Shape Resonances in ${\mathrm{H}}_2$ as Photolysis Reaction Intermediates

Shape resonances in ${\mathrm{H}}_2$, produced as reaction intermediates in the photolysis of ${\mathrm{H}}_2\mathrm{S}$ precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the $\mathrm{F}$ electronically excited state of ${\mathrm{H}}_2$. For $J=13$, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30 MHz (1.4 mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the ${\mathrm{H}}_2$ molecule, now tested at high accuracy over a wide range of internuclear separations, the $s$-wave scattering length for singlet $\mathrm{H}(1s)+\mathrm{H}(1s)$ scattering is determined at $a={0.2735}_{31}^{39}$ $a_0$.

Figure 1

Potential energy surfaces for the electronic ground states of ${\mathrm{H}}_2\mathrm{S}$ [27] and ${\mathrm{H}}_2$ [28]. The ${\mathrm{H}}_2\mathrm{S}$ equilibrium geometry is indicated with a magenta ellipse in the contour plot. For ${\mathrm{H}}_2$ the radial wave functions (not to scale) of the observed shape resonances and the respective rotational barriers are shown. The inset displays the $J$-independent contribution of beyond-Born-Oppenheimer contributions to the potential.

Figure 2

Overview spectra recorded in a two-laser scheme with two-photon UV photolysis of ${\mathrm{H}}_2\mathrm{S}$, followed by $2+1$ REMPI on $\mathrm{F}0\text{−}\mathrm{X}(v^{\prime \prime })$ bands with a UV-tunable frequency-doubled dye laser. Transitions are labeled with quantum numbers of the ground level. Excitations from quasibound resonances are indicated with an asterisk (*).

Figure 3

Color map displaying the magnitude of contributions to the energies of ($v$, $J$) levels in ${\mathrm{H}}_2$, for both bound and quasibound levels, resulting from nonadiabatic, relativistic, and radiative corrections to the BO energies.

Figure 4

High-resolution excitation spectrum of a two-photon transition in the $\mathrm{F}\text{−}\mathrm{X}$ system probing the shape resonance (10,15) via a $\mathrm{Q}$ line. The lower panel shows the ac Stark extrapolation to deduce the field-free transition frequency.