原子核中的无规相互作用以及基态0^+主导向群表示论的推广(英文)  

Random Interactions in Nuclei and Extension of 0^+ Dominance in Ground States to Irreps of Group Symmetries

作　　者：V.K.B.Kota 

机构地区：[1]国家物理实验室

出　　处：《高能物理与核物理》2004年第12期1307-1312,共6页High Energy Physics and Nuclear Physics

摘　　要：在相互作用玻色子模型框架下 ,使用U(N ) U(N1) U(N2 ) O(N1) O(N2 )和U(N ) O(N ) O(N1) O(N2 )群链下具有O(N1) O(N2 )对称性的无规单体及两体哈密顿量来研究给定的不可约表示(ω1ω2 )成为偶偶核基态的出现几率 ,其中 [ω1]和 [ω2 ]分别为O(1)和O(2 )的对称表示 .采用 5 0 0个无规矩阵系综对具有 10— 2 5个玻色子的体系进行研究后发现 ,当N1,N2 ≥ 3时 ,(ω1ω2 ) =(0 0 )出现的几率～ 5 0 % ;而 (0N)和 (N0 )出现的几率为 2 5 % .类似地 ,当N1≥ 3,N2 =1时 ,对N对偶数情形 ,ω1=0出现的几率约为75 % ;ω1=N出现的几率约为 2 5 % ;对N为奇数情形 ,ω1=0出现的几率约为 5 0 % ,而ω1=1或N出现的几率都约为 2 5 % .采用了一种推广的Hatree Bose平均场理论来解释所有的这些结果 .Random one plus two-body hamiltonians invariant with respect to O(N_1)O(N_2)symmetry in the group-subgroup chains U(N )U(N_1)U(N_2)O(N_1)O(N_2)and U(N )O(N )O(N_1)O(N_2) of a variety of interacting boson models are used to investigate the probability of occurrence of a given(ω_1ω_2)irreducible representation(irrep)to be the ground state in even-even nuclei;[ω_1] and [ω_2] are symmetric irreps of O(N_1) and O(N_2) respectively. Employing a 500 member random matrix ensemble for N boson systems (with N=10-25),it is found that for N_1,N_2≥3 the (ω_1ω_2)=(00) irrep occurs with～50% and (ω_1ω_2)=(N0) and (0N) irreps each with～25% probability. Similarly,for N_1≥3,N_2=1,for even N the ω_1=0 occurs with～75% and ω_1=N with～25% probability and for odd N,ω_1=0 occurs with～50% and ω_1=1,N each with～25% probability. An extended Hartree-Bose mean-field analysis is used to explain all these results.

关 键 词：几率 基态 群表示论 不可约表示 玻色子 类似 偶偶核 相互作用 发现 研究 

分 类 号：O571[理学—粒子物理与原子核物理] O414[理学—物理]