Emission Spectrum of Fundamental Strings: An Algebraic Approach

We formulate a linear difference equation which yields averaged semi-inclusive decay rates for arbitrary, not necessarily large, values of the masses. We show that the rates for decays $M \to m+\M'$ of typical heavy open strings are independent of the masses $M$ and $m$, and compute the ``mass deffect''$M-m-M'$. For closed strings we find decay rates proportional to $M m_{R}^{(1-D)/2}$, where $m_{R}$ is the reduced mass of the decy products. Our method yields exact interaction rates valid for all mass ranges and may provide a fully microscopic basis, not limited to the long string approximation, for the interactions in the Boltzmann equation approach to hot string gases.