School of Chemistry, The University of Manchester, Manchester M13 9PL, England.
J Chem Phys. 2012 Jan 28;136(4):044315. doi: 10.1063/1.3677229.
We make the first application of semiclassical (SC) techniques to the plane-wavepacket formulation of time-domain (T-domain) scattering. The angular scattering of the state-to-state reaction, H + D(2)(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D, is analysed, where v and j are vibrational and rotational quantum numbers, respectively. It is proved that the forward-angle scattering in the T-domain, which arises from a delayed mechanism, is an example of a glory. The SC techniques used in the T-domain are: An integral transitional approximation, a semiclassical transitional approximation, a uniform semiclassical approximation (USA), a primitive semiclassical approximation and a classical semiclassical approximation. Nearside-farside (NF) scattering theory is also employed, both partial wave and SC, since a NF analysis provides valuable insights into oscillatory structures present in the full scattering pattern. In addition, we incorporate techniques into the SC theory called "one linear fit" and "two linear fits", which allow the derivative of the quantum deflection function, Θ̃(')(J), to be estimated when Θ̃J exhibits undulations as a function of J, the total angular momentum variable. The input to our SC analyses is numerical scattering (S) matrix data, calculated from accurate quantum collisional calculations for the Boothroyd-Keogh-Martin-Peterson potential energy surface No. 2, in the energy domain (E-domain), from which accurate S matrix elements in the T-domain are generated. In the E-domain, we introduce a new technique, called "T-to-E domain SC analysis." It half-Fourier transforms the E-domain accurate quantum scattering amplitude to the T-domain, where we carry out a SC analysis; this is followed by an inverse half-Fourier transform of the T-domain SC scattering amplitude back to the E-domain. We demonstrate that T-to-E USA differential cross sections (DCSs) agree well with exact quantum DCSs at forward angles, for energies where a direct USA analysis in the E-domain fails.
我们首次将半经典（SC）技术应用于时域（T 域）散射的平面波包公式。分析了态态反应 H + D(2)(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D 的角散射，其中 v 和 j 分别是振动和转动量子数。证明了 T 域中源于延迟机制的前向角散射是一种耀斑的例子。在 T 域中使用的 SC 技术包括：积分跃迁逼近、半经典跃迁逼近、均匀半经典逼近（USA）、原始半经典逼近和经典半经典逼近。还采用了近-远侧（NF）散射理论，包括部分波和 SC，因为 NF 分析提供了对全散射模式中存在的振荡结构的有价值的见解。此外，我们将“一次线性拟合”和“两次线性拟合”等技术纳入 SC 理论中，当量子偏转角函数Θ̃(')(J)作为 J 的函数表现出波动时，允许估计Θ̃J，其中 J 是总角动量变量。我们的 SC 分析的输入是从 Boothroyd-Keogh-Martin-Peterson 势能面 No.2 的精确量子碰撞计算在能量域（E 域）中计算得到的数值散射（S）矩阵数据，从中生成 T 域中的精确 S 矩阵元素。在 E 域中，我们引入了一种称为“T 到 E 域 SC 分析”的新技术。它对半傅里叶变换 E 域中准确的量子散射振幅到 T 域，在那里我们进行 SC 分析；然后将 T 域 SC 散射振幅的逆半傅里叶变换回 E 域。我们证明，对于直接 USA 分析在 E 域中失败的能量，T 到 E USA 微分截面（DCS）在前沿角度与精确量子 DCS 吻合良好。
