Oscillation of Branching Ratios Between the $\mathrm{D}(2s)+\mathrm{D}(1s)$ and the $\mathrm{D}(2p)+\mathrm{D}(1s)$ Channels in Direct Photodissociation of ${\mathrm{D}}_2$

The direct photodissociation of ${\mathrm{D}}_2$ at excitation energies above 14.76 eV occurs via two channels, $\mathrm{D}(2s)+\mathrm{D}(1s)$ and $\mathrm{D}(2p)+\mathrm{D}(1s)$. The branching ratios between the two have been measured from the dissociation threshold to $3200{\mathrm{cm}}^{-1}$ above it, and it is found that they show cosine oscillations as a function of the fragment wave vector magnitudes. The oscillation is due to an interference effect and can be simulated using the phase difference between the wave functions of the two channels, analogous to Young’s double-slit experiment. By fitting the measured branching ratios, we have determined the depths and widths of the effective spherical potential wells related to the two channels, which are in agreement with the effective depths and widths of the ab initio interaction potentials. The results of this Letter illustrate the importance of the relative phase between the fragments in controlling the branching ratios of the photodissociation channels.

Figure 1

Fragment $\mathrm{D}(2s,2p)$ intensities as a function of the time delay between the XUV pump and the UV probe laser pulses under field-free conditions. The XUV pump laser is set at $119689.0{\mathrm{cm}}^{-1}$, or $659.3{\mathrm{cm}}^{-1}$ above the $\mathrm{D}(1s)+\mathrm{D}(2s)$ dissociation threshold.

Figure 2

(a) The $\mathrm{D}(2s,2p)$ fragment yield spectrum from the photodissociation of ${\mathrm{D}}_2$. (b) The branching ratios $\mathrm{D}(2s)/[\mathrm{D}(2s)+\mathrm{D}(2p)]$ from the direct dissociations of ${\mathrm{D}}_2$. The photon energies for the measured branching ratios are set at the flat region of the fragment yield spectrum. The experimental results are for the $R(0)$ transitions ($p$-wave), and the theoretical results are for the $P(1)$ transitions ($s$-wave) [15]. The threshold for the production of $\mathrm{D}(1s)+\mathrm{D}(2s)$ is $119029.7{\mathrm{cm}}^{-1}$ [19].

Figure 3

(a) Experimental and (b) theoretical $\mathrm{D}(2s)/[\mathrm{D}(2s)+\mathrm{D}(2p)]$ branching ratios [15]. The corresponding fits to determine the widths and depths of the effective spherical potential wells are also shown. Near the threshold region the oscillations are out of phase between the theory ($s$-wave) and experiment ($p$-wave).

Figure 4

PECs of the $3p\sigma B^{\prime }{}^1{\mathrm{\Sigma }}_u^{+}$ and $2p\sigma B{{}^1\mathrm{\Sigma }}_u^{+}$ states of ${\mathrm{D}}_2$ [24], and the corresponding effective spherical potential wells determined from the fit of the measured branching ratios. Two scattering $p$-wave functions for the effective spherical potential wells are also shown. The wave functions are calculated by $r[\sin (\tau r)/{(\tau r)}^2-\cos (\tau r)/\tau r]$ and $r[\sin (kr+{\delta }_1)/{(kr)}^2-\cos (kr+{\delta }_1)/kr]$ inside and outside of the wells, respectively. ${\delta }_1$ is the phase shift.