In the reversed field pinch plasmas produced by the reversed field experiment (RFX), neutral particle measurements reveal the presence in the radial direction of a small population of non-thermal energetic ions (E = 103 eV to 8 × 103 eV). In this work supra-thermal electrons at the plasma edge are considered to be the free-energy source for the ion acceleration. Fast electrons, moving in the same direction of the main magnetic field, excite an ~pi electrostatic wave which gives energy to the ions which are accelerated in the direction perpendicular to the local equilibrium magnetic field. The theoretical predictions for the neutral particle fluxes are in agreement with the experimental measurements. Moreover, a correlation between the experimental fast-ion and fast-electron energy densities has been found.