原子核壳修正方法研究
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摘要
近几十年来核物理高速发展,其中对超重核的研究已经成为当前核物理研究领域中的热点课题之一。壳效应对超重核非常重要,它可以提供超重核存在所需要的微观量子壳效应。原子核壳修正能计算方法的研究对于完善原子核理论及超重核合成具有重要意义和一定的应用价值。
本工作主要是采用Woods-Saxon势,对Strutinsky壳修正方法做了一些检验、验证和计算分析。我们首先对核结构模型做了简要回顾,简单地介绍了核的单粒子能级,用接近实际单粒子势的Woods-Saxon势计算出一些核的单粒子能级。然后,我们详细地介绍了基于宏观-微观模型中的Strutinsky壳修正的方法,对该方法数学表达做了分析推导。针对能级密度的高斯厄米展开最大阶数P=6阶时,对高斯展开宽度γ的传统取值做了检查以及具体取值做了探讨;对Woods-Saxon势的参数对壳修正能的影响做了程序计算分析,给出了由轻到重四个典型幻数核相应的壳修正能。分析比较发现原子核半径参数R对壳修正能的影响比较大。Strutinsky壳修正方法对于计算原子核质量有重要的意义,对超重核的基态性质有一定影响作用。本工作最后介绍了该方法的应用,在基态质量公式的改进,基态形变与形状共存以及超重核的壳修正等方面。考察了Strutinsky壳修正方法的有效性,发现该方法在实际应用中还是比较成功的。
Nuclear physics is developing very rapidly in recent decades. Super-heavy nuclei research has already become one of the hot subjects in the research field of present nuclear physics. The shell effect is essential to the super-heavy nuclei, because it can offer the microscopic quantity shell effect which provides a possibility for the super-heavy nuclei to survive. The research on the calculation of the nuclear shell correction energy is of great importance for improving the nuclear theory and for the synthesis of super-heavy nuclei.
In this thesis, we first review some nuclear structure models briefly. The single particle energy level which is necessary for the calculation of the shell correction is introduced briefly. Using the realistic Woods-Saxon single-particle potential, we calculate the simple particle energy level of some spherical and axially deformed nuclei. The method of the shell correction which is proposed by Strutinsky based on the macroscopic-microscopic model is introduced in detail. The expressions in the Strutinsky shell correction method have been checked. In this work, we study the influence of the width parameters on the shell energy when the order p=6 of the Gauss-Hermite polynomials is fixed. The influence of the Woods-Saxon potential parameters, i.e. the potential depth V0, the radius R and the surface diffuseness a, on the shell energy is also investigated. The calculation shows that the shell correction is relatively more sensitive to the parameter R by comparing the corresponding shell correction energy of the four magic nuclei from light to heavy. The Strutinsky shell correction method plays an important role in the nuclear mass calculation based on macroscopic-microscopic method, and in the description of the nucleus ground state properties of super-heavy nucleus. Finally, we study the nuclear ground state deformation, shape coexistence and the nuclear mass formula by applying the macroscopic-microscopic method. By investigating the validity of the Strutinsky shell correction method, we found that the method is successful in general.
本工作主要是采用Woods-Saxon势,对Strutinsky壳修正方法做了一些检验、验证和计算分析。我们首先对核结构模型做了简要回顾,简单地介绍了核的单粒子能级,用接近实际单粒子势的Woods-Saxon势计算出一些核的单粒子能级。然后,我们详细地介绍了基于宏观-微观模型中的Strutinsky壳修正的方法,对该方法数学表达做了分析推导。针对能级密度的高斯厄米展开最大阶数P=6阶时,对高斯展开宽度γ的传统取值做了检查以及具体取值做了探讨;对Woods-Saxon势的参数对壳修正能的影响做了程序计算分析,给出了由轻到重四个典型幻数核相应的壳修正能。分析比较发现原子核半径参数R对壳修正能的影响比较大。Strutinsky壳修正方法对于计算原子核质量有重要的意义,对超重核的基态性质有一定影响作用。本工作最后介绍了该方法的应用,在基态质量公式的改进,基态形变与形状共存以及超重核的壳修正等方面。考察了Strutinsky壳修正方法的有效性,发现该方法在实际应用中还是比较成功的。
Nuclear physics is developing very rapidly in recent decades. Super-heavy nuclei research has already become one of the hot subjects in the research field of present nuclear physics. The shell effect is essential to the super-heavy nuclei, because it can offer the microscopic quantity shell effect which provides a possibility for the super-heavy nuclei to survive. The research on the calculation of the nuclear shell correction energy is of great importance for improving the nuclear theory and for the synthesis of super-heavy nuclei.
