  We consider the nonlinear Dirac equation, also known as the Soler model:
$i\p\sb t\psi=-i\alpha \cdot \nabla \psi+m \beta \psi-f(\psi\sp\ast \beta \psi)
\beta \psi$, $\psi(x,t)\in\mathbb{C}^{N}$, $x\in\mathbb{R}^n$, $n\le 3$, $f\in
C\sp 2(\R)$, where $\alpha_j$, $j = 1,...,n$, and $\beta$ are $N \times N$
Hermitian matrices which satisfy $\alpha_j^2=\beta^2=I_N$, $\alpha_j
\beta+\beta \alpha_j=0$, $\alpha_j \alpha_k + \alpha_k \alpha_j =2 \delta_{jk}
I_N$. We study the spectral stability of solitary wave solutions
$\phi(x)e^{-i\omega t}$. We study the point spectrum of linearizations at
solitary waves that bifurcate from NLS solitary waves in the limit $\omega\to
m$, proving that if $k>2/n$, then one positive and one negative eigenvalue are
present in the spectrum of the linearizations at these solitary waves with
$\omega$ sufficiently close to $m$, so that these solitary waves are linearly
unstable. The approach is based on applying the Rayleigh--Schroedinger
perturbation theory to the nonrelativistic limit of the equation. The results
are in formal agreement with the Vakhitov--Kolokolov stability criterion.
