School of Chemistry, The University of Manchester, Manchester M13 9PL, UK.
Phys Chem Chem Phys. 2011 Jul 28;13(28):12981-97. doi: 10.1039/c1cp21044k. Epub 2011 Jun 22.
State-of-the-art differential cross sections (DCSs) have been reported by Wang et al. [Proc. Nat. Acad. Sci. (U.S.), 2008, 105, 6227] for the state-to-state F + H(2)→ FH + H reaction using fully quantum-state-selected crossed molecular beams. We theoretically analyze the angular scattering of this reaction, in order to quantitatively understand the physical content of structure in the DCSs. Three transitions are studied, v(i)=0, j(i)=0, m(i)=0 → v(f)=3, j(f)=0, 1, 2, m(f)=0 at a translational energy of 0.04088 eV, where v, j, m are the vibrational, rotational and helicity quantum numbers respectively for the initial and final states. The input to our analyses consists of accurate quantum scattering (S) matrix elements computed for the Fu-Xu-Zhang potential energy surface, as used by Wang et al. in a computational simulation of their experimental DCSs. We prove that the pronounced peak at forward angles observed in the experimental and simulated DCSs for all three transitions is a glory. At larger angles, it is demonstrated that the 000 → 300 and 000 → 310 DCSs both possess a broad farside rainbow, which is accompanied by diffraction oscillations. We confirm the conjecture of Wang et al. that these diffraction oscillations arise from nearside-farside (NF) interference. We find that the reaction is N dominant for all three transitions. The theoretical techniques used to analyze the angular scattering include uniform semiclassical theories of glory and of rainbow scattering. We also make the first application of a semiclassical formula that is uniform for both glory + rainbow scattering. In addition, structure in the DCSs is analyzed using NF theory and local angular momentum theory, in both cases with three resummations of the partial wave series for the scattering amplitude. We make the first explicit application of the Thiele rational interpolation formula to extract the position and residue of the leading Regge pole from a set of S matrix elements, thereby making contact with complex angular momentum theories of DCSs, which interpret the angular scattering in terms of Regge resonances. Our calculations complement the exit-valley vibrationally-adiabatic analysis of Wang et al.
Wang 等人 [Proc. Nat. Acad. Sci. (U.S.), 2008, 105, 6227] 报道了使用完全量子态选择的交叉分子束研究 F+H(2)→FH+H 反应的最新态态微分截面 (DCS)。为了定量理解 DCS 中的结构物理内容，我们对该反应的角散射进行了理论分析。研究了三个跃迁，v(i)=0，j(i)=0，m(i)=0→v(f)=3，j(f)=0，1，2，m(f)=0 在 0.04088 eV 的平移能下，其中 v、j、m 分别为初始和最终态的振动、旋转和螺旋量子数。我们分析的输入包括由 Wang 等人在他们实验 DCS 的计算模拟中使用的 Fu-Xu-Zhang 势能表面计算的准确量子散射 (S) 矩阵元。我们证明，实验和模拟 DCS 中所有三个跃迁的前向角度处观察到的明显峰值是荣耀。在较大的角度下，证明 000→300 和 000→310 DCS 都具有广泛的远侧虹彩，伴随着衍射振荡。我们证实了 Wang 等人的猜测，即这些衍射振荡来自近侧远侧 (NF) 干涉。我们发现，对于所有三个跃迁，反应都是 N 主导的。用于分析角散射的理论技术包括荣耀和彩虹散射的统一半经典理论。我们还首次应用了适用于荣耀+彩虹散射的统一半经典公式。此外，还使用 NF 理论和局部角动量理论分析了 DCS 中的结构，在这两种情况下，散射振幅的部分波级数都进行了三次重排。我们首次明确应用 Thiele 有理插值公式从一组 S 矩阵元中提取主导 Regge 极点的位置和残差，从而与 DCS 的复角动量理论联系起来，该理论根据 Regge 共振来解释角散射。我们的计算补充了 Wang 等人的出口谷振动绝热分析。
