836 research outputs found
Strong Field Ionization Rate for Arbitrary Laser Frequencies
A simple, analytical, nonrelativistic ionization rate formula for atoms and
positive ions in intense ultraviolet and x-ray electromagnetic fields is
derived. The rate is valid at arbitrary values of the Keldysh parameter and
confirmed by results from ab initio numerical solutions of the single active
electron, time-dependent Schroedinger equation. The proposed rate is
particularly relevant for experiments employing the new free electron laser
(FEL) sources under construction worldwide.Comment: 4 pages, 1 figure, REVTe
The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons
We construct a relativistic potential quark model of , , , and
mesons in which the light quark motion is described by the Dirac equation
with a scalar-vector interaction and the heavy quark is considered a local
source of the gluon field. The effective interquark interaction is described by
a combination of the perturbative one-gluon exchange potential
and the long-range Lorentz-scalar and
Lorentz-vector linear potentials and , where
. Within the quasiclassical approximation, we obtain
simple asymptotic formulas for the energy and mass spectra and for the mean
radii of , , , and mesons, which ensure a high accuracy of
calculations even for states with the radial quantum number . We
show that the fine structure of P-wave states in heavy-light mesons is
primarily sensitive to the choice of two parameters: the strong-coupling
constant and the coefficient of mixing of the long-range
scalar and vector potentials and .
The quasiclassical formulas for asymptotic coefficients of wave function at
zero and infinity are obtained.Comment: 22 pages, 6 figure
Spherical model of the Stark effect in external scalar and vector fields
The Bohr-Sommerfeld quantization rule and the Gamow formula for the width of
quasistationary level are generalized by taking into account the relativistic
effects, spin and Lorentz structure of interaction potentials. The relativistic
quasi-classical theory of ionization of the Coulomb system (V_{Coul}=-\xi/r) by
radial-constant long-range scalar (S_{l.r.}=(1-\lambda)(\sigma r+V_0)) and
vector (V_{l.r.}=\lambda(\sigma r+V_0)) fields is constructed. In the limiting
cases the approximated analytical expressions for the position E_r and width
\Gamma of below-barrier resonances are obtained. The strong dependence of the
width \Gamma of below-barrier resonances on both the bound level energy and the
mixing constant \lambda is detected. The simple analytical formulae for
asymptotic coefficients of the Dirac radial wave functions at zero and infinity
are also obtained.Comment: 25 pages, 4 figures. Submitted to Int. J. Mod. Phys.
Algebraic approach to the spectral problem for the Schroedinger equation with power potentials
The method reducing the solution of the Schroedinger equation for several
types of power potentials to the solution of the eigenvalue problem for the
infinite system of algebraic equations is developed. The finite truncation of
this system provides high accuracy results for low-lying levels. The proposed
approach is appropriate both for analytic calculations and for numerical
computations. This method allows also to determine the spectrum of the
Schroedinger-like relativistic equations. The heavy quarkonium (charmonium and
bottomonium) mass spectra for the Cornell potential and the sum of the Coulomb
and oscillator potentials are calculated. The results are in good agreement
with experimental data.Comment: 17 pages, including 6 PostScript figures (epsf style
Scaling of Dirac Fermions and the WKB approximation
We discuss a new method for obtaining the WKB approximation to the Dirac
equation with a scalar potential and a time-like vector potential. We use the
WKB solutions to investigate the scaling behavior of a confining model for
quark-hadron duality. In this model, a light quark is bound to a heavy di-quark
by a linear scalar potential. Absorption of virtual photons promotes the quark
to bound states. The analog of the parton model for this case is for a virtual
photon to eject the bound, ground-state quark directly into free continuum
states. We compare the scaling limits of the response functions for these two
transitions
Coulomb focusing at above-threshold ionization in elliptically polarized mid-infrared strong laser fields
The role of Coulomb focusing in above-threshold ionization in an elliptically
polarized mid-infrared strong laser field is investigated within a
semiclassical model incorporating tunneling and Coulomb field effects. It is
shown that Coulomb focusing up to moderate ellipticity values is dominated by
multiple forward scattering of the ionized electron by the atomic core that
creates a characteristic low-energy structure in the photoelectron spectrum and
is responsible for the peculiar energy scaling of the ionization normalized
yield along the major polarization axis. At higher ellipticities, the electron
continuum dynamics is disturbed by the Coulomb field effect mostly at the exit
of the ionization tunnel. Due to the latter, the normalized yield is found to
be enhanced, with the enhancement factor being sharply pronounced at
intermediate ellipticities
Developing communication and thinking skills in English as a Foreign Language Education undergraduate students: a proposal for a syllabus model
It is our aim to share a proposal for a new syllabus model and learner-centered methodology for English as a Foreign Language students in the Degree in Teaching in Primary Education at the Universidad de Zaragoza (Spain), presenting the theoretical tenets and analyzing samples of resources and materials that have been designed. In a context of great diversity of levels and learning profiles in the abovementioned educational setting, it is no longer valid to conceive this part of teacher training only in terms of language proficiency, but rather it is necessary to equip students with learning to learn tools and metacognitive strategies as well as materials and resources purposefully designed bearing in mind their context, professional interests and linguistic needs. As a result, throughout the three 6 ECTS courses in the Degree (English in Primary Education I, II and III, for ist, 2nd and 4th year students respectively) we seek to implement active methodologies and make use of a variety of resources following Communicative Language Teaching and Task-based Instruction principles, such as the following: (i) Deep Learning (Clark, 2009a, 2009b) and Scaffolded, Visible Thinking (Ritchhart, Church, and Morrison, 2011); (ii) Cooperative Learning (Kagan and Kagan, 1994); (iii) ICTs and EdTech; (iv) reflective learning, promoting self-assessment and peer-assessment, and (v) Project Based Learning (BIE, 2003). Overall, the teaching proposal designed has enabled us to partially respond to heterogeneity in our large classes and make our students'' learning of a language relevant and meaningful
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