On the relation between E(5)−E(5)-models and the interacting boson model

The connections between the $E(5)-$models (the original E(5) using an infinite square well, $E(5)-\beta^4$, $E(5)-\beta^6$ and $E(5)-\beta^8$), based on particular solutions of the geometrical Bohr Hamiltonian with $\gamma$-unstable potentials, and the interacting boson model (IBM) are explored. For that purpose, the general IBM Hamiltonian for the $U(5)-O(6)$ transition line is used and a numerical fit to the different $E(5)-$models energies is performed, later on the obtained wavefunctions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce very well all these $E(5)-$models. The agreement is the best for $E(5)-\beta^4$ and reduces when passing through $E(5)-\beta^6$, $E(5)-\beta^8$ and E(5), where the worst agreement is obtained (although still very good for a restricted set of lowest lying states). The fitted IBM Hamiltonians correspond to energy surfaces close to those expected for the critical point. A phenomenon similar to the quasidynamical symmetry is observed

Triaxial Shapes in the Interacting Vector Boson Model

A new dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U^{\ast}(3) \otimes SU(1,1) \supset SU^{\ast}(3) \supset SO(3)$, is introduced. The $SU^{\ast}(3)$ algebra considered in the present paper closely resembles many properties of the $SU^{\ast}(3)$ limit of IBM-2, which have been shown by many authors geometrically to correspond to the rigid triaxial model. The influence of different types of perturbations on the $SU^{\ast}(3)$ energy surface, in particular the addition of a Majorana interaction and an O(6) term to the model Hamiltonian, is studied. The effect of these perturbations results in the formation of a stable triaxial minimum in the energy surface of the IVBM Hamiltonian under consideration. Using a schematic Hamiltonian which possesses a perturbed $SU^{\ast}(3)$ dynamical symmetry, the theory is applied for the calculation of the low-lying energy spectrum of the nucleus $^{192}$Os. The theoretical results obtained agree reasonably with the experimental data and show a very shallow triaxial minimum in the energy surface for the ground state in $^{192}$Os, suggesting that the newly proposed dynamical symmetry might be appropriate for the description of the collective properties of different nuclei, exhibiting triaxial features.Comment: 10 pages, 9 figure

Phase Structure of the Interacting Vector Boson Model

The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a dynamical group possesses a rich algebraic structure of physical interesting subgroups that define its distinct exactly solvable dynamical limits. The classical images corresponding to different dynamical symmetries are obtained by means of the coherent state method. The phase structure of the IVBM is investigated and the following basic phase shapes, connected to a specific geometric configurations of the ground state, are determined: spherical, $U_{p}(3)\otimes U_{n}(3)$, $\gamma-$unstable, O(6), and axially deformed shape, $SU(3)\otimes U_{T}(2)$. The ground state quantum phase transitions between different phase shapes, corresponding to the different dynamical symmetries and mixed symmetry case, are investigated.Comment: 9 pages, 10 figure

A simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling

We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Niels Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained because the scaling leaves invariant the position-momentum commutator. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential energy curves for the lowest singlet, triplet and excited states of H_2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Letter

Comment on "Limits of the measurability of the local quantum electromagnetic-field amplitude"

It is argued that the findings of a recent reanalysis by Compagno and Persico [Phys. Rev. A 57, 1595 (1998)] of the Bohr--Rosenfeld procedure for the measurement of a single space-time-averaged component of the electromagnetic field are incorrect when the field measurement time is shorter than that required for light to traverse the measurement's test body. To this end, the time-averaged "self-force" on the test body, assumed for simplicity to be of a spherical shape, is evaluated in terms of a one-dimensional quadrature for the general trajectory allowed for the test body by Compagno and Persico, and in closed form for the limiting steplike trajectory used by Bohr and Rosenfeld.Comment: 5 pages, REVTe

New results for the missing quantum numbers labeling the quadrupole and octupole boson basis

The many $2^k$-pole boson states, $|N_kv_k\alpha_k I_kM_k>$ with $k=2,3$, realize the irreducible representation (IR) for the group reduction chains $SU(2k+1)\supset R_{2k+1}\supset R_3\supset R_2$. They have been analytically studied and widely used for the description of nuclear systems. However, no analytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$'s IR, determined by the reduction $R_{2k+1}\supset R_3$, is available. Thus, the number of distinct values taken by $\alpha_k$ has been so far obtained by solving some complex equations. Here we derive analytical expressions for the degeneracy $d_v(I)$ characterizing the octupole and quadrupole boson states, respectively. The merit of this work consists of the fact that it completes the analytical expressions for the $2^k$-pole boson basis.Comment: 10page

Fluctuations in the level density of a Fermi gas

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many--body density of states, related to shell effects, are obtained. The fluctuations depend non-trivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single--particle motion.Comment: 4 pages, 1 figur

Macroscopic quantum jumps and entangled state preparation

Recently we predicted a random blinking, i.e. macroscopic quantum jumps, in the fluorescence of a laser-driven atom-cavity system [Metz et al., Phys. Rev. Lett. 97, 040503 (2006)]. Here we analyse the dynamics underlying this effect in detail and show its robustness against parameter fluctuations. Whenever the fluorescence of the system stops, a macroscopic dark period occurs and the atoms are shelved in a maximally entangled ground state. The described setup can therefore be used for the controlled generation of entanglement. Finite photon detector efficiencies do not affect the success rate of the state preparation, which is triggered upon the observation of a macroscopic fluorescence signal. High fidelities can be achieved even in the vicinity of the bad cavity limit due to the inherent role of dissipation in the jump process.Comment: 14 pages, 12 figures, proof of the robustness of the state preparation against parameter fluctuations added, figure replace

Investigation of Pygmy Dipole Resonances in the Tin Region

The evolution of the low-energy electromagnetic dipole response with the neutron excess is investigated along the Sn isotopic chain within an approach incorporating Hartree-Fock-Bogoljubov (HFB) and multi-phonon Quasiparticle-Phonon-Model (QPM) theory. General aspects of the relationship of nuclear skins and dipole sum rules are discussed. Neutron and proton transition densities serve to identify the Pygmy Dipole Resonance (PDR) as a generic mode of excitation. The PDR is distinct from the GDR by its own characteristic pattern given by a mixture of isoscalar and isovector components. Results for the $^{100}$Sn-$^{132}$Sn isotopes and the several N=82 isotones are presented. In the heavy Sn-isotopes the PDR excitations are closely related to the thickness of the neutron skin. Approaching $^{100}$Sn a gradual change from a neutron to a proton skin is found and the character of the PDR is changed correspondingly. A delicate balance between Coulomb and strong interaction effects is found. The fragmentation of the PDR strength in $^{124}$Sn is investigated by multi-phonon calculations. Recent measurements of the dipole response in $^{130,132}$Sn are well reproduced.Comment: 41 pages, 10 figures, PR

Observing the spin of a free electron

Long ago, Bohr, Pauli, and Mott argued that it is not, in principle, possible to measure the spin components of a free electron. One can try to use a Stern-Gerlach type of device, but the finite size of the beam results in an uncertainty of the splitting force that is comparable with the gradient force. The result is that no definite spin measurement can be made. Recently there has been a revival of interest in this problem, and we will present our own analysis and quantum-mechanical wave-packet calculations which suggest that a spin measurement is possible for a careful choice of initial conditions