58 Ni as an Electron Diffraction Grating with 48 Ca as an Inert Core | Ibn AL-Haitham Journal For Pure and Applied Sciences

Authors

Ali A. Mohammed Department of Physics, College of Science, University of Baghdad ,Baghdad, Iraq. https://orcid.org/0009-0008-1924-6701
Dr. Firas Z. Majeed Department of Physics, College of Science, University of Baghdad ,Baghdad, Iraq. https://orcid.org/0000-0001-6527-3913

DOI:

https://doi.org/10.30526/38.2.4005

Keywords:

Electron scattering, Shell model, Nickel-58, M3Y interaction

Abstract

The configurations of the nuclear shell model were employed to study and inspect the form factor of a scattering electron in the ⁵⁸Ni nucleus. The wave function of the model space was obtained through the (fp-orbits) and (fpd6) effective interactions within the model space by utilizing the Harmonic Oscillator wave functions as a single particle's wave function. In the (fp-LS) shell, the correction for the main calculations of model space was performed by the 1^st-order perturbation theory to estimate the effects of core polarization with the (2ℏω) energy of excitation that has been carried out. Core polarization combined the model space with the discarded space (higher configuration core). Via model space, the interaction of effective (M3Y-P2) for linking the active particles of a model space with the particle-hole pair. The interaction of two bodies of Michigan 3-range Yukawa (M3Y) was used as a residual interaction for calculating the matrix elements of core polarization. Eventually, form factor theoretical results and the available experimental results were compared.

Author Biographies

Ali A. Mohammed , Department of Physics, College of Science, University of Baghdad ,Baghdad, Iraq.

Department of Physics, College of Science, University of Baghdad ,Baghdad, Iraq.
Dr. Firas Z. Majeed, Department of Physics, College of Science, University of Baghdad ,Baghdad, Iraq.

Department of Physics, College of Science, University of Baghdad ,Baghdad, Iraq.

References

1. Mott NF. An Introduction to Particle Physics and the Standard Model. Soci Ser. 1929;A124:425.

2. Donnelly TW, Sick I. ). Elastic magnetic electron scattering from nuclei. Rev Mod Phys. 1984;56:461. https://doi.org/10.1103/RevModPhys.56.461

3. Majeed FZ, Hmood FM. Inelastic longitudinal electron scattering C2 form factors in 58Ni. Iraqi J Phys. 2016;14(29):15-26. https://doi.org/10.30723/ijp.v14i29.216

4. Radhi RA, Majeed FZ. Elastic magnetic electron scattering form factor in Ca-41 (M3Y fitting parameters consideration). Iraqi J Phys. 2010;8(13):18-27.https://doi.org/10.30723/itr.v14i29.205

5. Majeed FZ. M3Y-P0 as a residual interaction to study elastic magnetic electron scattering form factors for Ca-41. Al-Nahrain J Sci. 2013;16(3):141-147.https://anjs.edu.iq/index.php/anjs/article/view/598/535.

6. Majeed FZ, Qassim AA. 1f7/2 1d3/2 model space and inelastic longitudinal C6 electron scattering form factors in 50Ti (residual interactions consideration). Iraqi J Sci. 2012;53(4):807-813. https://doi.org/10.24996/236601.

7. Majeed FZ, Mashaan SS. Inelastic longitudinal electron scattering C2 form factors in 48Ca nucleus by using sigma meson as a residual interaction. Iraqi J Sci. 2014;55(1):151-160. https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/11939.

8. Majeed FZN, Albana'a MA, Qassim AA. Inelastic longitudinal C6 electron scattering form factors in 50Ti (residual interactions consideration). Iraqi J Sci. 2012;53(3):564-572. https://doi.org/10.13140/RG.2.2.12919.14243.

9. Hussien RM, Majeed FZ. The effective M3Y residual interaction in nuclear diffraction grating of electrons for Ca41. Baghdad Sci J. 2022;19(6):1393-1398. https://doi.org/10.21123/bsj.2022.6776.

10. Falih R, Majeed FZ. Gogny interaction and nuclear charge distribution in 48Ca nucleus. Baghdad Sci J. 2023;20(3):815-824. https://doi.org/10.21123/bsj.2022.7007.

11. Radhi RA, Bouchebak A. Microscopic calculations of C2 and C4 form factors in sd-shell nuclei. Nucl Phys. 2003;A716:87. https://doi.org/10.1016/S0375-9474(02)01335-0.

