  For a smooth vectorial stationary Gaussian random field $X : \Omega \times
\mathbb{R}^d \to \mathbb{R}^d$, we give necessary and sufficient conditions to
have a finite second moment for the number of roots of $X(t) - u$. The results
are obtained by using a method of proof inspired on the one obtained by D.
Geman for stationary Gaussian processes long time ago. Afterwards the same
method is applied to the number of critical points of a scalar random field and
also to the level set of a vectorial process $X : \Omega \times \mathbb{R}^D
\to \mathbb{R}^d$ with $D > d$.
