Hydrogen molecule as seen in electron and positron scattering

Abstract

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 (1962)], 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.

GRAPHICAL ABSTRACT

Keywords:

• Electron scattering
• positron scattering
• molecular hydrogen

Acknowledgments

This paper is devoted to the memory of Lutoslaw Wolniewicz. GK acquired many of the ideas presented in this paper during his short stay at Wayne State University (Detroit) in 1990: discussions with prof. Walt Kauppila and Talbert Stein were remarkable. We thank prof. Dmitry Fursa for sending us tabulated values of CCC total and elastic cross-sections, and dr Jan Franz for his tabulated cross-sections.

Disclosure statement

No potential conflict of interest was reported by the author(s).