Annihilation on specific molecular sites

Measurements of the Doppler broadening of the annihilation radiation produced by various molecules has been related to annihilation at specific sites within molecules by Iwata, et al. [15]. Prom the observed 7-ray spectra, the line width of the dominate peak, which comes from valence electrons, was extracted. Thus, for each molecule there is a single measured quantity, the fine width. For a series of hydrocarbons, the observed fine widths were found to be linear in the fraction of electrons in C-C (or C-H) bonds. Each type of bond was assumed to contain two electrons. Prom a linear fit of this data, fine widths for the C-C and C-H bonds were extracted and found to be 2.06 and 2.42 keV, respectively. These agree reasonably with an old theoretical estimate in which the positron density was assumed to be constant over the molecule [16].  

Next these authors measured line widths for a series of fluorohydrocar-bons, CnH,Fm. The 7-ray spectrum for each was analyzed into components from the hydrogen and fluorine analogs, CnH +ro and CnF +m. The relative weight of the C F +m component was interpreted to be the fraction of annihilation on fluorine in C F +m. This fraction was then normalized by the fraction of valence electrons on F (assumed to be 8) in the molecule to account for annihilation in the C-C bond. The normalized fractions of annihilation on F for a large number of fluorohydrocarbons was found to be equal to the fraction of valence electrons on F in each molecule, to a good approximation. The conclusion of these authors is that annihilation in these molecules takes place with equal probability on any valence electron regardless of what atom it resides on. This is counterintuitive. 

The data analysis chosen by these authors departs from that used by Mogensen and others [17, 18], who fit each ID angular correlation curve to a set of Gaussian functions. The minimum number of Gaussians is used to achieve a good fit, and the width of each is optimized. The momentum components of each 7-ray spectrum are then interpreted in terms of annihilation of core vs. valence electrons without appeal to a preconceived chemical model. The experiment-theory connection can be made if one has an adequate wave function in hand, for then the Doppler profiles or angular correlation curves can be calculated and compared to those measured. 

use a model in which the electrons are assigned to categories, some of which are bond-related (C-C and C-H) and others, atomic (F). Assignment of electrons to various parts of a molecule is a very old practice in chemistry [19], but one that contains some unavoidable arbitrariness. One wonders whether the authors conclusion would stand if the interpretation of the data were more rigorous quantum mechanically. 

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