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