The expression for the angular correlation of two-photon nnnihilation radiation for positrons colliding with molecular hydrogen is derived. The one-state approximation is used, and a one-centre expansion of the hydrogen wave function is assumed. Results obtained using a simple Hz wave function yield n half-width of the angular distribution which is in agreement with the observed results for positrons annihilating in liquid hydrogen. Cornpal-ison is made with corresponding resi~lts for the annihilation I-ate.On calcule une expression poul.'la corl-elation angulaire du Ixyonnement d'annihilation il deux photons de positrons venlrnt en collision avec des molecules d'hydrogene. On utilise I'approxi-L mation i un etat et iln developpement autour d'un seul centre pour la fonction d'onde de I'hydrogtne. Les rCsultats obtenus en employant une fonction d'onge simple p o u~ Hz donnent pour 121 distribution angulaire une demi-largeur en accord avec les resultats obse~.ves pour I'annihilation des positrons dans I'hydrogtne liquide. On fait la cornparaison avec les resultats correspondant pour le taux d'annihilation. Can. J. Phys.. 57. 1027 (1979) [Traduit par le journal] The scattering of low energy positrons by molecular hydrogen has been recently investigated theoretically (see, for example, Baille et al. (1, 2), Darewych et al. (3), Hara (4) and papers cited therein) and experimentally (5, 6). The theoretical investigations have involved the calculation of the low energy elastic, momentum transfer, rotational and vibrational excitation cross sections as well as the annihilation rate, using a simple one-state approximation in which only the electrostatic potential and the adiabatic distortion potential of the H, molecule are taken into account, whereas the vibrational and rotational excitations are calculated using the adiabatic-nuclei approximation (see, for example, the review article by Golden et al. (7)). The measurements, to date, have been of the total (elastic plus inelastic) cross section above 1 eV and the annihilation rate for thermalized positrons.It is well known that there exists another measurable quantity for positron collisions, namely the angular correlation of the annihilation radiation, which, like the annihilation rate, is determined from the distribution (8, 9):x Y(r,, ..., r,; vk) d3rk / 'n d3rj j # k part of) the approximatewave functionY(v,, . . . , r,;x) than are the scattering cross sections. Thus calculations which give reasonable results for the cross sections can yield poor values of the annihilation rate.For positron-gas scattering and annihilation, the angular correlation function I@), which is related to S(q) by 121 I(O) = 2 r J m ~( q ) q dq, qz = nice 11 = is the parameter for which the least number of calculations and measurements have been done. (In fact, to the author's knowledge, no measurements of I(0) for gaseous targets have ever been done.)There exist a number of calculations of I(0) for atomic targets such as H (lo), He (11, 12), Li (13,14), and Ne (1 5). In the present article we...