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Pramana

, 92:39 | Cite as

The effects of core polarisation on some even–even sd-shell nuclei using Michigan three-range Yukawa and modified surface delta interactions

  • Ehsan M RaheemEmail author
  • Raheem O Kadhim
  • Nadher A Salman
Article
  • 8 Downloads

Abstract

Elastic and inelastic electron scattering from even–even \(Z=N\) sd-shell (\(^{28}\hbox {Si}, {}^{32}\hbox {S}\) and \(^{36}\hbox {Ar}\)) nuclei has been studied using the nuclear shell-model configurations. The transition rates \(B\left( {C2\uparrow } \right) \) from the ground 0\(^{+}\) state to the first excited \(2_{1}^{+}\) state, the electric quadrupole moments Q, the elastic longitudinal C0 and inelastic longitudinal C2 form factors are calculated. SDBA and USDA model spaces have been used. The radial wave functions of the single-particle matrix elements have been calculated in terms of the harmonic oscillator (HO) and Skyrme–Hartree–Fock (SHF) potentials. The configurations higher than the core and the model space are taken into account within a microscopic theory that includes one particle–one hole excitations from the core and model space orbits to higher allowed orbits with 2\(\hbar \omega \) excitations. These effects are defined as core polarisation (CP) effects. Two-body Michigan three-range Yukawa (M3Y) effective nucleon–nucleon interaction and the modified surface delta interaction (MSDI) have been used as residual interactions for the CP matrix elements. The calculations are performed using the shell-model code Nushell@MSU, where the deduced results, including CP, are more compatible with the available experimental and theoretical results.

Keywords

Electron scattering form factors electric quadrupole moments electric quadrupole transition rates core polarisation effects sd-shell nuclei 

PACS Nos

21.60.Cs 25.30.Bf 25.30.Dh 13.40.Gp 

References

  1. 1.
    B A Brown, A Etchegoyen, N S Godwin, W D M Rae, W A Richter, W E Ormand, E K Warburton, J S Winfield, L Zhao and C H Zimmerman, Oxbash for windows, MSU-NSCL Report Number 1289 (2004)Google Scholar
  2. 2.
    B A Brown and W D M Rae, NuShell@MSU, MSU-NSCL Report (2007)Google Scholar
  3. 3.
    B A Brown and W D M Rae, Nucl. Data Sheets 120, 115 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    B H Wildenthal, Prog. Part. Nucl. Phys. 11, 5 (1984)ADSCrossRefGoogle Scholar
  5. 5.
    B A Brown and B H Wildenthal, Annu. Rev. Nucl. Part. Sci. 38, 29 (1988)ADSCrossRefGoogle Scholar
  6. 6.
    B A Brown and W A Richter, Phys. Rev. C 74, 034315 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    M H Jensen, T S Kuo and E Osnes, Phys. Rep. 261, 125 (1995)ADSCrossRefGoogle Scholar
  8. 8.
    P J Brussaard and P W M Glademans, Shell-model applications in nuclear spectroscopy (North-Holland Publishing Company, Amsterdam, 1977)Google Scholar
  9. 9.
    F Petrovich, H McManus, J Borysowicz and G R Hammerstein, Phys. Rev. C 16, 839 (1977)ADSCrossRefGoogle Scholar
  10. 10.
    R A Radhi, Nucl. Phys. A 707, 56 (2002)ADSCrossRefGoogle Scholar
  11. 11.
    R A Radhi and A Bouchebak, Nucl. Phys. A 716, 87 (2003)ADSCrossRefGoogle Scholar
  12. 12.
    A D Salman, J. Kerbala Univ. 5(4), 134 (2007)Google Scholar
  13. 13.
    K S Jassim, Phys. Scr. 86(3), 035202 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    K S Jassim, A A Al-Sammarrae, F I Sharrad and H A Kassim, Phys. Rev. C 89, 014304 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    K S Jassim, R A Radhi and N M Hussain, Pramana – J. Phys. 86(1), 87 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    G Berstch, J Borysowicz, H McManus and W G Love, Nucl. Phys. A 284, 399 (1977)ADSCrossRefGoogle Scholar
  17. 17.
    R A Radhi, Calculations of elastic and inelastic electron scattering in light nuclei with shell-model wave functions, Ph.D. thesis (Michigan State University, USA, 1983)Google Scholar
  18. 18.
    R A Radhi, Eur. Phys. J. A 16, 387 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    B A Brown, Phys. Rev. C 58, 220 (1998)ADSCrossRefGoogle Scholar
  20. 20.
    H Nakada, Phys. Rev. C 68, 014316 (2003)ADSCrossRefGoogle Scholar
  21. 21.
    T W Donnely and I Sick, Rev. Mod. Phys. 56, 461 (1984)ADSCrossRefGoogle Scholar
  22. 22.
    B A Brown, B H Wildenthal, C F Williamson, F N Rad, S Kowalski, H Crannell and J T O’Brien, Phys. Rev. C 32, 1127 (1985)ADSCrossRefGoogle Scholar
  23. 23.
    L I Galanina, N S Zelenskaya, V M Lebedev, N V Orlova and A V Spassky, Bull. Russ. Acad. Sci. Phys. 77(7), 920 (2013)CrossRefGoogle Scholar
  24. 24.
    R D Lawson, Theory of the nuclear shell model (Clarendon Press, Oxford, 1980)Google Scholar
  25. 25.
    B A Brown, G Shen, G C Hillhouse, J Meng and A Trzcinska, Phys. Rev. C 76, 034305 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    B A Brown, W Chung and B H Wildenthal, Phys. Rev. C 22, 774 (1980)ADSCrossRefGoogle Scholar
  27. 27.
    G C Li, M R Yearian and I Sick, Phys. Rev. C 9, 1861 (1974)ADSCrossRefGoogle Scholar
  28. 28.
    B Pritychenko, M Birch, B Singh and M Horoi, At. Data Nucl. Tables 107, 1 (2016)ADSCrossRefGoogle Scholar
  29. 29.
    R H Spear, Phys Rep. 73(5), 369 (1981)ADSCrossRefGoogle Scholar
  30. 30.
    L Zamick and D C Zheng, Phys. Rev. C 54, 956 (1996)ADSCrossRefGoogle Scholar
  31. 31.
    N J Stone, At. Data. Nucl. Tables 90, 75 (2005)ADSCrossRefGoogle Scholar
  32. 32.
    N J Stone, At. Data. Nucl. Tables 111–112, 1 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    D Schwalm, A Bamberger, P G Bizzeti, B Povh, G A P Engelbertink, J W Olness and E K Warburton, Nucl. Phys. A 192, 449 (1972)ADSCrossRefGoogle Scholar
  34. 34.
    J M Finn, H Crannell, P L Hallowell, J T O’brien and S Penner, Nucl. Phys. A 274, 28 (1976)ADSCrossRefGoogle Scholar
  35. 35.
    B A Brown, R Radhi and B H Wildenthal, Phys. Rep. 101(5), 313 (1983)ADSCrossRefGoogle Scholar
  36. 36.
    J M Finn, H Crannell, P L Hallowell, J T O’brien and S Penner, Nucl. Phys. A 290, 99 (1977)Google Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Ministry of Science and TechnologyDirectorate of Nuclear Researches and ApplicationsBaghdadIraq

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