325,162 research outputs found
Relativistic Coulomb Green's function in -dimensions
Using the operator method, the Green's functions of the Dirac and
Klein-Gordon equations in the Coulomb potential are derived for
the arbitrary space dimensionality . 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
pair production in the collisions of two nuclei at low relative
velocity . Both free-free and bound-free pair production is
considered. The parameters are assumed to be small
compared to unity but arbitrary compared to ( are the charge
numbers of the nuclei and is the fine structure constant). Due to a
suppression of the Born term by high power of , the first Coulomb
correction to the amplitude appears to be important at . The effect of a finite nuclear mass is discussed. In contrast to the
result obtained in the infinite nuclear mass limit, the terms
are not suppressed by the high power of 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
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