Jambrina P G, Menéndez M, Aoiz F J
Departamento de Química Física Aplicada , Universidad Autonoma de Madrid , 28049 , Madrid , Spain . Email:
Departamento de Química Física I , Facultad de Ciencias Químicas , Universidad Complutense de Madrid , 28040 Madrid , Spain . Email:
Chem Sci. 2018 Apr 26;9(21):4837-4850. doi: 10.1039/c7sc05489k. eCollection 2018 Jun 7.
A natural generalization of the classical deflection function, the functional dependence of the deflection angle on the angular momentum (or the impact parameter), is the joint probability density function of these two quantities, revealing the correlation between them. It provides, at a glance, detailed information about the reaction mechanisms and how changes in the impact parameter affect the product angular distribution. It is also useful to predict the presence of quantum phenomena such as interference. However, the classical angular momentum-scattering angle correlation function has a limited use whenever quantum effects become important. Rigorously speaking, there is not a quantum equivalent of the classical joint distribution, as the differential cross section depends on the coherences between the different values of caused by the cross terms in the expansion of partial waves. In this article, we present a simple method to calculate a quantum analog of this correlation, a generalized deflection function that can shed light onto the reaction mechanism using just quantum mechanical results. Our results show that there is a very good agreement between the quantum and classical correlation functions as long as quantum effects are not all relevant. When this is not the case, it will also be shown that the quantum correlation function is most useful to observe the extent of quantum effects such as interference among different reaction mechanisms.
作为经典偏折函数的自然推广，偏转角与角动量（或碰撞参数）的函数依赖关系，是这两个量的联合概率密度函数，揭示了它们之间的相关性。它一眼就能提供有关反应机制以及碰撞参数的变化如何影响产物角分布的详细信息。它对于预测诸如干涉等量子现象的存在也很有用。然而，只要量子效应变得重要，经典角动量 - 散射角关联函数的用途就有限。严格地说，不存在与经典联合分布等效的量子形式，因为微分截面取决于由分波展开中的交叉项引起的不同值之间的相干性。在本文中，我们提出了一种简单的方法来计算这种关联的量子类似物，即一种广义偏折函数，它仅使用量子力学结果就能阐明反应机制。我们的结果表明，只要量子效应并非都很重要，量子关联函数与经典关联函数之间就有非常好的一致性。当情况并非如此时，还将表明量子关联函数对于观察不同反应机制之间的干涉等量子效应的程度最为有用。
