  We report on the analysis of the root mean square curvature as a function of
the numerical resolution for a single reconnection of two quantized vortex
rings in superfluid helium. We find a similar scaling relation as reported in
the case of decaying thermal counterflow simulations by L. Kondaurova et al.
There the scaling was related to the existence of a Kelvin-wave cascade which
was suggested to support the L'vov-Nazarenko spectrum. Here we provide an
alternative explanation that does not involve the Kelvin-wave cascade but is
due to the sharp cusp generated by a reconnection event in a situation where
the maximum curvature is limited by the computational resolution. We also
suggest a method for identifying the Kelvin spectrum based on the decay of the
rms curvature by mutual friction. Our vortex filament simulation calculations
show that the spectrum of Kelvin waves after the reconnection is not simply
$n(k) \propto k^{-\eta}$ with constant $\eta$. At large scales the spectrum
seems to be close to the Vinen prediction with $\eta$ = 3 but becomes steeper
at smaller scales.
