21 research outputs found
Piecewise constant potentials and discrete ambiguities
This work is devoted to the study of discrete ambiguities. For parametrized
potentials, they arise when the parameters are fitted to a finite number of
phase-shifts. It generates phase equivalent potentials. Such equivalence was
suggested to be due to the modulo uncertainty inherent to phase
determinations. We show that a different class of phase-equivalent potentials
exists. To this aim, use is made of piecewise constant potentials, the
intervals of which are defined by the zeros of their regular solutions of the
Schr\"odinger equation. We give a classification of the ambiguities in terms of
indices which include the difference between exact phase modulo and the
numbering of the wave function zeros.Comment: 26 pages Subject: Mathematical Physics math-p
Using mixed data in the inverse scattering problem
Consider the fixed- inverse scattering problem. We show that the zeros
of the regular solution of the Schr\"odinger equation, , which are
monotonic functions of the energy, determine a unique potential when the domain
of the energy is such that the range from zero to infinity. This
suggests that the use of the mixed data of phase-shifts
, for which the zeros of the regular solution are monotonic in both domains,
and range from zero to infinity, offers the possibility of determining the
potential in a unique way.Comment: 9 pages, 2 figures. Talk given at the Conference of Inverse Quantum
Scattering Theory, Hungary, August 200
Determination of the moments of the proton charge density
A global analysis of proton electric form factor experimental data from
Rosenbluth separation and low squared four-momentum transfer experiments is
discussed for the evaluation of the spatial moments of the proton charge
density based on the recently published integral method \cite{Hob20}. Specific
attention is paid to the evaluation of the systematic errors of the method,
particularly the sensitivity to the choice of the mathematical expression of
the form factor fitting function. Within this comprehensive analysis of proton
electric form factor data, the moments of the proton charge density are
determined for integer order moments, particularly: =0.682(02)(11)~fm, =0.797(10)(58)~fm, and =1.02(05)(31)~fm. This analysis leads to the
proton charge radius 0.8459(12)(76)~fm once relativistic
effects are taken into account.Comment: 10 pages, 3 figure
Sufficient conditions for the existence of bound states in a central potential
We show how a large class of sufficient conditions for the existence of bound
states, in non-positive central potentials, can be constructed. These
sufficient conditions yield upper limits on the critical value,
, of the coupling constant (strength), , of the
potential, , for which a first -wave bound state appears.
These upper limits are significantly more stringent than hitherto known
results.Comment: 7 page
Upper and lower limits on the number of bound states in a central potential
In a recent paper new upper and lower limits were given, in the context of
the Schr\"{o}dinger or Klein-Gordon equations, for the number of S-wave
bound states possessed by a monotonically nondecreasing central potential
vanishing at infinity. In this paper these results are extended to the number
of bound states for the -th partial wave, and results are also
obtained for potentials that are not monotonic and even somewhere positive. New
results are also obtained for the case treated previously, including the
remarkably neat \textit{lower} limit with (valid in the Schr\"{o}dinger case, for a class of potentials
that includes the monotonically nondecreasing ones), entailing the following
\textit{lower} limit for the total number of bound states possessed by a
monotonically nondecreasing central potential vanishing at infinity: N\geq
\{\{(\sigma+1)/2\}\} {(\sigma+3)/2\} \}/2 (here the double braces denote of
course the integer part).Comment: 44 pages, 5 figure
Necessary and sufficient conditions for existence of bound states in a central potential
We obtain, using the Birman-Schwinger method, a series of necessary
conditions for the existence of at least one bound state applicable to
arbitrary central potentials in the context of nonrelativistic quantum
mechanics. These conditions yield a monotonic series of lower limits on the
"critical" value of the strength of the potential (for which a first bound
state appears) which converges to the exact critical strength. We also obtain a
sufficient condition for the existence of bound states in a central monotonic
potential which yield an upper limit on the critical strength of the potential.Comment: 7 page
Quantum Molecular Dynamics Approach to the Nuclear Matter Below the Saturation Density
Quantum molecular dynamics is applied to study the ground state properties of
nuclear matter at subsaturation densities. Clustering effects are observed as
to soften the equation of state at these densities. The structure of nuclear
matter at subsaturation density shows some exotic shapes with variation of the
density.Comment: 21 pages of Latex (revtex), 9 Postscript figure
Critical strength of attractive central potentials
We obtain several sequences of necessary and sufficient conditions for the
existence of bound states applicable to attractive (purely negative) central
potentials. These conditions yields several sequences of upper and lower limits
on the critical value, , of the coupling constant
(strength), , of the potential, , for which a first
-wave bound state appears, which converges to the exact critical value.Comment: 18 page
Physics of Neutron Star Crusts
The physics of neutron star crusts is vast, involving many different research
fields, from nuclear and condensed matter physics to general relativity. This
review summarizes the progress, which has been achieved over the last few
years, in modeling neutron star crusts, both at the microscopic and macroscopic
levels. The confrontation of these theoretical models with observations is also
briefly discussed.Comment: 182 pages, published version available at
<http://www.livingreviews.org/lrr-2008-10
Modes de consommation et caractéristiques du produit : le cas du poulet
[fre] Les qualités de produits prennent une importance grandissante dans l'explication de la consommation alimentaire. Dans le cas du poulet, la progression de consommation s'explique par une forte diversification de ses caractéristiques dans le sens d'une qualité d'usage accrue et ce malgré l'augmentation de prix moyen qui en résulte. [eng] Broiler consumption and products characteristics: convenience food are developping despite increasing price levels - The Development of broiler consumption depends on improvments of their convenient characteristics. When Life Conditions require changes in consumption patterns, Consumers with high and average income prefer these kinds of products, under the assumption they are satisfied with their quality.