  In a recent paper published in this journal [J. Phys. A: Math. Theor. 42
(2009) 495004] we studied a one-dimensional particles system where nearest
particles attract with a force inversely proportional to a power \alpha of
their distance and coalesce upon encounter. Numerics yielded a distribution
function h(z) for the gap between neighbouring particles, with
h(z)=z^{\beta(\alpha)} for small z and \beta(\alpha)>\alpha. We can now prove
analytically that in the strict limit of z\to 0, \beta=\alpha for \alpha>0,
corresponding to the mean-field result, and we compute the length scale where
mean-field breaks down. More generally, in that same limit correlations are
negligible for any similar reaction model where attractive forces diverge with
vanishing distance. The actual meaning of the measured exponent \beta(\alpha)
remains an open question.

Statistical Mechanics