Boson-fermion mappings for odd systems from supercoherent states

We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both complex and Grassmann variables. In addition to a known mapping for the full so(2$N$+1) algebra, we also uncover some other formal mappings, together with mappings relevant to collective subspaces.Comment: 40 pages, REVTE

Pairing and repulsive effective interactions

A two-level model with particles interacting via monopole pairing forces is used to show that the ground state can exhibit superfluidity even in cases where the interaction is seemingly repulsive. This mechanism is expected to play a role in the understanding of pairing correlations obtained for meson exchange forces, where the interaction has repulsive as well as attractive components.Articl

Semiclassical analysis of the interacting boson model for dipole resonances

The interacting boson model for giant dipole resonances in deformed nuclei is analyzed by semiclassical means. A geometrical form of the dipole interactions is derived. Deformed dipole states are introduced in the interacting boson model formulation. They are related to dipole states in the dynamic collective model. This makes it possible to show that all the matrix elements of the dipole interaction between the lowest-energy states in the boson and the geometrical model agree to leading order in N. It is concluded that no structural differences exist between the two models for the low-lying states and for large N. © 1986 The American Physical Society.Articl

Propagation by pairing excitations in open shells

The propagator method for elementary excitations is applied to three particles outside a closed shell. It is shown that the propagator contains no spurious contributions and that the overcompleteness of the basis has the advantage that coefficients of fractional parentage can be extracted.La méthode de la fonction de propagation des excitations fondamentales est appliquée au cas de trois particules en dehors d'une couche saturée. Il est démontré que la fonction de propagation ne contient pas de contributions parasites. Le fait que la base est surabondante a l'avantage de permettre l'extraction de coefficients de parentage fractionné

Algebraic versus geometrical approach to the dipole resonances

The dynamic collective model and the dipole boson model are compared and the possibility of translating one into the other is investigated for deformed and SU(3) nuclei, respectively. It is shown that in one respect the two models are basically different. While it is natural in the dynamic collective model to have strong interactions between dipole and surface modes in deformed nuclei, the natural choice in the dipole boson model is that this coupling to the side bands is small for SU(3) nuclei. The latter is shown to be in agreement with the available experimental data. An analysis for 168Er shows that it is possible to obtain parameters for the dipole boson model from the hydrodynamic model which give a good account of all the experimental data. © 1987.Articl

Vibrations and rotations for the proton-neutron interacting boson model

The interacting proton-neutron boson model (IBM-2) is analyzed in terms of the concepts of a geometrical picture. The centre of mass and relative-motion deformations are determined, and for the deformed systems, rotational and vibrational modes are identified. The parameters in an intrinsic hamiltonian which govern these modes are calculated. For the SU(3) dynamical symmetry a one-to-one mapping is given between low-lying basis states in the geometrical and the algebraic model. The magnetic dipole operator in the geometrical model is derived from its counterpart in IBM-2. This serves as an example for the calculation of static and transition operators, generally. © 1988.Articl

Geometrical representation of interacting boson models: U(3) model

A method is presented by which a geometrical interpretation can be given for boson models without leaving the domain of quantum mechanics. This approach turns out to be particularly useful in symmetry-preserving treatments of deformed boson systems. A U(3) boson model having an SO(2) symmetry, which is to be preserved throughout, is analyzed in detail. For a well-deformed system, rotational and vibrational modes are identified. A procedure is developed by which the parameters of the geometrical description for the deformed case can be calculated in a series expansion controlled by the inverse of the boson number. The method is compared with the corresponding random phase approximation approach. © 1987 The American Physical Society.Articl

Quasi-Hermitian operators in quantum mechanics and the variational principle

We establish a general criterion for a set of non-Hermitian operators to constitute a consistent quantum mechanical system, which allows for the normal quantum-mechanical interpretation. This involves the construction of a metric (if it exists) for the given set of non-Hermitian observables. We discuss uniqueness of this metric. We also show that it is not always necessary to construct the metric for the whole set of observables under consideration, but that it is sufficient for some calculational purposes to construct it for a subset only, even though this metric is, in general, not unique. The restricted metric turns out to be particularly useful in the implementation of a variational principle, which we also formulate. © 1992.Articl

