A comparison of Fraunhofer-type diffraction from an atomic single-slit and a molecular double-slit

Abstract

We measured the Q-value and the scattering angle distributions for non-dissociative state selective single electron capture in collisions of 7.5 keV H$^+$ and 15 keV H$_2^+$ with He. The experimental data are compared with semiclassical close-coupling calculations and predictions from the classical trajectory Monte Carlo simulations. By analogy with Fraunhofer diffraction, we also developed a toy model to reconstruct an imaginary screen that reflects the reaction impact-parameter dependence, in channels where the magnetic quantum number remains unchanged. It is well established that H$_2^+$ acts as a molecular double-slit in scattering processes. By demodulating the Young's double-slit-type interference pattern, we extracted the individual slit diffraction pattern of H$_2^+$ and compared it with that of the H$^+$ atomic single-slit. For ground state electron capture, we found that the single and the double slit diffraction patterns have equal fringe width, whereas for excited state electron capture, diffraction patterns are quite different.

Figures (4)

• Figure 1: Density plot of Q-value with scattering angle for 7.5 keV/u projectiles. Panel (a) presents spectrum for $\mathrm{H_2^+}$ and (b) presents spectrum for $\mathrm{H^+}$.
• Figure 2: Measured state selective differential cross-sections along with theoretical predictions. Panels (a) and (b) present results for electron capture to the ground state of $\mathrm{H_2}$ and H, respectively. Panels (c), (d) present the results for electron capture to the excited electronic states of the same projectiles. The experimental data are represented in black solid square, the TC-AOCC results in a solid red curve, the SCASCC results in a blue dashed curve, CTMC simulation results in purple dotted curves. Results derived from our toy model for the ground state electron capture are plotted in panels (a) and (b) in a light green short dashed curve with a little offset for better visibility. The orientation averaged state selective double-slit interference patterns for $\mathrm{H_2^+}$ projectile are plotted in dark cyan dash-double-dotted curves for inter-nuclear separation of 2 a.u., in panels (a) and (c). Error bars in the experimental data are statistical in nature ($\sqrt{n}$).
• Figure 3: Impact parameter dependent probability of electron capture to the ground state. Panel (a) presents results for 7.5 keV H$^+$ and (b) presents 15 keV H$_2^+$ results. The TC-AOCC, SCASCC, and CTMC results are represented by red solid, blue dashed, and purple dotted curves, respectively. The toy model estimations are represented by a green short-dashed curve.
• Figure 4: Imaginary Fraunhofer screen evaluated by toy model. In the $\mathrm{H^+}$ projectile rest frame, the origin coincides with the $\mathrm{H^+}$ position. In the $\mathrm{H_2^+}$ projectile rest frame origin is taken as the center of mass of $\mathrm{H_2^+}$. Panel (a) depicts the coordinate system in $\mathrm{H_2^+}$ rest frame. Panel (b) presents 2d screen for $\mathrm{H^+}$ projectile. Panels (c), (d), (e) presents 2d screen for the $\mathrm{H_2^+}$ projectile at three different orientations during collision. Molecular axis was at an angle $\theta_P$ with respect to relative velocity $\mathrm{\boldsymbol{v_0}}$. Color bar represents relative probability amplitude $|\mathcal{\tilde{A}}(\boldsymbol{B})|$.