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

Abstract

A new statistical interpretation of the nuclear collective states is suggested and applied to analysis of states, found 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 a linear approximation of the 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. The symmetry breaking of states with the fixed projection of angular momenta is discussed in terms of degree of symmetry – the number of independent integrals of motion beyond the system energy – in relation to the periodic orbit theory.

Keywords

• statistical analysis
• nuclear collective states
• quantum and classical chaos
• nearest neighbor-spacing distributions
• Wigner and Poisson distributions.