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1、随机相互作用下原子核结构 研究的新进展,上海交通大学物理系,赵玉民,提纲,随机相互作用原子核低激发态主要结果 最近其他研究组几个工作 我们最近的工作 展望,Part I,随机相互作用下原子核的 规则结构的主要结果,Wigner introduced Gaussian orthogonal ensemble of random matrices (GOE) in understanding the spacings of energy levels observed in resonances of slow neutron scattering on heavy nuclei. Ref: An
2、n. Math. 67, 325 (1958) 1970s French, Wong, Bohigas, Flores introduced two-body random ensemble (TBRE) Ref: Rev. Mod. Phys. 53, 385 (1981); Phys. Rep. 299, (1998); Phys. Rep. 347, 223 (2001). Original References: J. B. French and S.S.M.Wong, Phys. Lett. B33, 449(1970); O. Bohigas and J. Flores, Phys
3、. Lett. B34, 261 (1970). Other applications: complicated systems (e.g., quantum chaos),Two-body Random ensemble (TBRE),What does 0 g.s. dominance mean ? In 1998, Johnson, Bertsch, and Dean discovered that spin parity =0+ ground state dominance can be obtained by using random two-body interactions. T
4、his result is called the 0 g.s. dominance. Similar phenomenon was found in other systems, say, sd-boson systems. C. W. Johnson et al., PRL80, 2749 (1998); R. Bijker et al., PRL84, 420 (2000); L. Kaplan et al., PRB65, 235120 (2002).,One usually choose Gaussian distribution for two-body random interac
5、tions There are some people who use other distributions, for example, A uniform distribution between -1 and 1. For our study, it is found that these different distribution present similar statistics.,Two-body random ensemble（）,A Simple example,Where this result is interesting?,Available Results,Empi
6、rcal method Zhao off-diagonal matrix elements for I=0 states Drozdz et al. (2001) Highest symmetry &Time Reveral Otsuka&Shimizu(2004-2007) Spectral Radius Papenbrock & Weidenmueller (2004-2007) Semi-empirical formula Yoshinaga, Arima and Zhao(2006-2007),References after Johnson, Bertsch and Dean,R.
7、Bijker, A. Frank, and S. Pittel, Phys. Rev. C60, 021302(1999); D. Mulhall, A. Volya, and V. Zelevinsky, Phys. Rev. Lett.85, 4016(2000); Nucl. Phys. A682, 229c(2001); V. Zelevinsky, D. Mulhall, and A. Volya, Yad. Fiz. 64, 579(2001); D. Kusnezov, Phys. Rev. Lett. 85, 3773(2000); ibid. 87, 029202 (2001
8、); L. Kaplan and T. Papenbrock, Phys. Rev. Lett. 84, 4553(2000); R.Bijker and A.Frank, Phys. Rev. Lett.87, 029201(2001); S. Drozdz and M. Wojcik, Physica A301, 291(2001); L. Kaplan, T. Papenbrock, and C. W. Johnson, Phys. Rev. C63, 014307(2001); R. Bijker and A. Frank, Phys. Rev. C64, (R)061303(2001
9、); R. Bijker and A. Frank, Phys. Rev. C65, 044316(2002); P.H-T.Chau, A. Frank, N.A.Smirnova, and P.V.Isacker, Phys. Rev. C66, 061301 (2002); L. Kaplan, T.Papenbrock, and G.F. Bertsch, Phys. Rev. B65, 235120(2002); L. F. Santos, D. Kusnezov, and P. Jacquod, Phys. Lett. B537, 62(2002); T. Papenbrock a
10、nd H. A. Weidenmueller, Phys. Rev. Lett. 93, 132503 (2004); T. Papenbrock and H. A. Weidenmueller, Phys. Rev. C 73 014311 (2006); Y.M. Zhao and A. Arima, Phys. Rev.C64, (R)041301(2001); A. Arima, N. Yoshinaga, and Y.M. Zhao, Eur.J.Phys. A13, 105(2002); N. Yoshinaga, A. Arima, and Y.M. Zhao, J. Phys.
11、 A35, 8575(2002); Y. M. Zhao, A. Arima, and N. Yoshinaga, Phys. Rev.C66, 034302(2002); Y. M. Zhao, A. Arima, and N. Yoshinaga, Phys. Rev. C66, 064322(2002); Y.M.Zhao, A. Arima, N. Yoshinaga, Phys.Rev.C66, 064323 (2002); Y. M. Zhao, S. Pittel, R. Bijker, A. Frank, and A. Arima, Phys. Rev. C66, R41301
12、 (2002); Y. M. Zhao, A. Arima, G. J. Ginocchio, and N. Yoshinaga, Phys. Rev. C66,034320(2003); Y. M. Zhao, A. Arima, N. Yoshinga, Phys. Rev. C68, 14322 (2003); Y. M. Zhao, A. Arima, N. Shimizu, K. Ogawa, N. Yoshinaga, O. Scholten, Phys. Rev. C70, 054322 (2004); Y.M.Zhao, A. Arima, K. Ogawa, Phys. Re
13、v. C71, 017304 (2005); Y. M. Zhao, A. Arima, N. Yoshida, K. Ogawa, N. Yoshinaga, and V.K.B.Kota , Phys. Rev. C72, 064314 (2005); N. Yoshinaga, A. Arima, and Y. M. Zhao, Phys. Rev. C73, 017303 (2006); Y. M. Zhao, J. L. Ping, A. Arima, Phys. Rev. C76, 054318 (2007); J. J. Shen, Y. M. Zhao, A. Arima, N
14、. Yoshinaga, Physic. Rev. C77, 054312 (2008); J. J. Shen, A. Arima, Y. M. Zhao, N. Yoshinagan, Phys. Rev. C78, in press (2008); etc. Review paper： Y.M. Zhao , A. Arima, and N. Yoshinaga, Physics Reports 400, 1 (2004).,Phenomenological method by our group (Zhao, Arima and Yoshinaga): reasonably appli
15、cable to all systems Mean field method by Bijker and Frank group: sd, sp boson systems (Kusnezov also considered sp bosons in a similar way) Geometric method suggested by Chau, Frank, Smirnova, and Isacker goes along the same line of our method (provided a foundation of our method for simple systems
16、 in which eigenvalues are in linear combinations of two-body interactions).,Applications of our method to realistic systems,Spin Imax Ground state probabilities,By using our phenomenological method, one can trace back what interactions, not only monopole pairing interaction but also some other terms with specific features, are responsible for 0 g.s. dominance. We understand that the Imax g.s. probability comes from the Jmax pairing interaction for single-j shell (also for bo
