  Experimental and simulational studies of the dynamics of vortex reconnections
in quantum fluids showedthat the distance $d$ between the reconnecting vortices
is close to a universal time dependence $d=D[\kappa|t_0-t|]^\alpha$ with
$\alpha$ fluctuating around 1/2 and $\kappa=h/m$ is the quantum of circulation.
Dimensional analysis, based on the assumption that the quantum of circulation
$\kappa=h/m$ is the only relevant parameter in the problem, predicts
$\alpha=1/2$. The theoretical calculation of the dimensionless coefficient $D$
in this formula remained an open problem. In this Letter we present an analytic
calculation of $D$ in terms of the given geometry of the reconnecting vortices.
We start from the numerically observed generic geometry on the way to vortex
reconnection and demonstrate that the dynamics is well described by a
self-similar analytic solution which provides the wanted information.
