Structure Of Sm Isotopes And Study Of Cubic Term

The interacting boson model (IBM) has been successful in the description of nuclear collective excitation of medium and heavy nuclei. Different from the geometrical picture, it has an inherent group structure. In the first version (IBM-1), only pairs with angular momentum L=0 (called s boson) and L=2 (called d boson) are included. Despite of its simplicity, it describes the properties of many nuclei.First, the basic idea of the interacting boson model(IBM-1) is introduced, including the basic states, Hamiltonian, the reduction of group chains, intrinsic states and potential energy surface, etc.In chapter 3, the positive parity colletive states in the even-even 148-158Sm isotopes are studied systematically in the framework of the original interacting boson model(IBM-1). The positive states of the Sm isotopic chain and the electric quadrupole transition rates are calculated. Good agreements is obtained through the comparison between experimental data and calculated values. The isotopes can be well described by a schematic Hamiltonian in transition from U(5) to SU(3) dynamic symmetry.In chapter 4, we introduced cubic term in the Hamiltonian of the IBM-1, the positive parity colletive states and the electric quadrupole transition rates in the even-even 148-158Sm isotopes are studied. Comparing the low-lying spectra and E2 transition rate of Sm isotopes between the original IBM without cubic terms and the IBM with cubic terms, we obtain some new results which show the effect of the cubic term. Furthermore, we introduced QQQ term in the above Hamiltonian and calculated the spectrum of Sm isotopes to learn the effect of higher terms.In addition, we also calculate the classic limit of the Hamiltonians to obtain potential energy surfaces in terms of β and γ from which we can get a more intuitive insight. We show the effect of cubic terms on the nucleus in the transition from U(5) symmetry to SU(3) symmetry. In this range, although we don't obtain a stable triaxial shape which can be got in O(6) nucleus, the cubic term intends to form a extremum at γ=30。 with the same β value, that will lead to a triaxial deformation. Meanwhile, we note that the extremum at about β=1 is shallow, namely the effect of the cubic term is weak about that place which can explain the fact that the cubic term only change the levels in high energy but leaves the levels of low-lying state unchanged as we discussed in the thesis. We conclude that when we simulate high energy levels of nucleus we should consider to include the cubic terms, so that the IBM can discribe nucleus better.