Relativistic Coulomb Green's function in dd-dimensions

Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these Green's functions are considered in detail.Comment: 9 page

Quasiclassical Green function in an external field and small-angle scattering

The quasiclassical Green functions of the Dirac and Klein-Gordon equations in the external electric field are obtained with the first correction taken into account. The relevant potential is assumed to be localized, while its spherical symmetry is not required. Using these Green functions, the corresponding wave functions are found in the approximation similar to the Furry-Sommerfeld-Maue approximation. It is shown that the quasiclassical Green function does not coincide with the Green function obtained in the eikonal approximation and has a wider region of applicability. It is illustrated by the calculation of the small-angle scattering amplitude for a charged particle and the forward photon scattering amplitude. For charged particles, the first correction to the scattering amplitude in the non-spherically symmetric potential is found. This correction is proportional to the scattering angle. The real part of the amplitude of forward photon scattering in a screened Coulomb potential is obtained.Comment: 20 pages, latex, 1 figur

Electron-positron pair production in ion collisions at low velocity beyond Born approximation

We derive the spectrum and the total cross section of electromagnetic $e^{+}e^{-}$ pair production in the collisions of two nuclei at low relative velocity $\beta$. Both free-free and bound-free $e^{+}e^{-}$ pair production is considered. The parameters $\eta_{A,B}=Z_{A,B}\alpha$ are assumed to be small compared to unity but arbitrary compared to $\beta$ ($Z_{A,B}$ are the charge numbers of the nuclei and $\alpha$ is the fine structure constant). Due to a suppression of the Born term by high power of $\beta$, the first Coulomb correction to the amplitude appears to be important at $\eta_{A,B}\gtrsim \beta$. The effect of a finite nuclear mass is discussed. In contrast to the result obtained in the infinite nuclear mass limit, the terms $\propto M^{-2}$ are not suppressed by the high power of $\beta$ and may easily dominate at sufficiently small velocities.Comment: 9 pages, 1 figur

Graded Lie algebras of maximal class IV

We describe the isomorphism classes of certain infinite-dimensional graded Lie algebras of maximal class, generated by an element of weight one and an element of weight two, over fields of odd characteristic.Comment: 38 pages. See also http://www-math.science.unitn.it/~caranti/ and http://users.ox.ac.uk/~vlee

A Proposal to Measure the Quasiparticle Poisoning Time of Majorana Bound States

We propose a method of measuring the fermion parity lifetime of Majorana fermion modes due to quasiparticle poisoning. We model quasiparticle poisoning by coupling the Majorana modes to electron reservoirs, explicitly breaking parity conservation in the system. This poisoning broadens and shortens the resonance peak associated with Majorana modes. In a two lead geometry, the poisoning decreases the correlation in current noise between the two leads from the maximal value characteristic of crossed Andreev reflection. The latter measurement allows for calculation of the poisoning rate even if temperature is much higher than the resonance width.Comment: 5 pages, 5 figure

A New Method for Estimating Dark Matter Halo Masses using Globular Cluster Systems

All galaxies are thought to reside within large halos of dark matter, whose properties can only be determined from indirect observations. The formation and assembly of galaxies is determined from the interplay between these dark matter halos and the baryonic matter they host. Although statistical relations can be used to approximate how massive a galaxy's halo is, very few individual galaxies have direct measurements of their halo masses. We present a method to directly estimate the total mass of a galaxy's dark halo using its system of globular clusters. The link between globular cluster systems and halo masses is independent of a galaxy's type and environment, in contrast to the relationship between galaxy halo and stellar masses. This trend is expected in models where globular clusters form in early, rare density peaks in the cold dark matter density field and the epoch of reionisation was roughly coeval throughout the Universe. We illustrate the general utility of this relation by demonstrating that a galaxy's supermassive black hole mass and global X-ray luminosity are directly proportional to their host dark halo masses, as inferred from our new method.Comment: 6 pages, 4 colour figures. Accepted by MNRAS Letters. Data catalogue available from the first autho