  A new statistical interpretation of the nuclear collective states is
suggested and applied recently in rare earths and actinide nuclei by the
two-neutron transfer reactions in terms of the nearest neighbor-spacing
distributions (NNSDs). Experimental NNSDs were obtained by using the complete
and pure sequences of the collective states through an unfolding procedure. The
two-neutron transfer reactions allow to obtain such a sequence of the
collective states that meets the requirements for a statistical analysis. Their
theoretical analysis is based on the linear approximation of a repulsion level
density within the Wigner-Dyson theory. This approximation is successful to
evaluate separately the Wigner chaos and Poisson order contributions. We found
an intermediate behavior of NNSDs between the Wigner and Poisson limits. NNSDs
turn out to be shifted from a chaos to order with increasing the length of
spectra and the angular momentum of collective states. Perspectives for the
statistical analysis of the symmetry breaking of states with the fixed
projection of angular momenta $K$ are discussed.
