  The power-law reaction rate coefficient for the barrierless reactions is
studied if the reactions take place in systems with power-law distributions,
and a generalized rate formula for the barrierless reactions in Gorin model is
derived. We show that due to barrierless, different from those for bimolecular
and unimolcular reactions, the power-law rate coefficient for the barrierless
reactions does not have the factor of power-law distribution function and thus
it is not very strongly dependent on the nu-parameter. Four barrierless
reactions are taken as the application examples to calculate the new rate
coefficients, which with larger fitting nu-parameters can be exactly in
agreement with the measurement values in experimental studies.
