34 research outputs found
Probing nuclear skins and halos with elastic electron scattering
I investigate the elastic electron scattering off nuclei far from the
stability line. The effects of the neutron and proton skins and halos on the
differential cross sections are explored. Examples are given for the charge
distribution in Sn isotopes and its relation to the neutron skin. The neutron
halo in Li and the proton halo in B are also investigated.
Particular interest is paid to the inverse scattering problem and its
dependence on the experimental precision. These studies are of particular
interest for the upcoming electron ion colliders at the GSI and RIKEN
facilities.Comment: 27 pages, 9 figures, accepted for publication in J. Phys.
Two approximate formulae for the binding energies in Lambda hypernuclei and light nuclei
Two approximate formulae are given for the binding energies in
Lambda-hypernuclei and light nuclei by means of the (reduced) Poeschl-Teller
and the Gaussian central potentials. Those easily programmable formulae combine
the eigenvalues of the transformed Jacobi eigenequation and an application of
the hypervirial theorems.Comment: Accepted for publication in Europhysics Letter
Systematical Approach to the Exact Solution of the Dirac Equation for A Special Form of the Woods-Saxon Potential
Exact solution of the Dirac equation for a special form of the Woods-Saxon
potential is obtained for the s-states. The energy eigenvalues and
two-component spinor wave functions are derived by using a systematical method
which is called as Nikiforov-Uvarov. It is seen that the energy eigenvalues
strongly depend on the potential parameters. In addition, it is also shown that
the non-relativistic limit can be reached easily and directly.Comment: 10 pages, no figures, submitted for Publicatio
Universal trend of the information entropy of a fermion in a mean field
We calculate the information entropy of single-particle states in
position-space and momentum-space for a nucleon in a nucleus, a
particle in a hypernucleus and an electron in an atomic cluster. It
is seen that and obey the same approximate functional form as
functions of the number of particles, ({\rm or}
in all of the above many-body systems in position- and momentum- space
separately. The net information content is a slowly varying
function of of the same form as above. The entropy sum is
invariant to uniform scaling of coordinates and a characteristic of the
single-particle states of a specific system. The order of single-particle
states according to is the same as their classification according to
energy keeping the quantum number constant. The spin-orbit splitting is
reproduced correctly. It is also seen that enhances with
excitation of a fermion in a quantum-mechanical system. Finally, we establish a
relationship of with the energy of the corresponding single-particle
state i.e. . This relation holds for all the
systems under consideration.Comment: 9 pages, latex, 6 figure
Improvement of the Heisenberg and Fisher-information-based uncertainty relations for D-dimensional central potentials
The Heisenberg and Fisher-information-based uncertainty relations are improved for stationary states of single-particle systems in a D-dimensional central potential. The improvement increases with the squared orbital hyperangular quantum number. The new uncertainty relations saturate for the isotropic harmonic oscillator wavefunction.We are very grateful for partial support to Junta de Andalucía (under the grants FQM-
0207 and FQM-481), Ministerio de Educaci´on y Ciencia (under the project FIS2005-00973),
and the European Research Network NeCCA (under the project INTAS-03-51-6637). RGF
acknowledges the support of Junta de Andalucía under the program of Retorno de Investigadores a Centros de Investigación Andaluces
Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry
We study the approximate analytical solutions of the Dirac equation for the
generalized Woods-Saxon potential with the pseudo-centrifugal term. In the
framework of the spin and pseudospin symmetry concept, the approximately
analytical bound state energy eigenvalues and the corresponding upper- and
lower-spinor components of the two Dirac particles are obtained, in closed
form, by means of the Nikiforov-Uvarov method which is based on solving the
second-order linear differential equation by reducing it to a generalized
equation of hypergeometric type. The special cases ( s-wave) and the non-relativistic limit can be reached easily
and directly for the generalized and standard Woods-Saxon potentials. Also, the
non-relativistic results are compared with the other works.Comment: 25 page