Extensions Of The Interacting Boson Model And Applications

The interacting boson model(IBM)has been proven to be successful in elucidating the structure and prop-erties of medium and heavy mass nuclei.However,it has been shown from extensive studies that appropriate extensions and modifications are necessary in order to provide a better description of the structure of transitional nuclei in the lower energy regime.Moreover,cross-shell multi-particle and multi-hole excitations are most likely to occur in nuclei,especially those near to the closed shells.Therefore,configuration mixing consideration is of practical significance.To modify level energies of higher angular momenta produced from the original IBM,which are too high in comparison to experimental results,and to improve the model results of B(E2)values and electric quadrupole moments,based on the IBM consistent-formulism,an exponential type modification to the strength of the quadrupole-quadrupole interaction and the three-,four-body,and the square of angular momentum terms,which are of the shell model origin,are considered resulting in the modified soft rotor model.To reveal configuration mixing effects in vibrational nuclei,an intruder configuration mixing scheme with 29)-particle and 29)-hole configurations up to9)??in the IBM U(5)limit is proposed and solved exactly by using the SU(1,1)coherent state method.As an application of the modified soft rotor model,except for 1⁺and other possible intruder states,low-lying positive parity level energies,B(E2)values and electric quadrupole moments of some low-lying states of^176-198Pt are fit and compared with the results of the original consistent-formulism.It is shown that,with the exponential type modification,excitation energies of high-lying excited states are effectively reduced in accordance to the experimental data,and the fitting results of electric quadrupole moments turn to be better than those of the original model,indicating the high order terms considered to be indispensable in describing the low-energy properties of these nuclei.In the U(5)limit multi-particle and multi-hole configuration mixing scheme,analytical expressions of excitation energies and B(E2)values of the model are provided explicitly.The rate of the boson number change and its fluctuation are taken as criterions to identify the configuration mixing.Some low-lying level energies and experimentally known B(E2)values of^108,110Cd are fit.It is also predicted that there may be other three low-lying intruder states around 2.5 Me V,for which further experimental verification is expected.Finally,it is shown that the extended one-dimensional dimer Bose-Hubbard model with multi-body interac-tions is exactly solvable by using the Bethe ansatz method with the help of the two-site permutation symmetry.The solution with three-particle hopping and three-body on-site interaction is demonstrated.Level energies and the ground-state entanglement of the system of 100 bosons are calculated to reveal the phase evolution pattern and the influence of the three-body on-site interaction to the system.It is shown the attractive three-body on-site interaction effectively enhances the entanglement,which is helpful to enhance the entanglement in design a system of ultra cold atoms on optical lattices and nonlinear superconducting quantum interference devices.