Analytic approximation for eigenvalues of a class of PT\mathcal{PT} symmetric Hamiltonians

An analytical approximation for the eigenvalues of $\mathcal{PT}$ symmetric Hamiltonian $\mathsf{H} = -d^{2}/dx^{2} - (\mathrm{i}x)^{\epsilon+2}$, $\epsilon > -1$ is developed via simple basis sets of harmonic-oscillator wave functions with variable frequencies and equilibrium positions. We demonstrate that our approximation provides high accuracy for any given energy level for all values of $\epsilon > -1$.Comment: 8 pages, 3 figure

Radical increase of the parametric X-ray intensity under condition of extremely asymmetric diffraction

Parametric X-ray radiation (PXR) from relativistic electrons moving in a crystal along the crystal-vacuum interface is considered. In this geometry the emission of photons is happening in the regime of extremely asymmetric diffraction (EAD). In the EAD case the whole crystal length contributes to the formation of X-ray radiation opposed to Laue and Bragg geometries, where the emission intensity is defined by the X-ray absorption length. We demonstrate that this phenomenon should be described within the dynamical theory of diffraction and predict a radical increase of the PXR intensity. In particular, under realistic electron-beam parameters, an increase of two orders of magnitude in PXR-EAD intensity can be obtained in comparison with conventional experimental geometries of PXR. In addition we discuss in details the experimental feasibility of the detection of PXR-EAD.Comment: 9 pages, 5 figure

Nonasymptotic analysis of relativistic electron scattering in the Coulomb field

It is shown that the conventional Born series for relativistic electron scattering in the Coulomb field cannot be used for calculating the scattering characteristics. The differential cross section at small scattering angles is found on the basis of the Furry-Sommerfeld-Maue solution of the Dirac equation. Propagation of the electron wave packet is considered in order to separate the incident and scattered fluxes. It is shown that the total scattering cross section proves to be finite but depends on the distance r between the scattering center and the observation point. It is also shown that the polarization characteristics of the scattered beam are changed due to the long-range character of the Coulomb potential. The results can be important because Coulomb scattering is often used for normalization of experimental data in high-energy physics

Nonasymptotic analysis of relativistic electron scattering in the Coulomb field

It is shown that the conventional Born series for relativistic electron scattering in the Coulomb field cannot be used for calculating the scattering characteristics. The differential cross section at small scattering angles is found on the basis of the Furry-Sommerfeld-Maue solution of the Dirac equation. Propagation of the electron wave packet is considered in order to separate the incident and scattered fluxes. It is shown that the total scattering cross section proves to be finite but depends on the distance r between the scattering center and the observation point. It is also shown that the polarization characteristics of the scattered beam are changed due to the long-range character of the Coulomb potential. The results can be important because Coulomb scattering is often used for normalization of experimental data in high-energy physics

Collapse-and-revival dynamics of strongly laser-driven electrons

The relativistic quantum dynamics of an electron in an intense single-mode quantized electromagnetic field is investigated with special emphasis on the spin degree of freedom. In addition to fast spin oscillations at the laser frequency, a second time scale is identified due to the intensity dependent emissions and absorptions of field quanta. In analogy to the well-known phenomenon in atoms at moderate laser intensity, we put forward the conditions of collapses and revivals for the spin evolution in laser-driven electrons starting at feasible $10^{18}$ W/cm$^2$.Comment: 18 pages, 4 figure