Low-energy cross sections for elastic scattering and recoil of protons from4 He nuclei (also known as α particles) are calculated directly by solving the Schrödinger equation for five nucleons interacting through accurate two-and three-nucleon forces derived within the framework of chiral effective field theory. Precise knowledge of these processes at various proton backscattering/recoil angles and energies is needed for the ion-beam analysis of numerous materials, from the surface layers of solids, to thin films, to fusion-reactor materials. Indeed, the same elastic scattering process, in two different kinematic configurations, can be used to probe concentrations and depth profiles of either hydrogen or helium. We compare our results to available experimental data and show that direct calculations with modern nuclear potentials can help to resolve remaining inconsistencies among different data sets and can be used to predict these cross sections when measurements are not available. He proton elastic recoil reactions are the leading means for determining the concentrations and depth profiles of, respectively, helium and hydrogen at the surface of materials or in thin films. Such analyses, known among specialists as (non-)Rutherford backscattering spectroscopy and elastic recoil detection analysis, are very important for characterizing the physical, chemical and electrical behavior of materials, for which hydrogen is one of the most common impurities, and for studying the implantation of helium for applications in, e.g., waveguides or fusion energy research [1,2]. To achieve good resolution e.g. in the case of thick samples, measurements are often performed at energies above the Rutherford threshold where the purely Coulomb elastic scattering paradigm does not hold anymore. In this regime, in which the incident particle energy is on the order of a few MeV per nucleon, nuclear physics becomes the main driver of the scattering process, particularly near low-lying resonances where the cross section can be enhanced by orders of magnitude with respect to the Rutherford rate. Therefore, the availability of accurate reference differential cross sections for a variety of proton/ 4 He incident energies and detection angles are key to the feasibility and quality of these analyses.