12. Brussaard PJ, Glademans PWM. Shell-model application in nuclear spectroscopy. Amsterdam: North-Holland Publishing Company; 1977. https://doi.org/10.1016/sr34-23(3)0123.

13. Hasan MK, Majeed FZ. FP shell effective interactions and nuclear shell structure of 44Sc. East Eur J Phys. 2023;1:89-93. https://doi.org/10.26565/2312-4334-2023-1-10.

14. Kadhum HA, Majeed FZ. Nuclear energy levels scheme of 46Cr using FPD6, FPY, and KB3G interactions. East Eur J Phys. 2023;3:187-191. https://doi.org/10.26565/2312-4334-2023-3-15.

15. Hasan MK, Majeed FZ. Nuclear energy levels in 44Ca using FPD6pn interaction. East Eur J Phys. 2023;1:69-74. https://doi.org/10.26565/2312-4334-2023-1-18.

16. Yokoyama A. Inelastic longitudinal C6 electron scattering form factors in 50Ti. J Phys Conf. 2005;20:143-146. https://doi.org/10.13140/RG.2.2.12919.14243.

17. Majeed FZ. Core polarization effects on electron scattering form factors for some fp-shell nuclei. Doctoral dissertation, University of Baghdad, Department of Physics, College of Science, Baghdad, Iraq; 2009:114-139. https://doi.org/10.24996/Iraqijournalofscience.v53i3.12760.

18. Elliott P, Skyrme THR. An effective interaction for inelastic scattering derived from the nucleon potential. Proc Roy Soc. 1955;A323:561-576. https://doi.org/10.1016/0375-9474(83)90487-6.

19. Yeslam HA. Core-polarization effects for electron scattering form factors in some sd-shell nuclei. Doctoral dissertation, University of Baghdad, Department of Physics, College of Science, Baghdad, Iraq; 2005:56-70.

20. Sakakura M, Arima A, Sebe T. Application to electron scattering of center-of-mass effects in the nuclear shell model. Phys Lett. 1976;61B:335-351. https://doi.org/10.1016/0370-2693(79)90909-2.

21. Nakada H, Sato M. Hartree-Fock approach to nuclear matter and finite nuclei with M3Y-type nucleon-nucleon interactions. Nucl Phys. 2002;A699:511-525. https://doi.org/10.48550/arXiv.nucl-th/0304021.

22. Brown BA, Etchgoyen A, Godwin NS, Rae WDM, Richter WA, Ormand WE, et al. Nuclear shell model code. MSU-NSCL report number 1289; 2005. https://doi.org/10.1016/j.nds.2014.07.022.

23. Heisenberg J, McCarthy JS, Sick I. Inelastic electron scattering from several Ca, Ti, and Fe isotopes. Nucl Phys. 1971;A164:353-374. https://doi.org/10.1016/0375-9474(71)90219.

24. Edmonds R. Angular Momentum in Quantum Mechanics. 3rd ed. Princeton: Princeton University Press; 1974. p. 70-113. https://doi.org/10.1515/9781400884186.

25. Walecka JD. Electron scattering for nuclear and nucleon structure. Cambridge: Cambridge Monographs on Physics, Nuclear Physics and Cosmology; 2004. p. 12-42. https://doi.org/10.1017/9781009290616.

26. Haxel O, Jensen JHD, Suess HE. On the "Magic Numbers" in nuclear structure. Phys Rev. 1949;75:1766-1780. https://doi.org/10.1103/PhysRev.75.1766.2.

27. Berstch G, Borysowicz J, McManus H, Love WG. An effective interaction for inelastic scattering derived from the Paris potential. Nucl Phys. 1977;A284:399-418. https://doi.org/10.1016/0375-9474(83)90487-6.

28. Goriely S, Tondeur F, Pearson JM. Atomic and nuclear datasheet. At Data Nucl Data Sheets. 2001;77:311-420. https://doi.org/10.1006/adnd.2000.0857.

29. Lalazissis GA, Koonig J, Ring P. Central and noncentral components of the effective sd-shell interaction. Phys Rev. 1997;C55:540-567. https://doi.org/10.1103/PhysRevC.15.1483.

30. Khoa DT, Von Oertzen W, Ogloblin AA. Study of the equation of state for asymmetric nuclear matter and interaction potential between neutron-rich nuclei using the density-dependent M3Y interaction. Nucl Phys. 1996;A602:98-213. https://doi.org/10.1016/0375-9474(96)00091-7