Ginocchio Model Research Articles

Bosonization from Quasiparticle Representation and Effects of Nucleon-Number Conservation

We discuss microscopic ground of the IBM from the quasiparticle viewpoint, paying attention to the effects of nucleon-number conservation. The OAI mapping is revisited, showing for a single-j system how the number conservation effects are taken into account. The number-conserving quasiparticle approximation exploited by Li is applied to incorporate the number conservation effects. The significance of the number conservation is confirmed via the tests in the Ginocchio model and in a 2j system. An effective boson number is evaluated based on the number-conserving quasiparticle method. It is shown that the nucleon-number conservation effects are well incorporated in the IBM, even for systems with non-degenerate single-particle orbits.

Bosonization from Quasiparticle Representation and Effects of Nucleon-Number Conservation

We discuss microscopic ground of the IBM from the quasiparticle viewpoint, paying attention to the effects of nucleon-number conservation. The OAI mapping is revisited, showing for a single-j system how the number conservation effects are taken into account. The number-conserving quasiparticle approximation exploited by Li is applied to incorporate the number conservation effects. The significance of the number conservation is confirmed via the tests in the Ginocchio model and in a 2j system. An effective boson number is evaluated based on the number-conserving quasiparticle method. It is shown that the nucleon-number conservation effects are well incorporated in the IBM, even for systems with non-degenerate single-particle orbits.

Multiphonon structure in a gamma -unstable fermionic model.

The multiphonon structure is shown for the ${\mathrm{SO}}_{6}$ limit of the Ginocchio model. We can see that the multiphonon description is valid strictly in this fermion system. The phonon states are created by the quadrupole operator ${\mathit{P}}^{2}$ with proper symmetrization. All the \ensuremath{\sigma}=N states can be described in this scheme in terms of phonon quanta and two-phonon anharmonicity. The dipole and octupole interactions are also included in the Hamiltonian for both the boson and fermion systems.

Spurious states in boson calculations — spectre or reality?

We discuss some prevailing misconceptions about the possibility that spurious states may in general contaminate boson calculations of fermion systems on either the phenomenological or microscopic level. Amongst other things we point out that the possible appearance of spurious states is not inherently a mapping problem, but rather linked to a choice of basis in the boson Fock space. This choice is mostly dictated by convenience or the aim to make direct contact with phenomenology. Furthermore, neither well established collectivity, nor the construction of boson operators in the Marumori or OAI fashion can as such serve as a guarantee against the appearance of spurious boson states. Within an SO(12) generalisation of the Ginocchio model where collective decoupling is complete, we illustrate how spurious states may appear in an IBM-type sdg-boson analysis. We also show how these states may be identified on the boson level. This enables us to present an example of an sdg-spectrum which, although it may be reasonably correlated with experimental data, nevertheless has the first few low lying states all spurious when interpreted from the microscopic point of view. We briefly speculate about the possibility that certain types of truncation may in fact automatically circumvent the appearance of spurious states.

Nuclear mass dependence of chaotic dynamics in the Ginocchio model.

The chaotic dynamics in nuclear collective motion is studied in the framework of a schematic shell model which has only monopole and quadrupole degrees of freedom. The model is shown to reproduce the experimentally observed global trend toward less chaotic motion in heavier nuclei. The relation between the current approach and the earlier studies with bosonic models is discussed.

Ginocchio model with isospin

Abstract We study the sp(8) subgroup of the isospin-invariant Ginnocchio model. The allowed quantum numbers are determined in terms of Young's diagrams. Using this result, we discuss the excitation energy of a model hamiltonian.

Collective boson realization for the nuclear Sp(6) model.

We demonstrate the construction of an exact sd-boson realization of the Sp(6) fermion dynamical symmetry model (Ginocchio model) from an application of the generalized Dyson mapping and subsequent truncation. This realization is an illustration of the validity of the procedure initiated by Geyer and Hahne and analyzed in full generality by Kim and Vincent. We discuss the connection of the Sp(6) model with the SU(3) limit of the interacting-boson model and the implications for the interpretation of its parameters.

The Shift Operators in Ginocchio Model11Projects supported by the National Natural Science Foundation of China

In fermion space, the vectors and are not orthogonal. The analytic expressions of the wave functions in Ginocchio model are more complicated than those in IBM. Using the shift operator method we can easily construct the wave functions in Ginocchio model. The wave functions of the irreducible representations of for nucleon number are given.

Non-degenerate single-particle energies in the Ginocchio model

A one-body operator expressing the breaking of the degeneracy of the single-nucleon energies is added to the pairing interaction of the Ginocchio model. This operator couples states inside the model's SD space to states outside it. The influence of this coupling on the effective interaction in the SD space and the possibility of expressing the results in terms of renormalization of parameters in the fermion hamiltonian or the IBM are investigated. The effective interaction is found to be almost diagonal in seniority, while splitting the previously-degenerate seniority multiplets. Appropriately renormalized Ginocchio and IBM hamiltonians can approximately reproduce the results, but fermion-number dependence of the hamiltonian parameters and explicit three-body interactions are needed to reproduce the computed effects exactly.

A unification of boson expansion theories: (III). Applications

A general scheme of constructing boson expansions that was proposed in earlier work is applied to a number of examples. The Fukutome expansion is obtained by considering the spinor representation of the SO(2 N + 1) group. Its hermitian, Holstein-Primakoff-type version is also derived. The generalized Dyson expansions for even and odd fermion systems are given in terms of two spinor representations of the SO(2 N) group. For fixed fermion number systems the relevant boson expansions are obtained by considering the fundamental representations of SU( N) while for fixed seniority those of Sp( N) are concerned. The collective boson expansions corresponding to the Ginocchio model, the interacting boson model of Arima and Iachello and the Elliott model are given for the symmetric representations of SO(8) and SU( l + 1) and any representation of SU(3).

Unveiling s- and d-bosons in even- and odd- A nuclei

The generalized Dyson-Maleev boson mapping is applied to the Ginocchio model which is formulated in terms of bifermion operators which are generators of an SO(8) algebra. For this algebra, three kinds of realizations are obtained. These are the fully collective realization in which s-and d-bosons emerge, a realization for odd- A nuclei in terms of ideal fermions in addition to the bosons, and a realization in which non-collective bosons are included. The hamiltonian obtained by this method bears a resemblance to the phenomenological IBM hamiltonian for even- and odd- A nuclei, except that it is generally non-hermitian in both cases.

Relation of the interacting boson model to the shell model

A microscopic foundation of the interacting boson model is discussed from the shell model point of view. The Ginocchio model and the single j-shell model are taken to study various approximations for deriving the boson Hamiltonian. In the neutron-proton interacting boson model, we show the importance of the coupling to non-collective states for renormalizing some parameters in the boson Hamiltonian.