91 research outputs found
New insight on pseudospin doublets in nuclei
The relevance of the pseudospin symmetry in nuclei is considered. New insight
is obtained from looking at the continuous transition from a model satisfying
the spin symmetry to another one satisfying the pseudospin symmetry. This study
suggests that there are models allowing no missing single-particle states in
this transition, contrary to what is usually advocated. It rather points out to
an association of pseudospin partners different from the one usually assumed,
together with a strong violation of the corresponding symmetry. A comparison
with results obtained from some relativistic approaches is made.Comment: 27 pages, 18 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
Pseudospin symmetry as a relativistic dynamical symmetry in the nucleus
Pseudospin symmetry in nuclei is investigated by solving the Dirac equation
with Woods-Saxon scalar and vector radial potentials, and studying the
correlation of the energy splittings of pseudospin partners with the nuclear
potential parameters. The pseudospin interaction is related to a
pseudospin-orbit term that arises in a Schroedinger-like equation for the lower
component of the Dirac spinor. We show that the contribution from this term to
the energy splittings of pseudospin partners is large. The near pseudospin
degeneracy results from a significant cancelation among the different terms in
that equation, manifesting the dynamical character of this symmetry in the
nucleus. We analyze the isospin dependence of the pseudospin symmetry and find
that its dynamical character is behind the different pseudospin splittings
observed in neutron and proton spectra of nuclei.Comment: 13 pages, 9 figures, uses REVTeX4 macro
Recommended from our members
Fermion dynamical symmetry and the nuclear shell model
The interacting boson model (IBM) has been very successful in giving a unified and simple description of the spectroscopic properties of a wide range of nuclei, from vibrational through rotational nuclei. The three basic assumptions of the model are that: (1) the valence nucleons move about a doubly closed core, (2) the collective low-lying states are composed primarily of coherent pairs of neutrons and pairs of protons coupled to angular momentum zero and two, and (3) these coherent pairs are approximated as bosons. In this review we shall show how it is possible to have fermion Hamiltonians which have a class of collective eigenstates composed entirely of monopole and quadrupole pairs of fermions. Hence these models satisfy the assumptions (1) and (2) above but no boson approximation need be made. Thus the Pauli principle is kept in tact. Furthermore the fermion shell model states excluded in the IBM can be classified by the number of fermion pairs which are not coherent monopole or quadrupole pairs. Hence the mixing of these states into the low-lying spectrum can be calculated in a systematic and tractable manner. Thus we can introduce features which are outside the IBM. 11 refs
Algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei
We extend the algebraic-eikonal approach to medium energy proton scattering
from odd-mass nuclei by combining the eikonal approximation for the scattering
with a description of odd-mass nuclei in terms of the interacting boson-fermion
model. We derive closed expressions for the transition matrix elements for one
of the dynamical symmetries and discuss the interplay between collective and
single-particle degrees of freedom in an application to elastic and inelastic
proton scattering from Pt.Comment: latex, 14 pages, 4 figures uuencoded, to be published in Physical
Review
Relativistic study of the energy-dependent Coulomb potential including Coulomb-like tensor interaction
The exact Dirac equation for the energy-dependent Coulomb (EDC) potential
including a Coulomb-like tensor (CLT) potential has been studied in the
presence of spin and pseudospin (p-spin) symmetries with arbitrary spin-orbit
quantum number The energy eigenvalues and corresponding eigenfunctions are
obtained in the framework of asymptotic iteration method (AIM). Some numerical
results are obtained in the presence and absence of EDC and CLT potentials.Comment: 13 pages, to appear in Canadian Journal of Physics (2012
F-spin as a Partial Symmetry
We use the empirical evidence that F-spin multiplets exist in nuclei for only
selected states as an indication that F-spin can be regarded as a partial
symmetry. We show that there is a class of non-F-scalar IBM-2 Hamiltonians with
partial F-spin symmetry, which reproduce the known systematics of collective
bands in nuclei. These Hamiltonians predict that the scissors states have good
F-spin and form F-spin multiplets, which is supported by the existing data.Comment: 14 pages, 1 figur
Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry
The energy spectra and the corresponding two- component spinor wavefunctions
of the Dirac equation for the Rosen-Morse potential with spin and pseudospin
symmetry are obtained. The wave ( state) solutions for this
problem are obtained by using the basic concept of the supersymmetric quantum
mechanics approach and function analysis (standard approach) in the
calculations. Under the spin symmetry and pseudospin symmetry, the energy
equation and the corresponding two-component spinor wavefunctions for this
potential and other special types of this potential are obtained. Extension of
this result to state is suggested.Comment: 18 page
Generator Coordinate Truncations
We investigate the accuracy of several schemes to calculate ground-state
correlation energies using the generator coordinate technique. Our test-bed for
the study is the interacting boson model, equivalent to a 6-level
Lipkin-type model. We find that the simplified projection of a triaxial
generator coordinate state using the subgroup of the rotation group is
not very accurate in the parameter space of the Hamiltonian of interest. On the
other hand, a full rotational projection of an axial generator coordinate state
gives remarkable accuracy. We also discuss the validity of the simplified
treatment using the extended Gaussian overlap approximation (top-GOA), and show
that it works reasonably well when the number of boson is four or larger.Comment: 19 pages, 6 eps figure
New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity
We discuss in some detail the self-similar potentials of Shabat and
Spiridonov which are reflectionless and have an infinite number of bound
states. We demonstrate that these self-similar potentials are in fact shape
invariant potentials within the formalism of supersymmetric quantum mechanics.
In particular, using a scaling ansatz for the change of parameters, we obtain a
large class of new, reflectionless, shape invariant potentials of which the
Shabat-Spiridonov ones are a special case. These new potentials can be viewed
as q-deformations of the single soliton solution corresponding to the
Rosen-Morse potential. Explicit expressions for the energy eigenvalues,
eigenfunctions and transmission coefficients for these potentials are obtained.
We show that these potentials can also be obtained numerically. Included as an
intriguing case is a shape invariant double well potential whose supersymmetric
partner potential is only a single well. Our class of exactly solvable
Hamiltonians is further enlarged by examining two new directions: (i) changes
of parameters which are different from the previously studied cases of
translation and scaling; (ii) extending the usual concept of shape invariance
in one step to a multi-step situation. These extensions can be viewed as
q-deformations of the harmonic oscillator or multi-soliton solutions
corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai
- …