  Using Landau-de Gennes effective theory for nematic liquid crystals we
analyse the structure of rectilinear n=1/2 smooth disclination line in the case
of equal elastic constants. We find that at certain temperature there is an
exact mathematical correspondence with a rectilinear vortex in superfluid
$^4He$. With a help of polynomial approximation difference of free energies of
the smooth and of a singular disclination lines is estimated. It turns out that
the smooth disclination line is energetically preferred only if temperature is
low enough. At higher temperatures a disordered core should be expected.
