Deformed fermion realization of sp(4) and its reductions

A specific q-deformation of the compact symplectic sp(4) algebra, one that is suitable for nuclear physics applications, is realized in terms of q-deformed fermion creation and annihilation operators of the shell-model. The generators of the algebra close on four distinct realizations of the u _q (2) subalgebra. These reductions, which correspond to different pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q-deformation is based on a comparison of the results for energies of the lowest isovector-paired 0⁺ states in the deformed and non-deformed cases.     

Quasi-SU(3) truncation scheme for even–even sd-shell nuclei

The quasi-SU(3) symmetry was uncovered in full pf and sdg shell-model calculations for both even–even and odd–even nuclei. It manifests itself through a dominance of single-particle and quadrupole–quadrupole terms in a Hamiltonian used to describe well-deformed nuclei. A practical consequence of the quasi-SU(3) symmetry is an efficient basis truncation scheme. In [C.E. Vargas et al., Phys. Rev. C 58 (1998) 1488] it is shown that when this type of Hamiltonian is diagonalized in an SU(3) basis, only a few irreducible representations (irreps) of SU(3) are needed to describe the yrast band, the leading S=0 irrep augmented with the leading S=1 irreps in the proton and neutron subspaces. In the present article the quasi-SU(3) truncation scheme is used, in conjunction with a “realistic but schematic” Hamiltonian that includes the most important multipole terms, to describe the energy spectra and B(E2) transition strengths of ^20,22Ne, ²⁴Mg and ²⁸Si. The effect of the size of the Hilbert space on both sets of observables is discussed, as well as the structure of the yrast band and the importance of the various terms in the Hamiltonian. The limitations of the model are explicitly discussed.     

Surface Delta-Interaction in Nucleon-Pair Shell Model

The effect of surface delta-interaction (SDI) in nucleon-pair shell model truncated to an SD-subspace isstudied. The results show that with the single-particle level splitting fully taken into account, for realistic SDI strength,the surface delta-interaction also enhance the E2 and M1 transitions of low-lying states.     

Quasi-exactly solvable decatic model description of nuclei near the X(5) critical point

The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decatic β-part potential is studied.It is shown that the decatic model can well reproduce the X(5)model results as far as the energy ratios in the ground and beta band and related B(E2)values are concerned.Fitting results to the low-lying energy ratios and relevant B(E2)values of even-even X(5)candidates ¹⁵⁰Nd,¹⁵⁶Dy,¹⁶⁴Yb,¹⁶⁸Hf,¹⁷⁴Yb,^176,178,180Os,and ^188,190Os show that the decatic model provides the best fitting results for the energy ratios,while the X(5)model is the best at reproducing the B(E2)values of these nuclei,in which the beta-bandhead energy is lower than that of the gamma band.While for even-even nuclei,such as ^154,156,158Gd,with bandhead energies of the beta and gamma bands more or less equal within the X(5)critical point to the axially deformed region,our numerical analysis indicates that the decatic model is better than the X(5)model in describing both the low-lying level energies and related B(E2)values.     

SD对壳模型下原子核形状相变（英文）

在SD 对壳模型的理论框架下讨论了原子核形状相变模式。研究结果表明,该理论模型可以把相互作用玻色子模型中U（5）-SU（3）以及U（5）-SO（6） 形状相变模式再现出来,相互作用玻色子模型中有关临界点对称性的特征也可以很好地描述。本文同时也发现原子核从振动到转动的形状相变可以通过改变相互作用强度来实现。The nuclear shape phase transitional patterns were studied in the SD-pair shell model. The results show that the transitional patterns similar to the U(5)-SU(3) and U(5)-SO(6) transitions in the interacting boson model can be produced. The signatures of the critical point symmetry in the interacting boson model are also produced approximately. It is also found that the shape phase transitional pattern between vibration and rotation can also be produced by changing the interactional strength.     

Orthogonal polynomial expansions for effective interactions in the modified Lipkin model

The effective interaction in a one-dimensional model is calculated in terms of an orthogonal polynomial (OP) expansion derived from spectral distribution considerations. Configuration densities are assumed to be gaussian. The results are compared with those of a Brillouin-Wigner (BW) perturbation expansion for the same model. While for a strong perturbation the BW series diverges, the OP expansion is shown to converge smoothly.