  This paper deals with explicit spectral gap estimates for the linearized
Boltzmann operator with hard potentials (and hard spheres). We prove that it
can be reduced to the Maxwellian case, for which explicit estimates are already
known. Such a method is constructive, does not rely on Weyl's Theorem and thus
does not require Grad's splitting. The more physical idea of the proof is to
use geometrical properties of the whole collision operator. In a second part,
we use the fact that the Landau operator can be expressed as the limit of the
Boltzmann operator as collisions become grazing in order to deduce explicit
spectral gap estimates for the linearized Landau operator with hard potentials.
