Three-body kinematical correlation in the dissociative recombination of ${\text{CH}}_2^{+}$ by three-dimensional imaging

A three-dimensional imaging technique installed at the Heidelberg Test Storage Ring (TSR) has been used to investigate the three-body breakup channels occurring in the dissociative recombination process of the methylene ion ${\text{CH}}_2^{+}$. By selecting dissociation planes perpendicular to the molecular beam direction the dissociation kinematics could be measured with unprecedented momentum resolution. Release energies, the relative branching ratio, and the kinematical correlations between the three fragments were determined for the two energetically allowed channels: $\text{C}\left({}^{3}P\right)+\text{H}\left({}^{2}S\right)+\text{H}\left({}^{2}S\right)$ and $\text{C}\left({}^{1}D\right)+\text{H}\left({}^{2}S\right)+\text{H}\left({}^{2}S\right)$.

Figure 1

(Color online) (a) The calibration function $k\left(x,y\right)$ derived from a measurement of ${\tilde{\Omega }}_i$ for $\left(t_g-t_i\right)\to \infty$. (b) The effective trigger time $t_g\left(x,y\right)$ (in ns) derived from one-spot frames.

Figure 2

(Color online) The measured time distribution $\Delta t_{\text{H,C}}=t\left(\text{H}\right)-t\left(\text{C}\right)$ (solid points). The solid (red) line is the result of a MC simulation assuming a time resolution of ${\sigma }_t=0.9\text{ns}$. The simulated curve was adjusted to the height of the measured distribution around $\left|\Delta t_{\text{H,C}}\right|=0\text{ns}$.

Figure 3

(Color online) Measured distribution of the orientation angle $\theta$ between the normal of the dissociation plane and the ion beam direction for events with $\left|\Delta t_{\text{H,C}}\right|<6.0\text{ns}$ (solid points). The MC simulation assuming a time resolution of ${\sigma }_t=0.9\text{ns}$ is shown by the solid (red) line (see also main text).

Figure 4

Dalitz plot for three-body final channel following the DR of ${\text{CH}}_2^{+}$, depicting the correspondence between the Dalitz coordinates $\left({\eta }_1,{\eta }_2\right)$ and the c.m. angles ${\chi }_D=\angle \left({\vec{p}}_{{\text{H}}_1},{\vec{p}}_{{\text{H}}_2}\right)$ (solid lines in the left half circle) and ${\xi }_D=\angle \left({\vec{p}}_{{\text{H}}_{>}},{\vec{p}}_{\text{C}}\right)$ (dashed lines in the right half circle), with ${\text{H}}_{>}$ denoting the hydrogen with the larger momentum. Note that the Dalitz plot is symmetric around ${\eta }_1=0$.

Figure 5

(Color online) Measured projected distances $D$ for three-fragment events observed in the DR of ${\text{CH}}_2^{+}$ for orientation angles $\left|\text{cos}\left(\theta \right)\right|>0.8$ (solid points). The solid (red) line represents the best fit of the two MC simulated distributions for the $\text{C}\left({}^{3}P\right)$ [dotted (black) line] and the $\text{C}\left({}^{1}D\right)$ channel [dashed (blue) line] to the measured spectrum. The dashed-dotted (green) curve shows a simulation of the projected distance distribution expected for the $\text{C}\left({}^{3}P\right)$ channel when assuming a time resolution of ${\sigma }_t=0.0\text{ns}$.

Figure 6

(Color online) (a) MC simulated transversal Dalitz distribution for some fixed $\left({\eta }_1,{\eta }_2\right)$ values, displaying the resolution obtained in the present experiment. (Note that the distribution was smoothed in the same way as the experimental ones.) Also shown are the c.m. angles ${\chi }_D=\angle \left({\vec{p}}_{{\text{H}}_1},{\vec{p}}_{{\text{H}}_2}\right)$ (solid lines in the left half-circle) and ${\xi }_D=\angle \left({\vec{p}}_{{\text{H}}_{>}},{\vec{p}}_{\text{C}}\right)$ (dashed lines in the right half-circle) for some values of ${\chi }_D$ and ${\xi }_D$. (b) Measured normalized transversal Dalitz distribution for the $\text{C}\left({}^{3}P\right)$ channel, and (c) for the $\text{C}\left({}^{1}D\right)$ channel (see also main text). Between the dotted lines and the Dalitz circle in (b) and (c) the detection efficiency was very small due to the minimum light spot distance that could be resolved in the experiment.

Figure 7

(Color online) Measured projected distances $D$ for three-fragment events observed in the DR of ${\text{CH}}_2^{+}$ for all orientation angles (solid points). The solid (red) line represents the best fit of the two MC simulated distributions for the $\text{C}\left({}^{3}P\right)$ [dotted (black) line] and the $\text{C}\left({}^{1}D\right)$ channel [dashed (blue) line] to the measured spectrum. The simulations were based on the measured Dalitz plots shown in Figs. 6c, 6d.