Theoretical studies of H2–H2 collisions. I. Elastic scattering of ground state para- and ortho-H2 in the rigid rotor approximation

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Abstract
Close coupling calculations of integral and differential elastic cross sections of hydrogen ground state molecule collisions have been performed, for c.m. energies below 0.5 eV. It is shown that the isotropic part of the potential, determined by the consistent ab initio potentials of five geometries, provides a very accurate (1%–2%) agreement with measured p‐H2/p‐H2 integral cross sections in the range of 900–2300 m/sec relative velocity. Detailed analysis of p‐H2/p‐H2 scattering results and the determination of a series of orbiting resonances provide a set of (virtual) quasi‐bound‐state energy levels. The fit formula of those levels gives two bound states of the (H2)2 system, for J=0 and 1, at −0.340×10−3 and −0.179×10−3 eV, respectively, which is close to the two binding energies found for the isotropic potential. However, the more attractive plane T configuration of the (H2)2 system gives larger binding energies when the zero point vibrations are neglected. Lifetimes and the periods of orbiting have been evaluated for the resonances. Since the resonaces are due to pure orbiting, we have compared the spacing of the p‐H2/p‐H2 partial integral cross section peaks with peaks of the opacities for p‐H2/o‐H2 and o‐H2/o‐H2 and found quantitative agreement almost everywhere, while the exceptions found for o‐H2/o‐H2 at very small energies can be explained by slightly different effective moments of inertia. The undulatory structure found for the ground state p‐H2/p‐H2 integral cross section is clearly due to symmetry restrictions which only allow even partial waves. For o‐H2/o‐H2, the cross sections of solely the symmetric or the asymmetric problem show undulatory structure as well because the even or odd partial wave contributions, respectively, dominate, while in the averaged curve these structures are completely damped. A few examples of differential cross sections and differential helicity transition cross sections at resonance energies are presented. The jz conservation in the body‐fixed frame used in the approximation of McGuire has been found to be not quantitatively valid in the energy range of the strong resonances while for increasing energies jz conserving cross sections become dominant. Generally for o‐H2/p‐H2 collisions jz is better conserved than for o‐H2/o‐H2.