The competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei is analyzed in the framework of the mean-field plus the dynamic quadurpole-quadurpole, pairing and particle-hole interactions, whose Hamiltonian is diagonalized in the basis U(24) ?(U(6) ? S U(3) ? S O(3))■(U(4) ? S US(2)■ S UT(2)) in the L = 0 configuration subspace. Besides the pairing interaction, it is observed that the quadurpole-quadurpole and particlehole interactions also play a significant role in determining the relative positions of low-lying excited 0^+ and 1^+ levels and their energy gaps, which can result in the ground state first-order quantum phase transition from J = 0 to J = 1.The strengths of the isovector and isoscalar pairing interactions in these even-even nuclei are estimated with respect to the energy gap and the total contribution to the binding energy. Most importantly, it is shown that although the mechanism of the particle-hole contribution to the binding energy is different, it is indirectly related to the Wigner term in the binding energy.
A new scheme was recently proposed in which the usual SU（3） quadrupole-quadrupole interaction was replaced by an O（6） cubic interaction in the Interacting Boson Model, and also successfully applied to the description of 152Sm for the N=90 rare earth isotones with X（5） symmetry. By using this new scheme, in the present work, we further explore the properties of another candidate of 150Nd for the N=90 with X（5） symmetry. The low-lying energy levels and E2 transition rates are calculated and compared with the experimental data. The results show that the new scheme can also reasonably describe the experimental low-lying spectrum and the intraband and the interband E2 transitions for 150Nd. However, for the low-lying spectrum, the O（6） cubic interaction seems better in describing the energy levels, especially in higher excited states and γ band, yet the 02＋ level within the β band is lower than the corresponding experimental value and the U（5）-SU（3） scheme seems better to describe the low-lying levels of β band; and for the B（E2） transition, for the intraband transitions within the ground band and some interband transitions between the β band and the ground band, the results from O（6） cubic interaction are better than those from SU（3） quadrupole-quadrupole interaction, yet of which seems better to describe the intraband E2 transitions within β band. The present work is very meaningful in helping us to understand in depth the new characteristics of symmetry by the higher order O（6） cubic interaction.
We study a mixture of s-bosons and like-nucleon pairs with the standard pairing interaction outside an inert core. Competition between the nucleon-pairs and s-bosons is investigated in this scenario. The robustness of the BCS-BEC coexistence and crossover phenomena are examined through an analysis of pf-shell nuclei with realistic single-particle energies, in which two configurations with Pauli blocking of nucleon-pair orbits due to the formation of the s-bosons is taken into account. When the nucleon-pair orbits are considered to be independent of the s-bosons, the BCS-BEC crossover becomes smooth, with the number of the s-bosons noticeably more than that of the nucleon-pairs near the half-shell point, a feature that is demonstrated in the pf-shell for several values of the standard pairing interaction strength. As a further test of the robustness of the BCS-BEC coexistence and crossover phenomena in nuclei, results are given for B（E2; 01^＋→21^＋） values of even-even ^102-130 Sn with ^100Sn taken as a core and valence neutron pairs confined within the 1d（5/2）, 0g（7/2）, 1d（3/2）, 2s（1/2）, 1h（11/2）orbits in the nucleon-pair orbit and the s-boson independent approximation. The results indicate that the B（E2） values are reproduced well.