In this thesis, we first review some nuclear structure models briefly. The single particle energy level which is necessary for the calculation of the shell correction is introduced briefly. Using the realistic Woods-Saxon single-particle potential, we calculate the simple particle energy level of some spherical and axially deformed nuclei. The method of the shell correction which is proposed by Strutinsky based on the macroscopic-microscopic model is introduced in detail. The expressions in the Strutinsky shell correction method have been checked. In this work, we study the influence of the width parameters on the shell energy when the order p=6 of the Gauss-Hermite polynomials is fixed. The influence of the Woods-Saxon potential parameters, i.e. the potential depth V0, the radius R and the surface diffuseness a, on the shell energy is also investigated. The calculation shows that the shell correction is relatively more sensitive to the parameter R by comparing the corresponding shell correction energy of the four magic nuclei from light to heavy. The Strutinsky shell correction method plays an important role in the nuclear mass calculation based on macroscopic-microscopic method, and in the description of the nucleus ground state properties of super-heavy nucleus. Finally, we study the nuclear ground state deformation, shape coexistence and the nuclear mass formula by applying the macroscopic-microscopic method. By investigating the validity of the Strutinsky shell correction method, we found that the method is successful in general.
引文
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[37]卢希庭.原子核物理[M].北京:原子能出版社,2008:39—53.
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[40]C.Samanta and S.Adhikari, Phys. Rev. C 65(2002)037301.
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[50]M.Bolsterli,J.R.NIX,Phys.Rev.,C2,871(1970).
[51]Wu Zheying,Xu Furong.Nuclear Physics Review,2004,21(4):363(in Chinese).
[52]D.Lunney,J.M.Pearson,and C.Thibault,Rev.Mod.Phys.75,1021(2003).
[53]P.M?ller,J.R.Nix et al.,At Data Nucl.Data Tables 59.185(1995).
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[56]J.Duflo and A.P.Zuker,Phys.Rev.C52,R23(1995).
[57]G.Audi,A.H.Wapstra,and C.Thibault,Nucl.Phys.A729,337(2003).
[58]孙杰,刘艳鑫,原子核形状共存问题的研究[J],湖州师范学院学报,2008,30(2):36-37.
[59]P.M?ller,G.A.Leander,and J.R.Nix,Z.Phys.A323,41(1986).
[60]Yu.Ts.Oganessian,V.K.Utyonkov et al.,Phys.Rev.C69,054607(2004).
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[2]Sobiczewski A,Gareev F A,Kalinkin B N.Closed Shells for Z>82 and N>126 in a Diffuse Potential Well[J].Phyw Lett,1966,22:500.
[3]Meldner H.Predictions of New Magic Regions and Masses for Super-heavy Nuclei from Calculations with Realistic Shell Model Single Particle Hamiltonians[J].Ark Fys 1967,36:593.
[4]Nilsson S G,Nix J R,Sobiczewski A,etal.On the Spontaneous Fisson of Nuclei with Z near 114and N near 184[J].Nucl Phys,1968,A115:545.
[5]Nilsson S G,Tsang C F,Sobicsewski A,etal.On the Nuclear Structure and Stability of Heavy and Superheavy Elements[J].Nucl Phys,1969,A131:1.
[6]MoselU,Greiner W.On the Stability of Superheavy Nuclei Against Fisson[J].Z Phys,1969,222:261.
[7]Wu C L,Guidry M,Feng D H.Z=110-111 Elements and the Stability of Heavy and Superheavy Elements[J].Phys Lett,1996,B387:449.
[8]Lalazissis G A,Sharma M M,Ring P,et al.Superheavy Nuclei in the Relativistic Mean-field Theory[J].Nucl Phys.19966,A608:202.
[9]Cwiok S,Dobaczewski J,Heenen P H,et al.Shell Structure of the Superheavy Elements[J].Nucl Phys,1996,A611:211.
[10]Rutz K,Bender M,Buervenich T,et al.Superheavy Nuclei in Self-consistent Nuclear Calculations[J].Phys Rev,1997,C56(1):238.
[11]Bender M,Rutz K,Reinhard P G,et al.Potential Energy Surfaces of Superheavy Nucei[J].Phys Rev,1998,C58(4):2126.
[12]Meng J.Relativistic Continuum Hatree-Bogoliubov Theory with Both Zero Range and Finite Range Gogny Force and Their Application[J]. Nucl Phys,1998,A635:3.
[13]Meng J,Takigawa N.Structure of Superheavy Elements Suggested in the Reaction of 86Kr with 208Pb [J].Phys Rev,2000,C61:064319.
[14]Long W,Meng J,Zhou S G.Structure of the New Nuclide 259and Itsα-decay Daughter Nuclei[J].Phys Rev,2002,C65:047306. Db
[15]S.CWIOK,J.DUDEK,W.NAZAREWICZ,J.SKALSKI and T.Werner,Computer Physics Communications 46(1987)379-399.
[16]Strutinsky M V.Shell Effects in Nuclear Masses and Deformation Energies[J].Nucl Phys,1967, A95:420.
[17]Strutinsky V M.”Shells”in Deformed Nuclei[J].Nucl Phys, 1968, A122:1.
