Quantum phase crossover in the spherical mean-field plus quadrupole-quadrupole and pairing model with two j-orbits

The shape phase crossover in the mean-field plus the geometric quadrupole-quadrupole and pairing model within two j-orbits is analyzed, for which a simple description of( )(10)(3-110)Sn confined in the lowest 1d(5/2) and 0g(7/2) orbits above the Sn-100 core is demonstrated to reveal the crossover behavior of the model. It is shown that B(E2;4(1)(+) -> 2(1)(+))/B(E2; 2(1)(+) -> 0(g)(+)), Q(4(1)(+))/Q(2(1)(+)) and B(E2; 9/2(1)(+) -> 5/2(1)(+))/B(E2; 11/2(1)(+) -> 7/2(1)(+)), Q(9/2(1)(+))/Q(7/2(1)(+)) in this case may serve as effective order parameters for even-even and odd-A systems, respectively, from which the shape phase crossover from the rotation-like phase to the superconducting-like phase can be observed with variation of the number of valence neutrons.