Experimental and quantum-chemical studies on the three-particle fragmentation of neutral triatomic hydrogen

Dissociation of well-defined ${\mathrm{H}}_3$ Rydberg states into three ground state hydrogen atoms reveals characteristic correlation patterns in the center-of-mass motion of the three fragments. We present an extensive experimental dataset of momentum correlation maps for all lower Rydberg states of ${\mathrm{H}}_3$ and ${\mathrm{D}}_3$. In particular the states with principal quantum number $n=2$ feature simple correlation patterns with regular occurence of mutual affinities. Energetically higher-lying states typically show more complex patterns which are unique for each state. Quantum-chemical calculations on adiabatic potential energy surfaces of ${\mathrm{H}}_3$ Rydberg states are presented to illuminate the likely origin of these differences. We discuss the likely dissociation mechanisms and paths which are responsible for the observed continuum correlation.

Figure 1

Cuts through the potential surfaces of ${\mathrm{H}}_3$. Left: $D_{\infty h}$-symmetry; center: transition conserving $C_{2v}$ from $D_{3h}$ to $D_{\infty h}$ (see text); right: $D_{3h}$. Full lines (in $D_{\infty h}$, $C_{2v}$, $D_{3h}$) ${\Sigma }_g^{+}$, ${\mathrm{A}}_1$, ${\mathrm{A}}_1^{\prime }$; dashed ${\Sigma }_u^{+}$, ${\mathrm{B}}_2$, ${\mathrm{E}}^{\prime }$; dot-dashed ${\Pi }_u$, ${\mathrm{B}}_1$, ${\mathrm{A}}_2^{″}$. The vertical lines indicate coordinates common to the middle panel.

Figure 2

Cuts through the potential surfaces of ${\mathrm{H}}_3$. The center panel shows the effect of a distortion conserving $\rho$ and the $C_{2v}$ symmetry; at left and right the energies of the distorted molecule are shown as functions of $\rho$ (see text). Symbols as in Fig. 1.

Figure 3

(Color online) Three-dimensional plot of the lower potential surfaces of ${\mathrm{H}}_3$ as functions of the hyperspherical coordinates $\rho$ and $\vartheta$ (restricted to $C_{2v}$ geometries). The surfaces labeled by (a)–(g) are (a) $-1{}^{2}A_1$, (b) $-1{}^{2}B_2$, (c) $-2{}^{2}A_1$, (d) $-1{}^{2}B_1$, (e) $-2{}^{2}B_2$, (f) $-3{}^{2}A_1$, (g) $-4{}^{2}A_1$ .

Figure 4

(Color online) Three-dimensional plot of the three lowest ${}^{2}A_1$ surfaces. The $3{}^{2}A_1$ surface lies energetically above $2{}^{2}A_2$ for all $C_{2v}$ geometries. As the system is restricted to $D_{\infty h}$ geometry $(\vartheta =0°)$, relabeling of the associated states induces a crossing of the curves $2{}^2\Sigma _g^{+}$ (upper white line) and $1{}^2\Pi _u$ (black line). The two curves $2{}^2\Sigma _g^{+}$ and $1{}^2\Sigma _g^{+}$ (upper and lower white line) have an avoided crossing at $\rho \approx 3.4a_0$ [compare Fig. 1a].

Figure 5

Typical kinetic energy spectrum observed after photoexcitation of the $3s{a}_1^{\prime }(0,0)$ level of ${\mathrm{D}}_3$. The dashed lines (a-k) indicate the expected position of particular states. These states are as follows: a, $2s{a}_1^{\prime }(0,0)$; b, $2s{a}_1^{\prime }(0,1)$; c, $2s{a}_1^{\prime }(1,0)$; d, $2s{a}_1^{\prime }(0,2)$; e, $2s{a}_1^{\prime }(1,1)$; f, $2s{a}_1^{\prime }(0,3)$; g, $2s{a}_1^{\prime }(1,2)$; h, $2s{a}_1^{\prime }(2,1)$; i, $2p{a}_2^{″}(0,0)$; j, $3p{e}^{\prime }(0,0)$; k, $3s{a}_1^{\prime }(0,0)$.

Figure 6

Momentum configurations in the Dalitz plot. The coordinates depend on the fragment momenta ${ϵ}_i={\mid {\vec{k}}_i\mid }^2∕\left(2mW\right)$. The orientation and the magnitude of the momentum vectors is indicated by arrows. Each triangle represents a configuration in momentum space.

Figure 7

Momentum correlation maps of ${\mathrm{D}}_{3}2{\mathrm{sa}}_1^{\prime }$ states. The two plots $(1,2)\left[a\right]$ and $(1,2)\left[b\right]$ originate from data sets obtained after photoexcitation of $3s{a}_1^{\prime }(0,0)\left(\left[a\right]\right)$ and $3d{e}^{″}(0,1)\left(\left[b\right]\right)$. Presumably, the two appearing structures indicate that in one case an $l=0$ and in the other case an $l=\pm 2$ vibrational state is primarily populated by the respective radiative transition ($l$ being the vibrational angular momentum quantum number). Usually, data sets assigned to equal vibronic states result in the same correlation pattern, though the radiative parents of these states might be different.

Figure 8

Momentum correlation maps of ${\mathrm{D}}_{3}2p{a}_2^{″}$ states.

Figure 9

Isotope effects in the $2s{a}_1^{\prime }$ and $2p{a}_2^{″}$ states. Here, similarities between ${\mathrm{D}}_3$ and ${\mathrm{H}}_3$ structures are obvious.

Figure 10

Compilation of momentum correlation maps of the energetically higher states of ${\mathrm{D}}_3$ and ${\mathrm{H}}_3$. Well-known rotational quantum numbers are indicated in square brackets. The two plots in the last row can be assigned to rotational levels of $3d{e}^{″}(0,1)$ as well as $3d{a}_1^{\prime }(0,1)$. The additional lettering $\left[a\right]$ and $\left[b\right]$ indicates that the states $[a∕b]$ of the last row are the respective radiative parents of the two ${\mathrm{D}}_3$ states $3p{e}^{\prime }(0,1)[a∕b]$ in the first row. Most likely, rotational levels are differently occupated in these transitions, which leads to a visible structural difference in the two plots $3p{e}^{\prime }(0,1)\left[a\right]$ and $3p{e}^{\prime }(0,1)\left[b\right]$.