclear ground state charge radii from electromagnetic interactions”. Atomic Data and Nuclear Data Tables, vol. 60, no. 2, pp. 177-285, 1995.
[11] F. I. Sharrad, A. K. Hamoudi, R. A. Radhi, H. Y. Abdullah, A. A. Okhunov and H. A. Kassim. “Elastic electron scattering from some light nuclei”. Chinese Journal of Physics, vol. 51, no. 3, pp. 452- 465, 2013.
[12] R. A. Radhi, A. A. Alzubadi and E. M. Rashed. “Shell model calculations of inelastic electron scattering for positive and negative parity states in 19F”. Nuclear Physics A, vol. 947, pp. 12-25, 2016.
[13] E. M. Raheem, R. O. Kadhim and N. A. Salman. “The effects of core polarization on some even-even sd-shell nuclei using Michigan three-range Yukawa and modified surface delta interactions”. Pramana, vol. 92, no. 3, p. 39, 2019.
[14] B. A. Brown, A. Etchegoyen, N. S. Godwin, W. D. M. Rae, W. A. Richter, W. E. Ormand and C. H. Zimmerman. “Oxbash for windows PC”. In: MSU-NSCL Report, pp. 1289, 2004.
[15] S. Mohammadi, B. N. Giv and N. S. Shakib. “Energy levels calculations of 24Al and 25Al isotopes”. Nuclear Science, vol. 2, no. 1, pp. 1-4, 2017.
[16] T. de Forest and J. D. Walecka. “Electron scattering and nuclear structure”. Advances in Physics, vol. 15, no. 57, pp. 1-109, 1966.
[17] L. J. Tassie and F. C. Barker. “Application to electron scattering of center-of-mass effects in the nuclear shell model”. Physical Review, vol. 111, no. 3, p. 940, 1958.
[18] K. S. Jassim, A. A. Al-sammarrae, F. I. Sharrad and H. A. Kassim. “Elastic and inelastic electron-nucleus scattering form factors of some light nuclei: Na 23, Mg 25, Al 27, and Ca 41”. Physical Review C, vol. 89, no. 1, p. 014304, 2014.
[19] H. Fatah, R. A. Radhi and N. R. Abdullah. “Analytical derivations of single-particle matrix elements in nuclear shell model”. Communications in Theoretical Physics, vol. 66, no. 1, p. 104, 2016.
[20] P. J. Brussaard and W. M. Glaudemans. “Shell-Model Application in Nuclear Spectroscopy”. North-Holland, Amsterdam, 1977.
[21] D. Salman, D. R. Kadhim. “Longitudinal electron scattering form factors for 54, 56 Fe”. International Journal of Modern Physics E, vol. 23, no. 10, p. 1450054, 2014.
[22] F. I. Sharrad, A. K. Hamoudi, R. A. Radhi, Y. Abdullah, A. A. Okhunov and H. A. Kassim. “Elastic electron scattering from some light nuclei”. Chinese Journal of Physics, vol. 51, no. 3, pp. 452-465, 2013.
[23] B. A. Brown, R. Radhi and B. H. Wildenthal. “Electric quadrupole and hexadecupole nuclear excitations from the perspectives of electron scattering and modern shell-model theory”. Physics Reports, vol. 101, no. 5, pp. 313-358, 1983.
[24] H. M. Dlshad and A. H. R. Fatah. “Using MSDI and M3Y core polarization for the coulomb electron scattering for some ground state nuclei”. JZS (Part-A), vol. 21, no. 2, pp. 11-20, 2019.
[25] G. S. Anagnostatos, A. N. Antonov, P. Ginis, J. Giapitzakis and M. K. Gaidarov. “On the central depression in density of”. Journal of Physics G: Nuclear and Particle Physics, vol. 25, no. 1, p. 69, 1999.
[26] G. Bertsch, J. Borysowicz, H. McManus and W. G. Love. “Interactions for inelastic scattering derived from realistic potentials”. Nuclear Physics A, vol. 284, no. 3, pp. 399-419, 1977.
[27] F. A. Majeed. “Longitudinal and transverse form factors from 12C”. Physica Scripta, vol. 76, no. 4, p. 332, 2007.
[28] J. P. Glickman, W. Bertozzi, T. N. Buti, S. Dixit, F. W. Hersman, C. E. Hyde-Wright and B. L. Berman. “Electron scattering from sup 9 be”. Physical Review C (Nuclear Physics) (USA), vol. 43, no. 4, pp. 1740-1757, 1991.
[29] Angeli and K. P. Marinova. “Table of experimental nuclear ground state charge radii: An update”. Atomic Data and Nuclear Data Tables, vol. 99, no. 1, pp. 69-95, 2013.
[2] D. J. Millener, D. I. Sober, H. Crannell, J. T. O’Brien, L. W. Fagg and L. Lapikas. “Inelastic electron scattering from 13C”. Physical Reviews, vol. 39, no. 1, pp.14-46, 1989.
[3] S. Cohen and D. Kurath. “Effective interactions for the 1p shell”. Nuclear Physics, vol. 73, no. 1, pp. 1-24, 1965.
[4] D. Salman, S. A. Al-Ramahi and M. H. Oleiwi. “Inelastic electron-nucleus scattering form factors for 64, 66, 68Zn isotopes”. Vol. 2144. In: AIP Conference Proceedings, p. 030029, 2019.
[5] K. S. Jassim. “Longitudinal form factor for some sd-shell nuclei using large scale model space”. International Journal of Science and Technology, vol. 1, no. 3, pp. 140-143, 2011.
[6] N. F. Mott. “Sir Nevill Mott: 65 Years in Physics”. Vol. 12. World Scientific, Singapore, 1995.
