  The one-particle density matrix $\gamma(x, y)$ is one of the key objects in
the quantum-mechanical approximation schemes. We prove the asymptotic formula
$\lambda_k \sim (Ak)^{-8/3}$, $A \ge 0$, as $k\to\infty$, for the eigenvalues
$\lambda_k$ of the self-adjoint operator $\boldsymbol\Gamma\ge 0$ with kernel
$\gamma(x, y)$.
