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

Abstract
HTML
Reference
Related

PDF

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

[1]

. 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

[1]	JIN Hua , ZHENG Ren-Rong , ZHU Shun-Quan , LI Jun-Qing . Chaotic Motion of Single Particle in the Potential of Nonaxial Octupole Deformation. Chinese Physics C, 2006, 30(2): 134-139.
[2]	LIU Shu-Xin , LEI Yi-An , ZENG Jin-Yan . Large Fluctuation in Odd-Even Differences and Nonadditivity of Nuclear Moments of Inertia. Chinese Physics C, 2006, 30(S2): 39-41.
[3]	YU Lei , LIU Shu-Xin , ZENG Jin-Yan . Microscopic Mechanism of Moments of Inertia and Odd-even Differences for Well-Deformed Actinide Nuclei. Chinese Physics C, 2004, 28(1): 56-60.
[4]	DI Yao-Min . Analysis by Synthesis of the Spin Assignment for the Superdeformed Single Bands in A≈190 Odd Nuclei. Chinese Physics C, 2003, 27(6): 503-506.
[5]	LI Wen-Fei , ZHANG Feng-Shou , CHEN Lie-Wen . On the Moment of Inertia and Surface Redshift of Neutron Star. Chinese Physics C, 2001, 25(10): 1006-1011.
[6]	YU Lei , LIU Shu-Xin , LEI Yi-An , ZENG Jin-Yan . Microscopic Mechanism of the ω Variation in Moments of Inertia for the Series of Yrast SD Bands ^192—198Pb(1) and ¹⁹⁸Po(1). Chinese Physics C, 2001, 25(2): 129-133.
[7]	GUO Jian-You , XU Fu-Xin , RUAN Tu-Nan . Odd-Even Difference of Moment of Inertia of NuclearSuperdeformed States in A～190 Region. Chinese Physics C, 2001, 25(8): 754-758.
[8]	FANG XiangZheng , RUAN TuNan . Description of Superdeformed Bands in ¹⁴⁸Gd in q-deformed Moment of Inertia. Chinese Physics C, 2000, 24(3): 269-274.
[9]	Zhou Shangui , Zheng Chunkai , Hu Jikmin . Odd-Even Differences in Moments of Inertia of Rare Earth Nuclei from the BCS Theory. Chinese Physics C, 1998, 22(12): 1143-1150.
[10]	Di Yaomin . Three-Body Heritage Mixing Interaction and the Variance of Nuclear Moment of Inertia. Chinese Physics C, 1995, 19(6): 554-561.
[11]	Jin Taihao , Zhao Zhengji , Zeng Jinyan . Particle-Number Conserving Calculation of the Bandhead Moments of Inertia of Identical SD Bands. Chinese Physics C, 1994, 18(3): 239-248.
[12]	ZHU Jian-Yang . The Moment of Inertia and Energy Spectrum for IBM Intrinsic Ground-State Single Phonon and Double Phonon Excited-States. Chinese Physics C, 1993, 17(9): 851-860.
[13]	ZHAO Zheng-Ji , JIN Tai-Hao . Microscopic Mechanism of the Variation of the Ground Band Moments of Inertia with Neutron Numbers in ^166—176Yb. Chinese Physics C, 1992, 16(8): 754-761.
[14]	CHEN Xin-Yi , HU Ji-Min . CALCULATION OF THE EFFECTIVE MOMENT OF INERTIA OF FISSIONING NUCLEI AT SADDLE POINT. Chinese Physics C, 1989, 13(4): 380-383.
[15]	LIU Yong , SANG Jian-Ping . THE MOMENT OF INERTIA IN THE INTERACTING BOSON-FERMION MODEL. Chinese Physics C, 1988, 12(5): 644-651.
[16]	LIU Guo-Xing . EFFECTIVE MOMENT OF INERTIA OF MEDIUM MASS NUCLEI AT THE SADDLE POINT. Chinese Physics C, 1987, 11(1): 98-103.
[17]	JING Xiao-Gong , LI Cheng-Zu , YANG Shan-De , WU Shi-Shu . SINGLE-PARTICLE AND SINGLE-HOLE SPECTRA IN ⁴⁰Ca. Chinese Physics C, 1986, 10(6): 744-751.
[18]	WU Chong-Shi , ZENG Jin-Yan . THE COLLECTIVE EXCITATION SPECTRA OF EVEN-EVEM DEFORMED NUCLEI. Chinese Physics C, 1985, 9(2): 214-219.
[19]	WANG ZHENG-DA , ZHENG MAN-JIAO . A SIMPLE METHOD OF CALCULATING MOMENT OF INERTIA AT GROUND STATES OF EVEN-EVEN NUCLEI. Chinese Physics C, 1981, 5(6): 765-768.
[20]	ZENG JIN-YAN . THE MOMENTS OF INERTIA OF MULTI-QUASI-PARTICLE EXCITATION BANDS AND THE BLOCKING EFFECT. Chinese Physics C, 1979, 3(1): 102-107.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(2922)
PDF Downloads(514)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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

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.

HTML

Reference (1)

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

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article