Precision measurement of quasi-bound resonances in H$_2$ and the H + H scattering length

Abstract

Quasi-bound resonances of H2 are produced via two-photon photolysis of H2S molecules as reactive intermediates or transition states, and detected before decay of the parent molecule into three separate atoms. As was previously reported [K.F. Lai et al., Phys. Rev. Lett. 127, 183001 (2021)] four centrifugally bound quantum resonances with lifetimes of multiple µs, lying energetically above the dissociation limit of the electronic ground state X 1 Σ + g of H2, were observed as X(v, J) = (7,21) * , (8,19) * , (9,17) * , and (10,15) * , while also the short-lived (∼ 1.5 ns) quasi-bound resonance X(11,13) * was probed. The present paper gives a detailed account on the identification of the quasi-bound or shape resonances, based on laser detection via F 1 Σ + g -X 1 Σ + g two-photon transitions, and their strongly enhanced Franck-Condon factors due to the shifting of the wave function density to large internuclear separation. In addition, the assignment of the rotational quantum number is verified by subsequent multi-step laser excitation into autoionization continuum resonances. Existing frameworks of full-fledged ab initio computations for the bound region in H2, including Born-Oppenheimer, adiabatic, non-adiabatic, relativistic and quantum-electrodynamic contributions, are extended into the energetic range above the dissociation energy. These comprehensive calculations are compared to the accurate measurements of energies of quasi-bound resonances, finding excellent agreement. They show that the quasi-bound states are in particular sensitive to non-adiabatic contributions to the potential energy. From the potential energy curve and the correction terms, now tested at high accuracy over a wide range of energies and internuclear separations, the s-wave scattering length for singlet H+H scattering is determined at a = 0.2735 39 31 a0. It is for the first time that such an accurate value for a scattering length is determined based on fully ab initio methods including effects of adiabatic, non-adiabatic, relativistic and QED with contributions up to mα 6 . * Tribute to the late Prof. Lutoslaw Wolniewicz and honoring him for his inspirational contributions over many decades to the theory of the hydrogen molecule.

The quasi bound spectrum of H 2

“…The values followed by † are the results obtained in Lai et al [23] from the previously quoted three VUV laser experiment performed in Amsterdam.…”

“…Comparison between different methods to compute the eigenvalues of quasibound levels of H 2 and experimental derivations. Eexp are the experimental values deduced from the VUV emission spectra [1] and reported in [5], except for the values with a † that are taken from the 3 VUV laser experiment [23]. E pw adiab is the value derived with our approximation of the modified potential displayed in Fig 1 . E used is the value used for deriving the transition wavenumbers displayed in Table 3.…”