Nuclear matter with scalar-vector interactions

The properties of cold nuclear matter are investigated in a class of nonlinear mean field - theories which includes a density dependence of the meson parameters. This dependence can be both explicit and implicit through the effective nucleon mass. We apply the theory to the case of an interaction between the scalar and the vector mesons and investigate the properties of neutron stars using the resulting equation of state. © 1994 The American Physical Society.Articl

Boson analyses in the Ge isotopes

The strong variation in energy of the first excited 0+ state in the even-even Ge isotopes is investigated with pairing type interactions in various model spaces. Although it had been possible in previous work to describe this variation in a BCSrandom-phase-approximation (RPA) calculation in the neutron configuration only, the corresponding exact diagonalization disagrees with the BCS-RPA results and experiment. It is furthermore shown that the behavior of the first excited 0+ state cannot be obtained by a reasonable variation of parameters in the exact neutron pair calculations. This suggests that the model space be enlarged to include proton, neutron, and proton-neutron pairing. The construction of the corresponding basis is then simplified by performing a boson mapping and employing the ideal collective boson basis. This, however, may lead to the occurrence of spurious states, even at fairly low energies, and three separate methods by means of which they can be identified are discussed. Although the enlarged model space gives a desired lowering of excitation energy of the first excited 0+ states in an exact diagonalization, the strong experimental variation could not be achieved with this simple interaction. Nevertheless, the analysis yields further and new insight into applications of boson mappings, specifically about how and when spurious states may be identified in calculations which are performed in a truncated space not invariant under a given collective algebra. © 1994 The American Physical Society.The strong variation in energy of the first excited 0+ state in the even-even Ge isotopes is investigated with pairing type interactions in various model spaces. Although it had been possible in previous work to describe this variation in a BCSrandom-phase-approximation (RPA) calculation in the neutron configuration only, the corresponding exact diagonalization disagrees with the BCS-RPA results and experiment. It is furthermore shown that the behavior of the first excited 0+ state cannot be obtained by a reasonable variation of parameters in the exact neutron pair calculations. This suggests that the model space be enlarged to include proton, neutron, and proton-neutron pairing. The construction of the corresponding basis is then simplified by performing a boson mapping and employing the ideal collective boson basis. This, however, may lead to the occurrence of spurious states, even at fairly low energies, and three separate methods by means of which they can be identified are discussed. Although the enlarged model space gives a desired lowering of excitation energy of the first excited 0+ states in an exact diagonalization, the strong experimental variation could not be achieved with this simple interaction. Nevertheless, the analysis yields further and new insight into applications of boson mappings, specifically about how and when spurious states may be identified in calculations which are performed in a truncated space not invariant under a given collective algebra. © 1994 The American Physical Society.The strong variation in energy of the first excited 0+ state in the even-even Ge isotopes is investigated with pairing type interactions in various model spaces. Although it had been possible in previous work to describe this variation in a BCSrandom-phase-approximation (RPA) calculation in the neutron configuration only, the corresponding exact diagonalization disagrees with the BCS-RPA results and experiment. It is furthermore shown that the behavior of the first excited 0+ state cannot be obtained by a reasonable variation of parameters in the exact neutron pair calculations. This suggests that the model space be enlarged to include proton, neutron, and proton-neutron pairing. The construction of the corresponding basis is then simplified by performing a boson mapping and employing the ideal collective boson basis. This, however, may lead to the occurrence of spurious states, even at fairly low energies, and three separate methods by means of which they can be identified are discussed. Although the enlarged model space gives a desired lowering of excitation energy of the first excited 0+ states in an exact diagonalization, the strong experimental variation could not be achieved with this simple interaction. Nevertheless, the analysis yields further and new insight into applications of boson mappings, specifically about how and when spurious states may be identified in calculations which are performed in a truncated space not invariant under a given collective algebra. © 1994 The American Physical Society.ArticleArticl