Polarization of the electron and positron produced in combined Coulomb and strong laser fields

The process of $e^+e^-$ production in the superposition of a Coulomb and a strong laser field is considered. The pair production rate integrated over the momentum and summed over the spin projections of one of the particles is derived exactly in the parameters of the laser field and in the Born approximation with respect to the Coulomb field. The case of a monochromatic circularly polarized laser field is considered in detail. A very compact analytical expression of the pair production rate and its dependence on the polarization of one of the created particles is obtained in the quasiclassical approximation for the experimentally relevant case of an undercritical laser field. As a result, the polarization of the created electron (positron) is derived.Comment: 16 pages, no figure

Critical nucleus charge in a superstrong magnetic field: effect of screening

A superstrong magnetic field stimulates the spontaneous production of positrons by naked nuclei by diminishing the value of the critical charge Z_{cr} . The phenomenon of screening of the Coulomb potential by a superstrong magnetic field which has been discovered recently acts in the opposite direction and prevents the nuclei with Z52 for a nucleus to become critical stronger B are needed than without taking screening into account.Comment: 13 pages, 2 figures, version to be published in Physical Review

Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields

Reformulating the instantons in a complex plane for tunneling or transmitting states, we calculate the pair-production rate of charged fermions in a spatially localized electric field, illustrated by the Sauter electric field E_0 sech^2 (z/L), and in a temporally localized electric field such as E_0 sech^2 (t/T). The integration of the quadratic part of WKB instanton actions over the frequency and transverse momentum leads to the pair-production rate obtained by the worldline instanton method, including the prefactor, of Phys. Rev. D72, 105004 (2005) and D73, 065028 (2006). It is further shown that the WKB instanton action plus the next-to-leading order contribution in spinor QED equals the WKB instanton action in scalar QED, thus justifying why the WKB instanton in scalar QED can work for the pair production of fermions. Finally we obtain the pair-production rate in a spatially localized electric field together with a constant magnetic field in the same direction.Comment: RevTex, 12 pages, two figures; replaced by the version accepted in Phys. Rev.

On the nature of bimodal initial velocity distribution of neutron stars

We propose that the bimodal nature of the kick velocity distribution of radio pulsars is connected with the dichotomy between hadronic stars ({\it i.e.} neutron stars with no quark matter content) and quark stars. Bimodality can appear due to different mechanisms of explosion which leads to the formation of two types of compact stars or due to two different sets of parameters mastering a particular kick mechanism. The low velocity maximum (at $\sim 100$ km s$^{-1}$) is connected with hadronic star formation, whereas the second peak corresponds to quark stars. In the model of delayed collapse of hadronic stars to quark stars (Berezhiani et al. 2003\nocite{bbd2003}) quark deconfinement leads to a second energy release, and to a second kick, in addition to the kick imparted to the newly formed hadronic star during the supernova explosion. If the electromagnetic rocket mechanism can give a significant contribution to pulsar kicks, then the high velocity peak can be connected with the shorter initial spin periods of quark stars with respect to hadronic stars. We discuss {\it pro et contra} of these scenarios.Comment: 8 pages with 2 figures; accepted to A&

Multidimensional Worldline Instantons

We extend the worldline instanton technique to compute the vacuum pair production rate for spatially inhomogeneous electric background fields, with the spatial inhomogeneity being genuinely two or three dimensional, both for the magnitude and direction of the electric field. Other techniques, such as WKB, have not been applied to such higher dimensional problems. Our method exploits the instanton dominance of the worldline path integral expression for the effective action.Comment: 22 pages, 13 figure

Population synthesis of DA white dwarfs: constraints on soft X-ray spectra evolution

Extending the population synthesis method to isolated young cooling white dwarfs we are able to confront our model assumptions with observations made in ROSAT All-Sky Survey (Fleming et al., 1996). This allows us to check model parameters such as evolution of spectra and separation of heavy elements in DA WD envelopes. It seems like X-ray spectrum temperature of these objects is given by the formula T_{X-ray} = min(T_eff, T_max). We have obtained DA WD's birth rate and upper limit of the X-ray spectrum temperature: DA birth rate $= 0.61\times 10^{-12}$ in cubic parsec per year and T_max = 41000 K. These values are in good correspondence with values obtained by other authors (Liebert et al., 2004; Wolff et al., 1996). From this fact we also conclude that our population synthesis method is applicable to the population of close-by isolated cooling white dwarfs as well as to the population of the isolated cooling neutron stars.Comment: 4 pages, 3 figures, conference "European White Dwarf Workshop, 2010", Tubingen, German

Electron-Positron Pair Production in Space- or Time-Dependent Electric Fields

Treating the production of electron and positron pairs by a strong electric field from the vacuum as a quantum tunneling process we derive, in semiclassical approximation, a general expression for the pair production rate in a $z$-dependent electric field $E(z)$ pointing in the $z$-direction. We also allow for a smoothly varying magnetic field parallel to $E(z)$. The result is applied to a confined field $E(z)\not=0$ for $|z|\lesssim \ell$, a semi-confined field $E(z)\not=0$ for $z\gtrsim 0$, and a linearly increasing field $E(z)\sim z$. The boundary effects of the confined fields on pair-production rates are exhibited. A simple variable change in all formulas leads to results for electric fields depending on time rather than space. In addition, we discuss tunneling processes in which empty atomic bound states are spontaneously filled by negative-energy electrons from the vacuum under positron emission. In particular, we calculate the rate at which the atomic levels of a bare nucleus of finite size $r_{\rm n}$ and large $Z\gg 1$ are filled by spontaneous pair creation.Comment: 33 pages and 9 figures. to appear in Phys. Rev.

Schwinger Pair Creation of Particles and Strings

I shortly review the worldline instanton method for calculating Schwinger pair production rates in (i) one-loop QED (ii) multiloop QED and (iii) one-loop open string theory.Comment: 8 pages, 3 figures, talk given at XIV Mexican School of Particles and Fields, November 8 - 12, 2010, Morelia, Mexico, to appear in the conference proceeding

Elastic scattering theory and transport in graphene

Electron properties of graphene are described in terms of Dirac fermions. Here we thoroughly outline the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential. While the massless limit is relevant for pristine graphene, keeping finite mass allows for generalizations onto situations with broken symmetry between the two sublattices, and provides a link to the scattering theory of electrons in a parabolic band. We demonstrate that the Dirac theory requires short-distance regularization for potentials which are more singular than 1/r. The formalism is then applied to scattering off a smooth short-ranged potential. Next we consider the Coulomb potential scattering, where the Dirac theory is consistent for a point scatterer only for the effective impurity strength below 1/2. From the scattering phase shifts we obtain the exact Coulomb transport cross-section in terms of the impurity strength. The results are relevant for transport in graphene in the presence of impurities that do not induce scattering between the Dirac points in the Brillouin zone.Comment: 17 pages, 4 figures. Published versio