摘要
本文第一部分求解了原子核在三轴形变势中,处在单j轨道及单N轨道上的单粒子的本征值方程,对单j轨道情况进行了从jZ表象到jy表象和jX表象的变换,讨论了单粒子本征波函数的对称性与势形状的关系。解释了单N基矢情况下本征波函数趋向于三轴形变参量γ=30的原因。
本文的第二部分首先以最简单的单粒子乘积波函数为例,通过对两个、三个到多个粒子最简单乘积态角动量投影算符矩阵元与CG系数关系的推导、论证了CG系数和积分两种计算方法的一致性和各自的优缺点,讨论了角动量投影算符矩阵元的性质;然后在推转壳模型K结构的基础上,以六粒子体系推转壳模型为例,将原来推转壳模型的基矢进行角动量投影,并正交规一化以后,作为新的基矢,求解推广的本征值方程得到确定角动量I值的晕带及第一、第二、第三激发带的K结构图,又将这些结果与原来推转壳模型结构进行比较;并分析了二者不同的原因。
最后论文分析了文中二个看似相对独立部份的内在联系。
In the first part of the thesis , the eigen-value equation of a single particle moving in a triaxial deformed potential is solved with two kinds of basis. One basis space is the single j particle orbit, another is single shell N orbits. The representation transformations are carried for the first case in order to see clearly the links between the symmetries of the potential and the eigen wave function. The explanation is made for the characteristics of the wave functions in the second basis space.
In the second part of the thesis, the connections between the matrix elements of angular momentum projection operator and the CG coefficients are provided by taking the simplest product wave function of two, and six particles as examples. The properties of the matrix elements of the angular momentum projection operator, the coincidence between the CG coefficients and integration methods are discussed. The advantages and the disadvantages of the two methods are analyzed. Then the angular momentum projection is performed for the basis of a six-particle system of the original cranking shell model. The diagrams of K structure for certain angular momentums versus cranking frequencies in the eigen-functions are plotted after solving the generalized eigen-value equations. The figures are compared with the original cranking shell model results. The differences between them are analyzed..
At last, the internal essential relations of the two seemingly independent parts are pointed .
引文
[1] 廖继志. 近代原子核模型 [M].成都: 四川大学出版社,1990.(P335)
[2]J.MEYER-TER-VEHN. Collective Model Description Of Transitional Odd-A Nuclei (I)The Triaxial-rotor-plus-particle modle[J]. Nuclear Physics A , 1975,49:111-140.
[3]M.Gmayer ,Phys.Rev.75(1949)1969:78(1950)16.
[4]O.Haxel,J.H.D.Jensen. and H.Esuess,Phys.Rev.75(1949)1766.
[5]M. Gmayer and J.H.D.Jensen.,Elementary Theory of Nuclear Structure (1995),Wiley.
[6] Bengtsson R, Gareat J D. Lund-Mph, 1984; 18: 1.
[7] Ring P, Shuck P. The Nuclear Many-Body Problem. New York: Springer-Verlag Inc, 1980: 130
[8] Hamamoto I. I, Eroglia R, Hagemann G P, Herskind B. Critical Aralysis of the C anking.Swiss: Elsevie: Science Publisheis B V, 1985: 129.
[9] C.S.Wu and J.Y.Zeng,Phys.Rev.C40,998(1989)
[10] C.S.Wu and J.Y.Zeng,Phys.Rev.C41,1822(1990)
[11] Peter Ring. Peter Schuck, The Nuclear Many Body Problem[M].Berlin Spring-Verlag New York Heidelberg, 1980:5-9.
[12] 曾谨言. 量子力学卷 II[M].北京:科学出版社,2001.
[13]杰尔 R N. 角动量——化学及物理学中的方位问题[M].北京: 科学出版社,1995.
[14] 四川大学高等数学教研组. 高等数学(物理专业用)第三册第一分册[M].北京:人民教育出版社,1997.
[15] 廖继志. 近代原子核模型 [M].成都: 四川大学出版社,1990.(P2)
[16]郑仁蓉,廖继志. 原子核对称性投影自洽场方法[M]. 成都: 四川大学出版社,1993. (P62)
[17] K.HARA and Y.SUN . Studies of high-spin states in rare-earth nuclei using angular momentum projection method(II) .Signature inversion in doubly odd nuclei . Nucl phys,1991,A531:221~236
[18]KENJI HARA and YANG SUN. PROJECTED SHELL MODOLE AND HIGG-SPIN SPECTROSCOPY. International Journal of Physics E,Vol.4,No.4(December,1995)637-785
[19]杨迎春,陆祺,郑仁蓉.多个角动量的耦合与角动量的投影方法[J].上海师范大学学报(自然科学版),2005,(4):32-36。
[20]赵伊君,张志杰. 角动量与原子能量[M]. 科学出版社,1982
[21]. Peter Ring, Peter Schuck. The Nuclear Many-Body Problem [m]. New York :Springer-Verlag,1980(chapter 5)
[22] 郑仁蓉,廖继志.原子核对称性投影自洽场方法[M].成都:四川大学出版社,1993.(P20-21).
[23] 杨迎春,硕士论文(2006),上海师范大学。
[24] 曾谨言,孙洪洲.原子核结构理论.上海科学技术出版社.1987(p334,p335,p336)
[25] J.Y.Zeng and T.S.Cheng.,Nucl.Phys.,A405(1983),1.
[26] Hamamoto,I.,Phenomena Exhibiting Triaxial Shape Induced by Rotation,Lund-Mph-86/15.
[27] Hamamoto I. Treatise On Heavy-ion Science, 1985; 3: 1.
[28] Job. Son A, Ryde H, Sztarkier J. Physics Letter, 1971; 34 B(605): 101
[29] Devoigt M J A, Dudek J, Szymanski Z. Reviews of Modern Physics. 1983; 55(4):958.
[30] Peter Ring. Peter Schuck, The Nuclear Many Body Problem[M].Berlin Spring-Verlag New York Heidelberg, 1980: 477
[31] 郑仁蓉,廖继志.原子核对称性投影自洽场方法[M].成都:四川大学出版社,1993.(P22).