Relativistic Generalization of the Gamow Factor for Fermion Pair Production or Annihilation

In the production or annihilation of a pair of fermions, the initial-state or final-state interactions often lead to significant effects on the reaction cross sections. For Coulomb-type interactions, the Gamow factor has been traditionally used to take into account these effects. However the Gamow factor needs to be modified when the magnitude of the coupling constant or the relative velocity of two particles increases. We obtain the relativistic generalization of the Gamow factor in terms of the overlap of the Feynman amplitude with the relativistic wave function of two fermions with an attractive Coulomb-type interaction. An explicit form of the corrective factor is presented for the spin-singlet S-wave state. While the corrective factor approaches the Gamow factor in the non-relativistic limit, we found that the Gamow factor significantly over-estimates the effects when the coupling constant or the velocity is large.Comment: 16 pages, 4 figures in LaTe

Rotating Black Hole Entropy from Two Different Viewpoints

Using the brick-wall method, we study the entropy of Kerr-Newman black hole from two different viewpoints, a rest observer at infinity and zero angular momentum observer near horizon. We investigate this with scalar field in the canonical quantization approach. An observer at infinity can take one of the two possible frequency ranges; one is with positive frequencies only and the other is with the whole range including negative frequencies. On the other hand, a zero angular momentum observer near horizon can take positive frequencies only. For the observer at infinity the superradiant modes appear in either choice of the frequency ranges and the two results coincide. For the zero angular momentum observer superradiant modes do not appear due to absence of ergoregion. The resulting entropies from the two viewpoints turn out to be the same.Comment: LaTeX 18 pages, 2 figures, Minor modifications in section 3(ZAMO

An Activating Mutation in sos-1 Identifies Its Dbl Domain as a Critical Inhibitor of the Epidermal Growth Factor Receptor Pathway during Caenorhabditis elegans Vulval Development

Proper regulation of receptor tyrosine kinase (RTK)-Ras-mitogen-activated protein kinase (MAPK) signaling pathways is critical for normal development and the prevention of cancer. SOS is a dual-function guanine nucleotide exchange factor (GEF) that catalyzes exchange on Ras and Rac. Although the physiologic role of SOS and its CDC25 domain in RTK-mediated Ras activation is well established, the in vivo function of its Dbl Rac GEF domain is less clear. We have identified a novel gain-of-function missense mutation in the Dbl domain of Caenorhabditis elegans SOS-1 that promotes epidermal growth factor receptor (EGFR) signaling in vivo. Our data indicate that a major developmental function of the Dbl domain is to inhibit EGF-dependent MAPK activation. The amount of inhibition conferred by the Dbl domain is equal to that of established trans-acting inhibitors of the EGFR pathway, including c-Cbl and RasGAP, and more than that of MAPK phosphatase. In conjunction with molecular modeling, our data suggest that the C. elegans mutation, as well as an equivalent mutation in human SOS1, activates the MAPK pathway by disrupting an autoinhibitory function of the Dbl domain on Ras activation. Our work suggests that functionally similar point mutations in humans could directly contribute to disease

Multi-Dimensional Simulations of the Accretion-Induced Collapse of White Dwarfs to Neutron Stars

We present 2.5D radiation-hydrodynamics simulations of the accretion-induced collapse (AIC) of white dwarfs, starting from 2D rotational equilibrium configurations of a 1.46-Msun and a 1.92-Msun model. Electron capture leads to the collapse to nuclear densities of these cores within a few tens of milliseconds. The shock generated at bounce moves slowly, but steadily, outwards. Within 50-100ms, the stalled shock breaks out of the white dwarf along the poles. The blast is followed by a neutrino-driven wind that develops within the white dwarf, in a cone of ~40deg opening angle about the poles, with a mass loss rate of 5-8 x 10^{-3} Msun/yr. The ejecta have an entropy on the order of 20-50 k_B/baryon, and an electron fraction distribution that is bimodal. By the end of the simulations, at >600ms after bounce, the explosion energy has reached 3-4 x 10^{49}erg and the total ejecta mass has reached a few times 0.001Msun. We estimate the asymptotic explosion energies to be lower than 10^{50}erg, significantly lower than those inferred for standard core collapse. The AIC of white dwarfs thus represents one instance where a neutrino mechanism leads undoubtedly to a successful, albeit weak, explosion. We document in detail the numerous effects of the fast rotation of the progenitors: The neutron stars are aspherical; the ``nu_mu'' and anti-nu_e neutrino luminosities are reduced compared to the nu_e neutrino luminosity; the deleptonized region has a butterfly shape; the neutrino flux and electron fraction depend strongly upon latitude (a la von Zeipel); and a quasi-Keplerian 0.1-0.5-Msun accretion disk is formed.Comment: 25 pages, 19 figures, accpeted to ApJ, high resolution of the paper and movies available at http://hermes.as.arizona.edu/~luc/aic/aic.htm

Focusing Capillary Optics for Use in Solution Small-Angle X-Ray Scattering

Measurements of the global conformation of macromolecules can be carried out using small-angle X-ray scattering (SAXS). Glass focusing capillaries, manufactured at the Cornell High Energy Synchrotron Source (CHESS), have been successfully employed for SAXS measurements on the heme protein cytochrome c. These capillaries provide high X-ray flux into a spot size of tens of micrometres, permitting short exposures of small-volume samples. Such a capability is ideal for use in conjunction with microfluidic mixers, where time resolution may be determined by beam size and sample volumes are kept small to facilitate mixing and conserve material

BRST Quantization of the Proca Model based on the BFT and the BFV Formalism

The BRST quantization of the Abelian Proca model is performed using the Batalin-Fradkin-Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is more simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev-Jackiw formalisms. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the St\"uckelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.Comment: 29 pages, plain Latex, To be published in Int. J. Mod. Phys.