A metastable hydrogen (deuterium) atom source in which groundstate atoms produced by a RF discharge dissociator are bombarded by electrons, provides a relatively large amount of slow metastable atoms (velocity 3-5 kin/s). Total integral cross sections for H*(D*)(2s) +H2(X1S~ +, v=O) collisions have been measured in a wide range of relative velocity (2,5-30 kin/s), by using the attenuation method. A significant improvement of accuracy is obtained, with respect to previous measurements, at low relative velocities. Total cross sections for H* and D*, as functions of the relative velocity, are different, especially in the low velocity range. H* + H2 total differential cross sections have also been measured, with an angular spread of 3.6 ° , for two different collision energy distributions, centered respectively at 100 meV and 390 meV. A first attempt of theoretical analysis of the cross sections, by means of an optical potential, is presented.PACS: 34.40.+n; 34.50.-s the H f potential energy presents also a well, the depth of which is comparable to that of H*, the entrance channel H* + H2 is coupled to the electronic continuum, leading to the associative ionization (Hf + e-). For all these reasons, the H~ system may be regarded as a model system, the study of which can provide information about various atom-diatom collisional processes.H*(2s) on H2 collisions at relatively low energies (E ~ 10-1 eV) have been intensively studied since many years. Nevertheless only integral total cross sections [1-4], quenching total cross sections [5] and reaction rates for the associative ionization [6] have been measured so far. Theoretical studies of H* and H f are of two different types (with no overlapping up to now): (i) molecular calculations [7]; (ii) treatment of the collisional quenching [4,8]. The purpose of the present work is to extend integral cross section measurements towards lower energies (down to 0.06 eV), to measure total differential cross sections, as well as to propose an interpretation in term of long range potentials.