521 research outputs found
Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion
We study the algebra Sp(n,R) of the symplectic model, in particular for the
cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we
derive a set of partial differential equations for the generators as functions
of classical canonical variables. We obtain a solution to these equations that
represents the classical limit of a boson mapping of the algebra. The
relationship to the collective dynamics is formulated as a theorem that
associates the mapping with an exact solution of the time-dependent Hartree
approximation. This solution determines a decoupled classical symplectic
manifold, thus satisfying the criteria that define an exactly solvable model in
the theory of large amplitude collective motion. The models thus obtained also
provide a test of methods for constructing an approximately decoupled manifold
in fully realistic cases. We show that an algorithm developed in one of our
earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.
A basis of cranking operators for the pairing-plus-quadrupole model
We investigate the RPA normal-mode coordinates in the pairing-plus-quadrupole
model, with an eye on simplifying the application of large amplitude collective
motion techniques. At the Hartree-Bogoliubov minimum, the RPA modes are exactly
the cranking operators of the collective coordinate approach. We examine the
possibility of representing the self-consistent cranking operator by linear
combinations of a limited number of one-body operators. We study the Sm nuclei
as an example, and find that such representations exist in terms of operators
that are state-dependent in a characteristic manner.Comment: 6 pages, 1 figure, using IOP journal style files, to be published in
J. Phys.
Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold
We consider 3-monopoles symmetric under inversion symmetry. We show that the
moduli space of these monopoles is an Atiyah-Hitchin submanifold of the
3-monopole moduli space. This allows what is known about 2-monopole dynamics to
be translated into results about the dynamics of 3-monopoles. Using a numerical
ADHMN construction we compute the monopole energy density at various points on
two interesting geodesics. The first is a geodesic over the two-dimensional
rounded cone submanifold corresponding to right angle scattering and the second
is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit
An Extension of the Fractional Parentage Expansion to Nonrelativistic and Relativistic Dibaryon Calculations
The fractional parentage expansion method is extended from
nonrelativistic to and relativistic dibaryon calculations. A
transformation table between physical bases and symmetry bases for the
dibaryon is provided. A program package has been written for
dibaryon calculation based on the fractional parentage expansion method.Comment: 15 pages text plus 18 pages tables, latex, no figure
Quark Delocalization, Color Screening and Dibaryons
The quark delocalization and color screening model, a quark potential model,
is used for a systematic search of dibaryon candidates in the and
three flavor world. Color screening which appears in unquenched lattice gauge
calculations and quark delocalization (which is similar to electron
delocalization in molecular physics) are both included. Flavor symmetry
breaking and channel coupling effects are studied. The model is constrained not
only by baryon ground state properties but also by the - scattering phase
shifts. The deuteron and zero energy di-nucleon resonance are both reproduced
qualitatively. The model predicts two extreme types of dibaryonic systems:
``molecular'' like the deuteron, and highly delocalized six-quark systems among
which only a few narrow dibaryon resonances occur in the and three
flavor world. Possible high spin dibaryon resonances are emphasized.Comment: 20 pages, latex, no figure
Semiclassical quantization of SU(3) skyrmions
Semiclassical quantization of the SU(3)-skyrmions is performed by means of
the collective coordinate method. The quantization condition known for the
SU(2)-solitons quantized with SU(3) collective coordinates is generalized for
the SU(3) skyrmions with strangeness content different from zero. Quantization
of the dipole-type configuration with large strangeness content found recently
is considered as an example, the spectrum and the mass splitting of the
quantized states are estimated. The energy and baryon number density of SU(3)
skyrmions are presented in the form emphasizing their symmetry in different
SU(2) subgroups of SU(3), and the lower boundary for the static energy of SU(3)
skyrmions is derived.Comment: 16 pages, 2 figures (available upon request). Submitted to JETP on
May 6, 1997; in print. A preliminary short version of this paper is
hep-th/960916
Zero mode quantization of multi-Skyrmions
A zero mode quantization of the minimal energy SU(2) Skyrmions for nucleon
numbers four to nine and seventeen is described. This involves quantizing the
rotational and isorotational modes of the configurations. For nucleon numbers
four, six and eight the ground states obtained are in agreement with the
observed nuclear states of Helium, Lithium and Beryllium. However, for nucleon
numbers five, seven, nine and seventeen the spins obtained conflict with the
observed isodoublet nuclear states.Comment: 37 pages, LaTeX, 4 figures. More careful treatment of double covers,
reference adde
Mass splittings of nuclear isotopes in chiral soliton approach
The differences of the masses of nuclear isotopes with atomic numbers between
\~10 and ~30 can be described within the chiral soliton approach in
satisfactory agreement with data. Rescaling of the model is necessary for this
purpose - decrease of the Skyrme constant by about 30%, providing the "nuclear
variant" of the model. The asymmetric term in Weizsaecker-Bethe- Bacher mass
formula for nuclei can be obtained as the isospin dependent quantum correction
to the nucleus energy. Some predictions for the binding energies of neutron
rich nuclides are made in this way, from, e.g. Be-16 and B-19 to Ne-31 and
Na-32. Neutron rich nuclides with high values of isospin are unstable relative
to strong interactions. The SK4 (Skyrme) variant of the model, as well as SK6
variant (6-th order term in chiral derivatives in the lagrangian as solitons
stabilizer) are considered, and the rational map approximation is used to
describe multiskyrmions.Comment: 16 pages, 10 tables, 2 figures. Figures are added and few misprints
are removed. Submitted to Phys. Atom. Nucl. (Yad. Fiz.
Multibaryons as Symmetric Multiskyrmions
We study non-adiabatic corrections to multibaryon systems within the bound
state approach to the SU(3) Skyrme model. We use approximate ansatze for the
static background fields based on rational maps which have the same symmetries
of the exact solutions. To determine the explicit form of the collective
Hamiltonians and wave functions we only make use of these symmetries. Thus, the
expressions obtained are also valid in the exact case. On the other hand, the
inertia parameters and hyperfine splitting constants we calculate do depend on
the detailed form of the ansatze and are, therefore, approximate. Using these
values we compute the low lying spectra of multibaryons with B <= 9 and
strangeness 0, -1 and -B. Finally, we show that the non-adiabatic corrections
do not affect the stability of the tetralambda and heptalambda found in a
previous work.Comment: 17 pages, RevTeX, no figure
Calculation of the properties of the rotational bands of Gd
We reexamine the long-standing problem of the microscopic derivation of a
particle-core coupling model. We base our research on the Klein-Kerman
approach, as amended by D\"onau and Frauendorf. We describe the formalism to
calculate energy spectra and transition strengths in some detail. We apply our
formalism to the rotational nuclei Gd, where recent experimental
data requires an explanation. We find no clear evidence of a need for Coriolis
attenuation.Comment: 27 pages, 13 uuencoded postscript figures. Uses epsf.st
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