  We study superradiance in a one-dimensional geometry, where N>>1 atoms are
randomly distributed along a line. We present an analytic calculation of the
photon escape rates based on the diagonalization of the N x N coupling matrix
Uij = cos xij, where xij is the dimensionless random distance between any two
atoms. We show that unlike a three-dimensional geometry, for a one- dimensional
atomic gas the single-atom limit is never reached and the photon is always
localized within the atomic ensemble. This localization originates from
long-range cooperative effects and not from disorder as expected on the basis
of the theory of Anderson localization.
