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In this paper we consider a representative a priori unstable Hamiltoniansystem with 2+1/2 degrees of freedom, to which we apply the geometric mechanismfor diffusion introduced in the paper Delshams et al., Mem. Amer. Math. Soc.2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provideexplicit, concrete and easily verifiable conditions for the existence ofdiffusing orbits.  The simplification of the hypotheses allows us to perform explicitly thecomputations along the proof, which contribute to present in an easilyunderstandable way the geometric mechanism of diffusion. In particular, wefully describe the construction of the scattering map and the combination oftwo types of dynamics on a normally hyperbolic invariant manifold

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems