The radical of a vertex operator algebra associated to a module

The radical of a vertex operator algebra associated to a module is defined and computed.Comment: Latex 14 pages. This is part of the original paper with a new titl

Estiamte of the two-photon exchange effect on deuteron electromagnetic form factors

The corrections of two-photon exchange on deuteron electromagnetic form factors are estimated based on an effective Lagrangian approach. Numerical results for the form factors $G_{C,M,Q}$ of the deuteron with the corrections are compared to its empirical ones. Moreover, the two new form factors, due to the two-photon exchange, are analyzed. Possible way to test the two-photon exchange corrections to the deuteron form factors is discussed.Comment: 17 pages, 10 figure

Atmospheres and Spectra of Strongly Magnetized Neutron Stars II: Effect of Vacuum Polarization

We study the effect of vacuum polarization on the atmosphere structure and radiation spectra of neutron stars with surface magnetic fields B=10^14-10^15 G, as appropriate for magnetars. Vacuum polarization modifies the dielectric property of the medium and gives rise to a resonance feature in the opacity; this feature is narrow and occurs at a photon energy that depends on the plasma density. Vacuum polarization can also induce resonant conversion of photon modes via a mechanism analogous to the MSW mechanism for neutrino oscillation. We construct atmosphere models in radiative equilibrium with an effective temperature of a few \times 10^6 K by solving the full radiative transfer equations for both polarization modes in a fully ionized hydrogen plasma. We discuss the subtleties in treating the vacuum polarization effects in the atmosphere models and present approximate solutions to the radiative transfer problem which bracket the true answer. We show from both analytic considerations and numerical calculations that vacuum polarization produces a broad depression in the X-ray flux at high energies (a few keV \la E \la a few tens of keV) as compared to models without vacuum polarization; this arises from the density dependence of the vacuum resonance feature and the large density gradient present in the atmosphere. Thus the vacuum polarization effect softens the high energy tail of the thermal spectrum, although the atmospheric emission is still harder than the blackbody spectrum because of the non-grey opacities. We also show that the depression of continuum flux strongly suppresses the equivalent width of the ion cyclotron line and therefore makes the line more difficult to observe.Comment: 21 pages, 21 figures; MNRAS; corrected minor typo

Atmospheres and Spectra of Strongly Magnetized Neutron Stars

We construct atmosphere models for strongly magnetized neutron stars with surface fields $B\sim 10^{12}-10^{15}$ G and effective temperatures $T_{\rm eff}\sim 10^6-10^7$ K. The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars, including radio pulsars, soft gamma-ray repeaters, and anomalous X-ray pulsars. In our models, the atmosphere is composed of pure hydrogen or helium and is assumed to be fully ionized. The radiative opacities include free-free absorption and scattering by both electrons and ions computed for the two photon polarization modes in the magnetized electron-ion plasma. Since the radiation emerges from deep layers in the atmosphere with \rho\ga 10^2 g/cm$^3$, plasma effects can significantly modify the photon opacities by changing the properties of the polarization modes. In the case where the magnetic field and the surface normal are parallel, we solve the full, angle-dependent, coupled radiative transfer equations for both polarization modes. We also construct atmosphere models for general field orientations based on the diffusion approximation of the transport equations and compare the results with models based on full radiative transport. In general, the emergent thermal radiation exhibits significant deviation from blackbody, with harder spectra at high energies. The spectra also show a broad feature (\Delta E/\Ebi\sim 1) around the ion cyclotron resonance \Ebi=0.63 (Z/A)(B/10^{14}{G}) keV, where $Z$ and $A$ are the atomic charge and atomic mass of the ion, respectively; this feature is particularly pronounced when \Ebi\ga 3k\Teff. Detection of the resonance feature would provide a direct measurement of the surface magnetic fields on magnetars.Comment: 29 pages, 11 figures; corrected factor of 2 in He models: minor changes to figs 4 and 9 as a result; other very minor change

Britain welcomes the world: Dressing up London

Copyright @ 2013 Routledgehttps://www.taylorfrancis.com/chapters/dressing-london-ozlem-edizel-graeme-evans-hua-dong/e/10.4324/9780203126486-9?context=ubx&refId=546b057b-44c2-4d37-91ac-982df6ff2fa