Average translational energy release

Average Translational Energy Release as a Function of Cluster Size... 

According to the modified prior distribution, the average translational energy release in a dissociation is given by a two-dimensional Boltzmann distribution. Thus the average translational energy release [see Eq. (9.17)] is ... 

Fig. 30. Contour plot of photoelectron-photodissociation coincidence spectrum as a distribution of photoelectron intensity (dark shade = low, light shade = high) against the electron binding energy and relative translational energy of the photofragments. Also shown on the left and at the bottom are the partially averaged distributions for the translational energy release and the electron binding energy, respectively.

This result is very different from the modified prior distribution (chapter 9). It implies that the average kinetic energy release is given by 2k T, that is, a four-dimensional translational energy distribution. When the expression for = [(s — l)/2]( ,) is substituted into Eq. (10.34), and the latter equation solved for , we finally obtain... 

The translational energy distribution of the product ion in the source (laboratory distribution) is still not what is needed. What is required is the distribution of energy released in the centre-of-mass framework. The conversion of the translational energy distribution in the laboratory framework to the energy release distribution in the centre-of-mass is not a simple exercise [723]. If mean or average energies are considered, however, an expression for conversion from laboratory to centre-of-mass coordinates can be written down [311]. 

A convenient method for deriving the dissociation rate is based on Fermi s Golden rule. Approximations inherent in this approach are similar to those required to separate (adiabatically via averaged interactions) the diatom and the van der Waals motions. The two states of interest are the excited complex in which the diatom has been excited to v = 1, and the final dissociated state in which the diatom is back in the ground state (v" = 0) with the energy released as translational (or rotational) energy. Within the approximation of separable motions, the system wave function in these two states are... 

Besides angular momentum and the total kinetic energy release, PST can also be used to evaluate the distribution and average of the purely translational part of the KER. This quantity is important because it can be experimentally measured by velocity map imaging. The spectrum of translational kinetic energy is sensitive to the interaction between the products, but also to their shape. In addition, its connection with the internal temperature of the products make it a valuable thermodynamic indicator from which phase transitions can be probed. 

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