Shell-model tests of the bimodal partial state densities in a 2x2 partitioned embedded random matrix ensemble

The mixing of well-separated subspaces of an interacting many-particle system, such as a nucleus with active nucleons distributed in more than one major shell, can be studied using partitioned embedded ensembles of random matrices. The bimodal form of partial state densities (one-point functions) predicted earlier for a 2x2 partitioned embedded ensemble, which may be regarded as a model for the mixing of two well-separated degenerate subspaces, is tested using nuclear shell-model calculations in the {(ds)^ (B (^)^(/7/2)^]^~^^~^ space. The theoretical forms predicted by the binary correlation approximation theory are in good agreement with the shell-model results. This suggests that with suitable extensions it might be feasible to use the binary correlation method to deal with several interacting subspaces involving multimodal distributions.