  We address the problem of achieving a random laser with a cloud of cold
atoms, in which gain and scattering are provided by the same atoms. In this
system, the elastic scattering cross-section is related to the complex atomic
polarizability. As a consequence, the random laser threshold is expressed as a
function of this polarizability, which can be fully determined by spectroscopic
measurements. We apply this idea to experimentally evaluate the threshold of a
random laser based on Raman gain between non-degenerate Zeeman states and find
a critical optical thickness on the order of 200, which is within reach of
state-of-the-art cold-atom experiments.
