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Experimental and simulational studies of the dynamics of vortex reconnectionsin quantum fluids showedthat the distance $d$ between the reconnecting vorticesis 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 analyticcalculation of $D$ in terms of the given geometry of the reconnecting vortices.We start from the numerically observed generic geometry on the way to vortexreconnection and demonstrate that the dynamics is well described by aself-similar analytic solution which provides the wanted information.

Analytic solution of the dynamics of quantum vortex reconnection