Total collision cross-section conservation

Now encounters between molecules, or between a molecule and the wall are accompanied by momentuin transfer. Thus if the wall acts as a diffuse reflector, molecules colliding wlch it lose all their axial momentum on average, so such encounters directly change the axial momentum of each species. In an intermolecuLar collision there is a lateral transfer of momentum to a different location in the cross-section, but there is also a net change in total momentum for species r if the molecule encountered belongs to a different species. Furthermore, chough the total momentum of a particular species is conserved in collisions between pairs of molecules of this same species, the successive lateral transfers of momentum associated with a sequence of collisions may terminate in momentum transfer to the wall. Thus there are three mechanisms by which a given species may lose momentum in the axial direction ... 

The integration of this set of coupled first-order differential equation can be done in a number of ways. Care must be taken since there are basically rather two different time scales involved, i.e. that of the nuclear dynamics and that of the normally considerably faster electron dynamics. It should be observed that this END takes place in a Cartesian laboratory reference frame, which means that the overall translation as well as overall rotation of the molecular system is included. This offers no complications since the equations of motion satisfy basic conservation laws and, thus, total momentum and angular momentum are conserved. At any time in the evolution of the molecular system can the overall translation be isolated and eliminated if so should be deemed necessary. This level of theory [16,19] is implemented in the program system ENDyne [20], and has been applied to atomic and molecular reactive collisions. Calculations of cross sections, differential as well as integral, yield results in excellent agreement with the best experiments. 

Above we discussed various types of collisions. A reverse process corresponds to each of these processes. Cross sections and rate constants of forward and reverse elementary processes are mutually related. This relationship is determined by the laws of conservation of energy and total angular moment. 

The experimentalist interested in reaction dynamics dreams of the day when it will be possible to select all, or nearly all, of the initial parameters for potentially reactive collisions and, at the same time, observe the products scattered at particular angles as a function of their quantum states. (In this ideal experiment, the distribution of final relative velocities could be obtained through the equation of energy conservation, since the total energy will be defined and the distribution of final internal energies will be measured.) These experiments would yield detailed (or state-to-state) differential cross sections. Of course, the reaction dynamicists millenium, like most others, is some way off and, until such time as this dream is fulfilled, we only have the... 

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