  We study radial symmetric point defects with degree $\frac {k}{2}$ in 2D disk
or $\mathbb{R}^2$ in $Q$-tensor framework with singular bulk energy, which is
defined by Bingham closure. First, we obtain the existence of solutions for the
profiles of radial symmetric point defects with degree $\frac k2$ in 2D disk or
$\mathbb{R}^2$. Then we prove that the solution is stable for $|k|=1$ and
unstable for $|k|>1$. Some identities are derived and used throughout the proof
of existence and stability/instability.
