Hydrogen molecule as seen in electron and positron scattering

By a historical overview, we show the importance of a laconic paper by Kolos and Wolniewicz dating to 1962 [Phys. Lett. 5(2), 222-223 (1%2)], in which they applied the variational method for the hydrogen molecule. In the first part of this perspective (say till 1996), the experiments on electron molecule scattering (including hydrogen) developed a vast range of techniques, even if the results were far from being congruent [Riv. Nuovo Cimento 19/3, 1996]. In turn, in the last years, we have observed the quickly rising applicability of theoretical methods, like convergent-close coupling [Zammit et al. Phys. Rev. Lett. 116, 233201 (2016)] and R-matrix [Meltzer & Tennyson, J. Phys. Phys. B 53, 245203 (2020)]. The mutual agreement between theories and experiments allows defining recommended cross-sections for electron and positron scattering from zero to sub-relativistic energies. This, in turn, enables to check the dispersion relation, i.e. the interdependence between the zero-energy integral elastic, the high-energy elastic differential at zero angle, and the integral of the total cross-section from zero to infinity. Such a relation holds, within the experimental uncertainties, for positrons. For electrons, a big discrepancy points to the importance of the exchange effects in the e(-) - H-2 scattering. [GRAPHICS] .