[18]MOLLER P,NIX J R,KARTZ K L.Nucler properties for astrophysical and radioactive-ion-beam application[J].Atomic Data and Nuclear Data Tables,1997,66:131-343.
[19]王永芬,原子核物理学基础[M].清华大学出版社,1986:105-106.
[20]胡济民,杨伯君,郑春开,原子核理论第一卷[M],1985:22.
[21]A,Bohr and B.R.Mottelson,Nuclear Structure, V.II,W.A.Benjamin, Inc.,Reading,Mass.,(1975)137-152.
[22]A.deShalit and H.Feshbach,Theoretical Nuclear Physics,V.I,John Wiley and Sons,Inc., NewYork,(1974)119-154.
[23]颜一鸣,原子核物理学[M].北京:原子能出版社,1990:48-50.
[24]Mayer M.,Phys.Rev.,75(1949)1766.
[25]Axel O.,J.H.D.Jensen,and H.E.Suess,Phys.Rev.,75(1949)1766.
[26]M.Goeppert-Mayer,Phys.Rev.75(1949)1969;78(1950)16.
[27]Min Liu,Ning Wang,et al.,Nucl.Phys.A768(2006)80.
[28]J.Blomqvist and S.Wahlborn,Ark.Fys.16(1960)543.
[29]V.A.Chepurnov,Yad.Fiz.6(1967)955.
[30]E.Rost,Phys.Lett.B26(1968)184.
[31]J.Dudek,Acta.Phys.Polon.B9(1978)919.
[32]支启军,令狐荣峰,吉世印.超重原子核区的壳效应研究[J].云南大学学报(自然科学版),2008,30 (5):494-497.
[33]Brueckner K A,Chirico J H,Meldner H W.Phys Rev,1971,C4:732.
[34]HuJimin,Zheng,Chunkai.Chinese Journal of Nuclear Physics,1985,7:1 (in Chinese).
[35]Audi G,Wapstra A H,Thibault C.Nucl Phys,2003,A729:337.
[36]Peng JinSong,Li Lulu,Zhou Shangui,Zhao Enguang.Nuclear Physics Review,2008,25(2):107.(in Chinese).
[37]卢希庭.原子核物理[M].北京:原子能出版社,2008:39—53.
[38]R.N.Sagaidak and A.N.Andreyev,Phys.Rev.C79(2009)054613.
[39]K.Heyde,Basic Idear and Concepts in Nuclear Physics(IOP,Bristol, 1999).
[40]C.Samanta and S.Adhikari, Phys. Rev. C 65(2002)037301.
[41]J.Mendoza-Temis,J.G.Hirsch,and A.P.Zuker,arXiv:0912.0882v1.
[42]Ning Wang, Min Liu, Xizhen Wu, Phys. Rev. C 81 (2010) 044322.
[43]P.M?ller,R.Nix,Nucl.Phys.A361(1981):117.
[44]C.Shen,Y.Abe,et al.,Int.J.Mod.Phys.E17(2008)66.
[45]Adam Romulo,International Conference on Advances in Nuclear Science and Engineering in Conjunction with LKSTN 2007(309-311).
[46]K.POMORSKI,ACTA PHRSICA POLONICA B36(2005)1221:1225.
[47]B.Mohammed-Azizi,D.E.Medjadi,Phys,Rev.C74(2006)054302.
[48]J.R.Nix,Physics and Chemistry of Fission,P.195.
[49]S.G.Nilsson et al.,Nucl.Phys.,A131,No.I,1(1969).
[50]M.Bolsterli,J.R.NIX,Phys.Rev.,C2,871(1970).
[51]Wu Zheying,Xu Furong.Nuclear Physics Review,2004,21(4):363(in Chinese).
[52]D.Lunney,J.M.Pearson,and C.Thibault,Rev.Mod.Phys.75,1021(2003).
[53]P.M?ller,J.R.Nix et al.,At Data Nucl.Data Tables 59.185(1995).
[54]S.Goriely,M.Samyn,and J.M.Pearson,Phys.Rev.C75,064312(2007).
[55]S.Goriely,N.Chamel,andJ.M.Pearson,Phys.Rev.Lett.102,152503(2009)
[56]J.Duflo and A.P.Zuker,Phys.Rev.C52,R23(1995).
[57]G.Audi,A.H.Wapstra,and C.Thibault,Nucl.Phys.A729,337(2003).
[58]孙杰,刘艳鑫,原子核形状共存问题的研究[J],湖州师范学院学报,2008,30(2):36-37.
[59]P.M?ller,G.A.Leander,and J.R.Nix,Z.Phys.A323,41(1986).
[60]Yu.Ts.Oganessian,V.K.Utyonkov et al.,Phys.Rev.C69,054607(2004).
[61]Yu.Ts.Oganessian,V.K.Utyonkov et al.,Phys.Rev.C74,044602(2006).
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