[7] Z. Czyżewski, D. O. N. MacCallum, A. Romig and D. C. Joy. “Calculations of Mott scattering cross section”. Journal of Applied Physics, vol. 68, no. 7, pp. 3066-3072, 1990.
[8] H. Uberall. “Electron Scattering from Complex Nuclei V36A”. Academic Press, New York, London, 2012.
[9] F. A. Majeed. “The effect of core polarization on longitudinal form factors in 10B”. Physica Scripta, vol. 85, no. 6, p. 065201, 2012.
[10] G. Fricke, C. Bernhardt, K. Heilig, L. A. Schaller, L. Schellenberg, E. B. Shera and C. W. Dejager. “Nuclear ground state charge radii from electromagnetic interactions”. Atomic Data and Nuclear Data Tables, vol. 60, no. 2, pp. 177-285, 1995.
[11] F. I. Sharrad, A. K. Hamoudi, R. A. Radhi, H. Y. Abdullah, A. A. Okhunov and H. A. Kassim. “Elastic electron scattering from some light nuclei”. Chinese Journal of Physics, vol. 51, no. 3, pp. 452- 465, 2013.
[12] R. A. Radhi, A. A. Alzubadi and E. M. Rashed. “Shell model calculations of inelastic electron scattering for positive and negative parity states in 19F”. Nuclear Physics A, vol. 947, pp. 12-25, 2016.
[13] E. M. Raheem, R. O. Kadhim and N. A. Salman. “The effects of core polarization on some even-even sd-shell nuclei using Michigan three-range Yukawa and modified surface delta interactions”. Pramana, vol. 92, no. 3, p. 39, 2019.
[14] B. A. Brown, A. Etchegoyen, N. S. Godwin, W. D. M. Rae, W. A. Richter, W. E. Ormand and C. H. Zimmerman. “Oxbash for windows PC”. In: MSU-NSCL Report, pp. 1289, 2004.
[15] S. Mohammadi, B. N. Giv and N. S. Shakib. “Energy levels calculations of 24Al and 25Al isotopes”. Nuclear Science, vol. 2, no. 1, pp. 1-4, 2017.
[16] T. de Forest and J. D. Walecka. “Electron scattering and nuclear structure”. Advances in Physics, vol. 15, no. 57, pp. 1-109, 1966.
[17] L. J. Tassie and F. C. Barker. “Application to electron scattering of center-of-mass effects in the nuclear shell model”. Physical Review, vol. 111, no. 3, p. 940, 1958.
[18] K. S. Jassim, A. A. Al-sammarrae, F. I. Sharrad and H. A. Kassim. “Elastic and inelastic electron-nucleus scattering form factors of some light nuclei: Na 23, Mg 25, Al 27, and Ca 41”. Physical Review C, vol. 89, no. 1, p. 014304, 2014.
[19] H. Fatah, R. A. Radhi and N. R. Abdullah. “Analytical derivations of single-particle matrix elements in nuclear shell model”. Communications in Theoretical Physics, vol. 66, no. 1, p. 104, 2016.
[20] P. J. Brussaard and W. M. Glaudemans. “Shell-Model Application in Nuclear Spectroscopy”. North-Holland, Amsterdam, 1977.
[21] D. Salman, D. R. Kadhim. “Longitudinal electron scattering form factors for 54, 56 Fe”. International Journal of Modern Physics E, vol. 23, no. 10, p. 1450054, 2014.
[22] F. I. Sharrad, A. K. Hamoudi, R. A. Radhi, Y. Abdullah, A. A. Okhunov and H. A. Kassim. “Elastic electron scattering from some light nuclei”. Chinese Journal of Physics, vol. 51, no. 3, pp. 452-465, 2013.
[23] B. A. Brown, R. Radhi and B. H. Wildenthal. “Electric quadrupole and hexadecupole nuclear excitations from the perspectives of electron scattering and modern shell-model theory”. Physics Reports, vol. 101, no. 5, pp. 313-358, 1983.
[24] H. M. Dlshad and A. H. R. Fatah. “Using MSDI and M3Y core polarization for the coulomb electron scattering for some ground state nuclei”. JZS (Part-A), vol. 21, no. 2, pp. 11-20, 2019.
[25] G. S. Anagnostatos, A. N. Antonov, P. Ginis, J. Giapitzakis and M. K. Gaidarov. “On the central depression in density of”. Journal of Physics G: Nuclear and Particle Physics, vol. 25, no. 1, p. 69, 1999.
[26] G. Bertsch, J. Borysowicz, H. McManus and W. G. Love. “Interactions for inelastic scattering derived from realistic potentials”. Nuclear Physics A, vol. 284, no. 3, pp. 399-419, 1977.
[27] F. A. Majeed. “Longitudinal and transverse form factors from 12C”. Physica Scripta, vol. 76, no. 4, p. 332, 2007.
[28] J. P. Glickman, W. Bertozzi, T. N. Buti, S. Dixit, F. W. Hersman, C. E. Hyde-Wright and B. L. Berman. “Electron scattering from sup 9 be”. Physical Review C (Nuclear Physics) (USA), vol. 43, no. 4, pp. 1740-1757, 1991.
[29] Angeli and K. P. Marinova. “Table of experimental nuclear ground state charge radii: An update”. Atomic Data and Nuclear Data Tables, vol. 99, no. 1, pp. 69-95, 2013.
Downloads
Published
2020-08-17
How to Cite
Dlshad, H. M., Fatah, A. H.-R., & Hussain, A. M. (2020). The Elastic and Inelastic Electron-Nucleus Scattering Form Factors for Be9 Nucleus. UHD Journal of Science and Technology, 4(2), 56–62. https://doi.org/10.21928/uhdjst.v4n2y2020.pp56-62
Issue
Section
Articles
