3,806 research outputs found
Exact averages of central values of triple product L-functions
We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product L-function proved by Gross and Kudla
The off-resonant dielectronic recombination in a collision of an electron with a heavy hydrogen-like ion
The recombination of an electron with an (initially) hydrogen-like ion is
investigated. The effect of the electron-electron interaction is treated
rigorously to the first order in the parameter 1/Z and within the
screening-potential approximation to higher orders in 1/Z, with Z being the
nuclear charge number. The two-electron correction contains the
dielectronic-recombination part, which contributes to the process not only
under the resonance condition for the projectile energy but also in the regions
far from resonances. The mechanism of the off-resonant dielectronic
recombination is studied in detail.Comment: 9 pages, 2 tables, 3 figure
Tail emission from a ring-like jet: its application to shallow decays of early afterglows and to GRB 050709
Similar to the pulsar, the magnetic axis and the spin axis of the gamma-ray
burst source may not lie on the same line. This may cause a ring-like jet due
to collimation of the precessing magnetic axis. We analyze the tail emission
from such a jet, and find that it has a shallow decay phase with temporal index
equal to -1/2 if the Lorentz factor of the ejecta is not very high. This phase
is consistent with the shallow decay phase of some early X-ray afterglow
detected by {\it{swift}}. The ring-like jet has a tail cusp with sharp rising
and very sharp decay. This effect can provide an explanation for the
re-brightening and sharp decay of the X-ray afterglow of GRB 050709.Comment: 6 pages, 2 figures. Accepted by ChJA
Asymptotic channels and gauge transformations of the time-dependent Dirac equation for extremely relativistic heavy-ion collisions
We discuss the two-center, time-dependent Dirac equation describing the
dynamics of an electron during a peripheral, relativistic heavy-ion collision
at extreme energies. We derive a factored form, which is exact in the
high-energy limit, for the asymptotic channel solutions of the Dirac equation,
and elucidate their close connection with gauge transformations which transform
the dynamics into a representation in which the interaction between the
electron and a distant ion is of short range. We describe the implications of
this relationship for solving the time-dependent Dirac equation for extremely
relativistic collisions.Comment: 12 pages, RevTeX, 2 figures, submitted to PR
Radiation Dosimetry of Binary Pulsars
Companion stars exposed to high energy radiation from a primary neutron star
or accreting black hole can experience significant spallation of their heavy
elements, so that their atmospheres would be extremely rich in lithium,
beryllium, and especially boron. In this paper we note that the detection or
non-detection of these elements, and their relative abundances if detected,
would provide a diagnostic of the high energy output of the primary, and
possibly the shock acceleration of particles at the companion's bow shock in a
pulsar wind.Comment: To appear in The Astrophysical Journal. Plain TeX file, 8 pages, no
figure
Diagnosing magnetars with transient cooling
Transient X-ray emission, with an approximate t^{-0.7} decay, was observed
from SGR 1900+14 over 40 days following the the giant flare of 27 Aug 1998. We
calculate in detail the diffusion of heat to the surface of a neutron star
through an intense 10^{14}-10^{15} G magnetic field, following the release of
magnetic energy in its outer layers. We show that the power law index, the
fraction of burst energy in the afterglow, and the return to persistent
emission can all be understood if the star is composed of normal baryonic
material.Comment: 9 pages, 1 eps figur
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