38 research outputs found
Self-consistent anisotropic oscillator with cranked angular and vortex velocities
The Kelvin circulation is the kinematical Hermitian observable that measures
the true character of nuclear rotation. For the anisotropic oscillator, mean
field solutions with fixed angular momentum and Kelvin circulation are derived
in analytic form. The cranking Lagrange multipliers corresponding to the two
constraints are the angular and vortex velocities. Self-consistent solutions
are reported with a constraint to constant volume.Comment: 12 pages, LaTex/RevTex, Phys. Rev. C4
Nonabelian density functional theory
Given a vector space of microscopic quantum observables, density functional
theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem
and the existence of the universal energy functional in the dual space are
proven. In this context ordinary density functional theory corresponds to the
space of one-body multiplication operators. When the operators close under
commutation to form a Lie algebra, the energy functional defines a Hamiltonian
dynamical system on the coadjoint orbits in the algebra's dual space. The
enhanced density functional theory provides a new method for deriving the group
theoretic Hamiltonian on the coadjoint orbits from the exact microscopic
Hamiltonian.Comment: 1 .eps figur
Toroidal quadrupole transitions associated to collective rotational-vibrational motions of the nucleus
In the frame of the algebraic Riemann Rotational Model one computes the
longitudinal, transverse and toroidal multipoles corresponding to the
excitations of low-lying levels in the ground state band of several even-even
nuclei by inelastic electron scattering (e,e'). Related to these transitions a
new quantity, which accounts for the deviations from the Siegert theorem, is
introduced. The intimate connection between the nuclear vorticity and the
dynamic toroidal quadrupole moment is underlined. Inelastic differential
cross-sections calculated at backscattering angles shows the dominancy of
toroidal form-factors over a broad range of momentum transfer.Comment: 11 pages in LaTex, 3 figures available by fax or mail, accepted for
publication in J.Phys.
Partial Dynamical Symmetry in the Symplectic Shell Model
We present an example of a partial dynamical symmetry (PDS) in an interacting
fermion system and demonstrate the close relationship of the associated
Hamiltonians with a realistic quadrupole-quadrupole interaction, thus shedding
new light on this important interaction. Specifically, in the framework of the
symplectic shell model of nuclei, we prove the existence of a family of
fermionic Hamiltonians with partial SU(3) symmetry. We outline the construction
process for the PDS eigenstates with good symmetry and give analytic
expressions for the energies of these states and E2 transition strengths
between them. Characteristics of both pure and mixed-symmetry PDS eigenstates
are discussed and the resulting spectra and transition strengths are compared
to those of real nuclei. The PDS concept is shown to be relevant to the
description of prolate, oblate, as well as triaxially deformed nuclei.
Similarities and differences between the fermion case and the previously
established partial SU(3) symmetry in the Interacting Boson Model are
considered.Comment: 9 figure
Non-semisimple Lie algebras with Levi factor \frak{so}(3), \frak{sl}(2,R) and their invariants
We analyze the number N of functionally independent generalized Casimir
invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{%
oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and
\frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a
representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that
for any dimension n >= 6 there exist Lie algebras
\frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition
such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.Comment: 16 page
Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations
It is shown here and in the preceeding paper (quant-ph/0201129) that vector
coherent state theory, the theory of induced representations, and geometric
quantization provide alternative but equivalent quantizations of an algebraic
model. The relationships are useful because some constructions are simpler and
more natural from one perspective than another. More importantly, each approach
suggests ways of generalizing its counterparts. In this paper, we focus on the
construction of quantum models for algebraic systems with intrinsic degrees of
freedom. Semi-classical partial quantizations, for which only the intrinsic
degrees of freedom are quantized, arise naturally out of this construction. The
quantization of the SU(3) and rigid rotor models are considered as examples.Comment: 31 pages, part 2 of two papers, published versio
Orbital M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule
Within the unified model of Bohr and Mottelson we derive the following linear
energy weighted sum rule for low energy orbital 1 excitations in even-even
deformed nuclei S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon
(B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2^2) \mu^2_N with B(E2) the E2
strength for the transition from the ground state to the first excited state in
the ground state rotational band, the charge r.m.s. radius squared and
the binding energy per nucleon in the nuclear ground state. It is
shown that this energy weighted sum rule is in good agreement with available
experimental data. The sum rule is derived using a simple ansatz for the
intrinsic ground state wave function that predicts also high energy 1
strength at 2 carrying 50\% of the total moment of the
orbital M1 operator.Comment: REVTEX (3.0), 9 pages, RU924
Commensurate anisotropic oscillator, SU(2) coherent states and the classical limit
We demonstrate a formally exact quantum-classical correspondence between the
stationary coherent states associated with the commensurate anisotropic
two-dimensional harmonic oscillator and the classical Lissajous orbits. Our
derivation draws upon earlier work of Louck et al [1973 \textit {J. Math.
Phys.} \textbf {14} 692] wherein they have provided a non-bijective canonical
transformation that maps, within a degenerate eigenspace, the commensurate
anisotropic oscillator on to the isotropic oscillator. This mapping leads, in a
natural manner, to a Schwinger realization of SU(2) in terms of the canonically
transformed creation and annihilation operators. Through the corresponding
coherent states built over a degenerate eigenspace, we directly effect the
classical limit via the expectation values of the underlying generators. Our
work completely accounts for the fact that the SU(2) coherent state in general
corresponds to an ensemble of Lissajous orbits.Comment: 11 pages, Latex2e, iopart.cls, replaced with published versio
An exactly solvable model of a superconducting to rotational phase transition
We consider a many-fermion model which exhibits a transition from a
superconducting to a rotational phase with variation of a parameter in its
Hamiltonian. The model has analytical solutions in its two limits due to the
presence of dynamical symmetries. However, the symmetries are basically
incompatible with one another; no simple solution exists in intermediate
situations. Exact (numerical) solutions are possible and enable one to study
the behavior of competing but incompatible symmetries and the phase transitions
that result in a semirealistic situation. The results are remarkably simple and
shed light on the nature of phase transitions.Comment: 11 pages including 1 figur
A mixed-mode shell-model theory for nuclear structure studies
We introduce a shell-model theory that combines traditional spherical states,
which yield a diagonal representation of the usual single-particle interaction,
with collective configurations that track deformations, and test the validity
of this mixed-mode, oblique basis shell-model scheme on Mg. The correct
binding energy (within 2% of the full-space result) as well as low-energy
configurations that have greater than 90% overlap with full-space results are
obtained in a space that spans less than 10% of the full space. The results
suggest that a mixed-mode shell-model theory may be useful in situations where
competing degrees of freedom dominate the dynamics and full-space calculations
are not feasible.Comment: 20 pages, 8 figures, revtex 12p