115 research outputs found
Wavelet Decompositions of Nonrefinable Shift Invariant Spaces
AbstractThe motivation for this work is a recently constructed family of generators of shift invariant spaces with certain optimal approximation properties, but which are not refinable in the classical sense. We try to see whether, once the classical refinability requirement is removed, it is still possible to construct meaningful wavelet decompositions of dilates of the shift invariant space that are well suited for applications
Pseudospin, Spin, and Coulomb Dirac-Symmetries: Doublet Structure and Supersymmetric Patterns
Relativistic symmetries of the Dirac Hamiltonian with a mixture of
spherically symmetric Lorentz scalar and vector potentials, are examined from
the point of view of supersymmetric quantum mechanics. The cases considered
include the Coulomb, pseudospin and spin limits relevant, respectively, to
atoms, nuclei and hadrons.Comment: 8 pages, 1 figure, Proc. Int. Workshop on "Blueprints for the
Nucleus: From First Principles to Collective Motion", May 17-23, 2004, Feza
Gursey Institute, Istanbul, Turke
Sensitivity of tensor analyzing power in the process to the longitudinal isoscalar form factor of the Roper resonance electroexcitation
The tensor analyzing power of the process , for forward
deuteron scattering in the momentum interval 3.7 to 9 GeV/c, is studied in the
framework of exchange in an algebraic collective model for the
electroexcitation of nucleon resonances. We point out a special sensitivity of
the tensor analyzing power to the isoscalar longitudinal form factor of the
Roper resonance excitation. The main argument is that the ,
and resonances have only isovector longitudinal
form factors. It is the longitudinal form factor of the Roper excitation, which
plays an important role in the dependence of the tensor analyzing power. We
discuss possible evidence of swelling of hadrons with increasing excitation
energy.Comment: 12 pages, 10 figure
An intrinsic state for an extended version of the interacting boson model
An intrinsic-state formalism for IBM-4 is presented. A basis of deformed
bosons is introduced which allows the construction of a general trial wave
function which has Wigner's spin-isospin SU(4) symmetry as a particular limit.
Intrinsic-state calculations are compared with exact ones showing good
agreement.Comment: 12 pages, TeX (ReVTeX). Content changed. Accepted in Phys. Rev.
Magnetic Dipole Sum Rules for Odd-Mass Nuclei
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are
derived within the single-j interacting boson-fermion model. We discuss the
physical content and geometric interpretation of these sum rules and apply them
to ^{167}Er and ^{161}Dy. We find consistency with the former measurements but
not with the latter.Comment: 13 pages, Revtex, 1 figure, Phys. Rev. Lett. in pres
Test of Nuclear Wave Functions for Pseudospin Symmetry
Using the fact that pseudospin is an approximate symmetry of the Dirac
Hamiltonian with realistic scalar and vector mean fields, we derive the wave
functions of the pseudospin partners of eigenstates of a realistic Dirac
Hamiltonian and compare these wave functions with the wave functions of the
Dirac eigenstates.Comment: 11 pages, 4 figures, minor changes in text and figures to conform
with PRL requirement
Pseudospin, supersymmetry and the shell structure of atomic nuclei
The evolution of single-particle energies with varying isospin asymmetry in
the shell model is an important issue when predicting changes in the shell
structure for exotic nuclei. In many cases pseudospin partner levels, that are
almost degenerate in energy for stable nuclei, are relevant in extracting the
size of the shell gaps. A breaking of the pseudospin symmetry can affect the
size of these gaps and change the magic numbers accordingly. The strength of
the pseudospin splitting is expected to depend in particular on
isovector-dependent and tensor contributions to the effective nuclear
interaction. A description employing supersymmetric quantum mechanics allows to
derive a pseudospin symmetry breaking potential that is regular in contrast to
the pseudospin-orbit potential in the conventional relativistic treatment. The
derived perturbation potential provides a measure to quantify the symmetry
breaking and it can be employed to improve mean-field calculations in order to
better reproduce the experimentally observed shell evolution. General
potentials with exact pseudospin symmetry are obtained that can be used in
relativistic mean-field Hamiltonians.Comment: 33 pages, 1 table, 6 figures, additional references, minor
corrections, note added in proof, accepted for publication in Nuclear Physics
Extended M1 sum rule for excited symmetric and mixed-symmetry states in nuclei
A generalized M1 sum rule for orbital magnetic dipole strength from excited
symmetric states to mixed-symmetry states is considered within the
proton-neutron interacting boson model of even-even nuclei. Analytic
expressions for the dominant terms in the B(M1) transition rates from the first
and second states are derived in the U(5) and SO(6) dynamic symmetry
limits of the model, and the applicability of a sum rule approach is examined
at and in-between these limits. Lastly, the sum rule is applied to the new data
on mixed-symmetry states of 94Mo and a quadrupole d-boson ratio
is obtained in a largely
parameter-independent wayComment: 19 pages, 3 figures, Revte
First order shape transition and critical point nuclei in Sm isotopes from relativistic mean field approach
The critical point nuclei in Sm isotopes, which marks the first order phase
transition between spherical U(5) and axially deformed shapes SU(3), have been
investigated in the microscopic quadrupole constrained relativistic mean field
(RMF) model plus BCS method with all the most used interactions, i.e., NL1,
NL3, NLSH and TM1. The calculated potential energy surfaces show a clear shape
transition for the even-even Sm isotopes with and the critical
point nuclei are found to be Sm, Sm and Sm. Similar
conclusions can also be drawn from the microscopic neutron and proton single
particle spectra.Comment: 6 figure
Role of the Coulomb and the vector-isovector potentials in the isospin asymmetry of nuclear pseudospin
We investigate the role of the Coulomb and the vector-isovector
potentials in the asymmetry of the neutron and proton pseudospin splittings in
nuclei. To this end, we solve the Dirac equation for the nucleons using central
vector and scalar potentials with Woods-Saxon shape and and dependent
Coulomb and potentials added to the vector potential. We study the
effect of these potentials on the energy splittings of proton and neutron
pseudospin partners along a Sn isotopic chain. We use an energy decomposition
proposed in a previous work to assess the effect of a pseudospin-orbit
potential on those splittings. We conclude that the effect of the Coulomb
potential is quite small and the potential gives the main contribution
to the observed isospin asymmetry of the pseudospin splittings. This isospin
asymmetry results from a cancellation of the various energy terms and cannot be
attributed only to the pseudospin-orbit term, confirming the dynamical
character of this symmetry pointed out in previous works.Comment: 9 pages, 11 figures, uses revtex4; title was changed and several
small corrections were made throughout the tex
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