Single Particle Schr dinger Fluid and Moments of Inertia of Deformed Nuclei

S.B.Doma

Chinese Physics C> 2002, Vol. 26> Issue(8) : 836-842

Single Particle Schr dinger Fluid and Moments of Inertia of Deformed Nuclei

S.B.Doma ^,

Mathematics Department, Alexandria University, Alexandria, Egypt

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Abstract：
We have applied the theory of the single-particle Schrodinger fluid to the nuclear collective motion of axially deformed nuclei. A counter example of an arbitrary number of independent nucleons in the anisotropic harmonic oscillator potential at the equilibrium deformation has been also given. Moreover, the ground states of the doubly even nuclei in the s-d shell ²⁰Ne,²⁴Mg,²⁸Si,³²S and ³⁶Ar are constructed by filling the single particle states corresponding to the possible values of the number of quanta of excitations n_x,n_y, and n_z. Accordingly, the cranking-model, the rigid-body model and the equilibrium-model moments of inertia of these nuclei are calculated as functions of the oscillator parameters ω_x,ω_yand ω_z which are given in terms of the non deformed value ω00 , depending on the mass number A, the number of neutrons N, the number of protons Z, and the deformation parameter β. The calculated values of the cranking-model moments of inertia of these nuclei are in good agreement with the corresponding experimental values and show that the considered axially deformed nuclei may have oblate as well as prolate shapes and that the nucleus ²⁴Mg is the only one which is highly deformed. The rigid body model and the equilibrium model moments of inertia of the two nuclei ²⁰Ne and ²⁴Mg are also in good agreement with the corresponding experimental values.

References

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. Bohr A. Mottelson B R. Nuclear Structure, Vol. 2. Benjamin, New York,1975 2. Shaker M O. Kresnin A A. Nucl. Phys.1967,A92:57 3. Doma S B.Shaker M O. El-Ashlimi A A. Proc. 3rd Inter. Conf. Statis.,Comp. Sci. and Soc. Res.,Ain Shams Univ, Cairo, Egypt,1978,128 4. Doma S B. FCAA Journal,1999,2(5):637 5. Doma S B. Amin M M. Tfiha A D. IJAM Journal,2000,2(6):725 6. Hill D L. Wheeler J A. Phys. Rev.,1953,89(5):11027. Kan K K. Griffin J J. Phys. Rev. 1977,C15:1126 8. Kan K K. Griffin J J. Nucl. Phys. 1978,A301:25 9. Nilsson S G. Kgl. Danske. Videnskab. Mat. Fys. Medd.,1955,29:1 10. Lalazissis G A. Panos C P. Phys. Rev. 1955,C51(3):124711. Inglis D R. Phys. Rev.,1955,96:903;1955,103:1786 12. Dunford C L. Kinsey R R. Nu. Dat. System for Access to Nuclear Data, IAEA-NDS-205(BNL- NCS-65687) IAEA, Vienna, Austria, 1998 13. Ring P. Schuck P. The Nuclear Many-Body Problem. Springer-Verlag, New York, 1980

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S.B.Doma. Single Particle Schr dinger Fluid and Moments of Inertia of Deformed Nuclei[J]. Chinese Physics C, 2002, 26(8): 836-842.

S.B.Doma. Single Particle Schr dinger Fluid and Moments of Inertia of Deformed Nuclei[J]. Chinese Physics C, 2002, 26(8): 836-842. shu

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Received: 2001-12-20
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Single Particle Schr dinger Fluid and Moments of Inertia of Deformed Nuclei

S.B.Doma ^,

Corresponding author: S.B.Doma,

Mathematics Department, Alexandria University, Alexandria, Egypt

Received Date: 2001-12-20
Accepted Date: 1900-01-01
Available Online: 2002-08-05

Abstract: We have applied the theory of the single-particle Schrodinger fluid to the nuclear collective motion of axially deformed nuclei. A counter example of an arbitrary number of independent nucleons in the anisotropic harmonic oscillator potential at the equilibrium deformation has been also given. Moreover, the ground states of the doubly even nuclei in the s-d shell ²⁰Ne,²⁴Mg,²⁸Si,³²S and ³⁶Ar are constructed by filling the single particle states corresponding to the possible values of the number of quanta of excitations n_x,n_y, and n_z. Accordingly, the cranking-model, the rigid-body model and the equilibrium-model moments of inertia of these nuclei are calculated as functions of the oscillator parameters ω_x,ω_yand ω_z which are given in terms of the non deformed value ω00 , depending on the mass number A, the number of neutrons N, the number of protons Z, and the deformation parameter β. The calculated values of the cranking-model moments of inertia of these nuclei are in good agreement with the corresponding experimental values and show that the considered axially deformed nuclei may have oblate as well as prolate shapes and that the nucleus ²⁴Mg is the only one which is highly deformed. The rigid body model and the equilibrium model moments of inertia of the two nuclei ²⁰Ne and ²⁴Mg are also in good agreement with the corresponding experimental values.