A quantum analogue to the defection function

Abstract

The classical deflection function is a valuable computational tool to investigate reaction mechanisms. It provides, at a glance, detailed information about how the reaction is affected by changes in reactant properties (impact parameter) and products properties (scattering angle), and, more importantly, it also shows how they are correlated. It is also useful to predict the presence of quantum phenomena such as interferences. However, rigorously speaking, there is not a quantum analogue as the differential cross section depends on the coherences between the different values of $J$ caused by the cross terms in the expansion of partial waves. Therefore, the classical deflection function has a limited use whenever quantum effects become important. In this article, we present a method to calculate a quantum deflection function that can shed light onto reaction mechanism using just quantum mechanical results. Our results show that there is a very good agreement between the quantum and classical deflection function as long as quantum effects are not all relevant. When this is not the case, it will be also shown that the quantum deflection function is most useful to observe the extent of quantum effects such as interferences. The present results are compared with other proposed quantum deflection functions, and the advantages and disadvantages of the different formulations will be discussed.