Transverse Electrical Conductivity of a Relativistic Gas in an Intense Magnetic Field

Abstract

The transverse electrical conductivity is computed for a system of degenerate relativistic electrons in a strong magnetic field $H\ensuremath{\approx}{10}^{10}\ensuremath{-}{10}^{13}$ G. As suggested by pulsar models, such fields exist in nature in collapsed bodies, like neutron stars. The present computation is valid in the outer regions of the star where the scatterers are not degenerate, while the electrons are taken to be at zero temperature. The scattering mechanism is assumed to be the electron-ion Coulomb scattering. Numerical values of the transverse conductivity are given in the range ${10}^{9}\ensuremath{\le}H\ensuremath{\le}{10}^{13}$ G, and a comparison is made with the longitudinal and zero-field conductivities. It is found that for densities ${10}^{7}\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}{10}^{7}$, ${\ensuremath{\sigma}}_{\mathrm{II}}\ensuremath{\approx}20{\ensuremath{\sigma}}_{0}$ and ${\ensuremath{\sigma}}_{0}\ensuremath{\approx}3{\ensuremath{\sigma}}_{\ensuremath{\perp}}$. As the density increases, both ${\ensuremath{\sigma}}_{\ensuremath{\perp}}$ and ${\ensuremath{\sigma}}_{\mathrm{II}}$ tend to ${\ensuremath{\sigma}}_{0}$.