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We study the fluctuation properties of ⌬Tϭ0 electromagnetic transition intensities and electromagnetic moments in Aϳ60 nuclei within the framework of the interacting shell model, using a realistic effective interaction for p f -shell nuclei with a 56 Ni core. The distributions of the transition intensities and of the electromagnetic moments are well described by the Gaussian orthogonal ensemble of random matrices. In particular, the transition intensity distributions follow a Porter-Thomas distribution. When diagonal matrix elements ͑i.e., moments͒ are included in the analysis of transition intensities, the distributions remain PorterThomas except for the isoscalar M 1. This deviation is explained in terms of the structure of the isoscalar M 1 operator.Random matrix theory ͑RMT͒ ͓1͔ was originally introduced to explain the statistical fluctuations of neutron resonances in compound nuclei ͓2͔. The theory assumes that the nuclear Hamiltonian belongs to an ensemble of random matrices that are consistent with the fundamental symmetries of the system. In particular, since the nuclear interaction preserves time-reversal symmetry, the relevant ensemble is the Gaussian orthogonal ensemble ͑GOE͒. The use of RMT in the compound nucleus was justified by the complexity of the nuclear system. Bohigas et al. ͓3͔ conjectured that RMT describes the statistical fluctuations of a quantum system whose associated classical dynamics is chaotic. RMT has become a standard tool for analyzing the universal statistical fluctuations in chaotic systems ͓4 -6͔.The chaotic nature of the single-particle dynamics in the nucleus can be studied in the mean-field approximation. The interplay between shell structure and fluctuations in the single-particle spectrum has been understood in terms of the classical dynamics of the nucleons in the corresponding deformed mean-field potential ͓7,8͔. However, the residual nuclear interaction mixes different mean-field configurations and affects the statistical fluctuations of the many-particle spectrum and wave functions. These fluctuations can be studied using various nuclear structure models. The statistics of the low-lying collective part of the nuclear spectrum have been studied in the framework of the interacting boson model ͓9,10͔, in which the nuclear fermionic space is mapped onto a much smaller space of bosonic degrees of freedom. Because of the relatively small number of degrees of freedom in this model, it was also possible to relate the statistics to the underlying mean-field collective dynamics. At higher excitations, additional degrees of freedom ͑such as broken pairs͒ become important ͓11͔, and the effects of interactions on the statistics must be studied in larger model spaces. The interacting shell model offers an attractive framework for such studies. In this model, realistic effective interactions are available, and the basis states are labeled by exact quantum numbers of angular momentum, isospin, and parity ͓12͔.RMT makes definite predictions for the statistical fluctuations of both the ...

An effective two-body density operator for point nucleon system folded with two-body correlation functions, which take account of the effect of the strong short range repulsion and the strong tensor force in the nucleon-nucleon forces, is produced and used to study the ground state two-body charge density distributionsare in opposite direction to those of SRC.

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