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A new statistical interpretation of the nuclear collective states issuggested and applied recently in rare earths and actinide nuclei by thetwo-neutron transfer reactions in terms of the nearest neighbor-spacingdistributions (NNSDs). Experimental NNSDs were obtained by using the completeand pure sequences of the collective states through an unfolding procedure. Thetwo-neutron transfer reactions allow to obtain such a sequence of thecollective states that meets the requirements for a statistical analysis. Theirtheoretical analysis is based on the linear approximation of a repulsion leveldensity within the Wigner-Dyson theory. This approximation is successful toevaluate separately the Wigner chaos and Poisson order contributions. We foundan intermediate behavior of NNSDs between the Wigner and Poisson limits. NNSDsturn out to be shifted from a chaos to order with increasing the length ofspectra and the angular momentum of collective states. Perspectives for thestatistical analysis of the symmetry breaking of states with the fixedprojection of angular momenta $K$ are discussed.

Two-neutron transfer reactions and quantum-chaos measure of nuclear spectra