Asymmetric deviation of the scattering cross section around Lyα by atomic hydrogen

We investigate the asymmetry of the scattering cross section of radiation around Lyalpha by atomic hydrogen, which may be applied to analyses of scattering media with high neutral hydrogen column densities, including damped Lyalpha absorption systems of quasars. The exact scattering cross section is given by the Kramers-Heisenberg formula obtained from fully quantum mechanical second-order time-dependent theory, where, in the case of hydrogen, each matrix element is given in a closed analytical form. The asymmetric deviation of the scattering cross section from the Lorentzian near the line center is computed by expanding the Kramers-Heisenberg formula in terms of Deltaomega/omega(Lyalpha), where omega(Lyalpha) is the angular frequency of the Lyalpha transition and Deltaomega is the deviation of incident radiation from omega(Lyalpha). To the first order of Deltaomega/omega(Lyalpha), we obtain sigma(omega) = sigma(T) (0.5f(12)omega(Lyalpha)/Deltaomega)(2) (1 - 1.79Deltaomega/(Lyalpha)), where sigma(T) is the Thomson scattering cross section and f(12) = 0.4162 is the oscillator strength for the Lyalpha transition. With this deviation, the line center of the damped wing pro. le apparently shifts blueward of the true Lyalpha line center. In the case of a damped Lyalpha system with an H I column density 5 x 10(21) cm(-2), the apparent line-center shift relative to the true center amounts to 0.2 Angstrom, resulting in an underestimation of the redshift by Deltaz similar to 10(-4). A measurable underestimation by an amount Deltaz similar to 10(-3) is expected for absorbing systems with N-HI greater than or equal to 4 x 10(22) cm(-2).