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 $D$, $D_s$, $B$, and $B_s$ 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 $V_{\mathrm{Coul}}(r)=-\xi/r$ and the long-range Lorentz-scalar and Lorentz-vector linear potentials $S_{\mathrm{l.r.}}(r)=(1-\lambda)(\sigma r+V_0)$ and $V_{\mathrm{l.r.}}(r)=\lambda(\sigma r+V_0)$, where $0\leqslant\lambda<1/2$. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of $D$, $D_s$, $B$, and $B_s$ mesons, which ensure a high accuracy of calculations even for states with the radial quantum number $n_r\sim 1$. 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 $\alpha_s$ and the coefficient $\lambda$ of mixing of the long-range scalar and vector potentials $S_{\mathrm{l.r.}}(r)$ and $V_{\mathrm{l.r.}}(r)$. 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