Interacting boson-fermion model of collective states II. Boson-fermion symmetries connected with the U(5) limit

The boson-fermion symmetries, which are connected with the U^(B)(5) limit of the interacting boson model are discussed. These symmetries arise when the bosons have U(5) symmetry and the fermions occupy a single-particle orbit with spin $\text{j =}\text{1}\text{2}$ (Spin(3) limit), $\text{j =}\text{3}\text{2}$ (Spin(5) limit), or $\text{j =}\text{3}\text{2}\text{,}\text{5}\text{2}$ (U^(B+F)(5) ? U^(F)(2) limit). Closed expressions for energy spectra, electromagnetic transition rates, static moments, and (one and two) nucleon transfer reaction intensities are derived.     

Interacting boson model of collective nuclear states IV. The O(6) limit

We discuss a third limit of the interacting boson model. We show that this limit is associated with the group O(6) of orthogonal transformations in six dimensions. We derive, within the framework of this symmetry, several closed expressions for energies and electromagnetic transition rates.     

Interacting boson model of collective nuclear states II. The rotational limit

We discuss the rotational limit of the interacting boson model and bring attention to the possible existence of an unbroken SU(3) symmetry. We derive, within the framework of this symmetry, several analytic relations for energies and electromagnetic transition rates.     

Interacting boson model of collective nuclear states III. The transition from SU(5) to SU(3)

We study the transition from the vibrational, SU(5), to the rotational, SU(3), limit of the interacting boson model. We show how this model can be used to calculate energies, electromagnetic transitions, multipole moments, nuclear radii, and two-nucleon transfer intensities in transitional nuclei.     

Negative-parity states of75As and the interacting boson-fermion model

The result of an IBFM multilevel calculation with the 2p_3/2, 1f_5/2 and 2p_1/2 single particle orbits is reported for the negative parity states of the odd mass nucleus⁷⁵As. Comparisons are made with experimental data for energy spectra, transition probabilities, mixing ratios, electric quadrupole and magnetic dipole moments. Also, an IBM-1 calculation is presented for the low-lying states in the even-even⁷⁴Ge core nucleus.     

Interacting physical states of the bosonic string. I

A preliminary discussion on the importance of the contact terms in relation with the existence of many string vacua is presented. The problem of the BRST invariance of the string states transition amplitudes is considered in the sigma model approach to the string. It is shown that the BRST invariance is controlled by a gravitational (Diff) anomaly, and its connections with the standard Virasoro constraints are illustrated. The tachyon amplitudes are analysed and the BRST invariant dilaton vertex operator for non flat world-sheet is constructed.     

Algebraic description of multiple quadrupole excitations of collective states in nuclei: (I). Representation matrices for U(6)

An algorithm for the calculation of representation matrices for the totally symmetric representations [N] of the group U(6) is described. Applications to multiple quadrupole excitation processes in nuclei are given.     

New coupling scheme in the interacting boson-fermion model: O(6) spectra in odd-A nuclei

We suggest that a new coupling scheme, based on the O(6) boson symmetry, may be useful in describing the spectra of odd-A nuclei towards the end of major shells. We describe the main properties of this scheme and show one example of it.     

Rotations as coherent states of SU(6) quadropole phonons in the SU(3) limit

Analytic expressions for the wavefunctions of the ground-state rotational band for even and odd nuclei are derived in terms of spherical quadropole phonons truncated at N_max phonons. For N_max → ∞ the Bohr-Mottelson rotational states are generated as an asymptotic gaussian distribution of quadropole phonons.     

On the boson-fermion model of superconductivity

Summary The existence of pair excitations in a Fermi gas interacting via a short-range attractive potential is investigated. Within the ladder approximation to the Bethe-Salpeter equation for the effective two-particle interaction, evidence of pair excitation is found at energies slightly larger than the chemical potential. The link between those excitations and a boson-fermion model of superconductivity (Phys. Lett. A,196 (1995) 359) is discussed. In particular it is shown that the charge carrier density dependence of the pair excitation (boson) energy, assumed phenomenologically in the boson-fermion model, is consistent with the properties of the interacting Fermi gas studied. These results give support to the microscopic origin of the phenomenological boson-fermion model of superconductivity. Within the polaron-bipolaron theory the assumption that bosons and fermions can be described as mobile particles has found support in ref.[6] where the small bipolaron (boson) delocalization is discussed and in ref.[7] where the large polaron delocalization is analysed.     

A coriolis-like effect of the dynamical boson-fermion interaction in the interacting boson-fermion model

It is shown that in a particular basis the dynamical interaction of IBFM for a boson core coupled to a single-j particle in the SU(3) limit takes a tridiagonal form, as does the Coriolis interaction. Interference between this Coriolis-like effect in the boson-fermion dynamical interaction and the genuine Coriolis effect results in interesting features of IBFM: For a particular ratio of the interaction strengths, depending only on the angular momentum of the odd particle, the K = j band exactly follows the rotational energy rule, is completely uncoupled from the other bands and has exactly the same moment of inertia as a ground-state band of the core. A possible interpretation of this feature in terms of spectrum-generating supersymmetry is suggested.     

A schematic model for collective states including non-locality effects: (I). Isoscalar quadrupole and rotational modes

Schematic forces including non-locality terms are derived in a self-consistent way in the framework of the time-dependent Hartree-Fock formalism. The usual dispersion relation of the vibrating potential model is generalized to include current effects. The model is explicitly solved for the isoscalar quadrupole and rotational modes and the role of the effective mass is pointed out.     

Spin waves,vortices, and the structure of equilibrium states in the classicalXY model

We prove that, for spin systems with a continuous symmetry group on lattices of arbitrary dimension, the surface tension vanishes at all temperatures. For the classicalXY model in zero magnetic field, this result is shown to imply absence of interfaces in the thermodynamic limit, at arbitrary temperature. We show that, at values of the temperature at which the free energy of that model is continuously differentiable, i.e. at all except possibly countably many temperatures, there iseither aunique translation-invariant equilibrium state, or all such states are labelled by the elements of the symmetry group, SO(2). Moreover, there areno non-translation-invariant, but periodic equilibrium states. We also reconsider the representation of theXY model as a gas of spin waves and vortices and discuss the possibility that, in four or more dimensions, translation invariance may be broken by imposing boundary conditions which force an (open) vortex sheet through the system. Among our main tools are new correlation inequalities.     

SU(6) model for odd-odd nuclei (OTQM/IBOM) and boson-aligned phase diagram inO(6) limit

We introduce the SU(6) model IBOM/OTQM for odd-odd nuclei and discuss the bands in O(6) limit. Bands are characterized by a particular type of phase correlations in the wave functions and exhibit splitting of the SU(3) analogs of Gallagher-Moszkowski bands.