2,467 research outputs found
On the relation between models and the interacting boson model
The connections between the models (the original E(5) using an
infinite square well, , and ), based
on particular solutions of the geometrical Bohr Hamiltonian with
-unstable potentials, and the interacting boson model (IBM) are
explored. For that purpose, the general IBM Hamiltonian for the
transition line is used and a numerical fit to the different 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 models. The agreement is the best for
and reduces when passing through ,
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 , is introduced.
The algebra considered in the present paper closely resembles
many properties of the 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 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 dynamical symmetry, the theory is applied for the
calculation of the low-lying energy spectrum of the nucleus 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 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,
, unstable, O(6), and axially deformed
shape, . 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 -pole boson states, with ,
realize the irreducible representation (IR) for the group reduction chains
. They have been analytically
studied and widely used for the description of nuclear systems. However, no
analytical expression for the degeneracy of the 's IR,
determined by the reduction , is available. Thus, the
number of distinct values taken by has been so far obtained by
solving some complex equations. Here we derive analytical expressions for the
degeneracy 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 -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 Sn-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 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 Sn is
investigated by multi-phonon calculations. Recent measurements of the dipole
response in 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
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