  The structure of the half-integer rectilinear disclination line within the
framework of the Landau-de Gennes effective theory of nematic liquid crystals
is investigated. The consistent perturbative expansion is constructed for the
case of $L_2\neq 0$. It turns out that such expansion can be performed around
only a discrete subset of an infinite set of the degenerate zeroth order
solutions. These solutions correspond to the positive and negative wedge
disclination lines and to four configurations of the twist disclination line.
The first order corrections to both the order parameter field as well as the
free energy of the disclination lines have been found. The results for the free
energy are compared with the ones obtained in the Frank-Oseen-Zocher director
description.
