Correction terms highly charged ions

The electron-electron interaction is usually supposed to be well described by the instantaneous Coulomb interaction operator l/rn. Also, all interactions with the nuclei whose internal structure is not resolved, like electron-nucleus attraction and nucleus-nucleus repulsion, are supposed to be of this type. Of course, corrections to these approximations become important in certain cases where a high accuracy is sought, especially in computing the term values and transition probabilities of atomic spectroscopy. For example, the Breit correction to the electron-electron Coulomb interaction should not be neglected in fine-structure calculations and in the case of highly charged ions. However, in general, and particularly for standard chemical purposes, these corrections become less important. 

Finally we present results of SE and VP calculations for ns valence electrons in heavy and superheavy atoms with n up to 8 and Z up to 119 [13], [14]. For the calculation of the SE contribution the PWR approach described in Sec.4.2 based on the multiple commutator expansion [71] was used. The corrections are given in Table 1. Since the B-spline approach requires the employment of the local potential, the local approximation to the DHF potential obtained by the direct parametrization [77] was used. The VP contribution was treated in the Uehling approximation. One can expect that the Uehling term will suffice not only for highly charged ions but in screened systems as well. The Uehling potential was corrected for the extended nucleus [78] - [80]. The Uehling potential for the point-like nucleus (233) was replaced by the expression ... 

For many electron systems, QED corrections must also include many-body contributions. For the time being only a limited number of results, besides semi-empirical extrapolations, are available for heavy elements where a perturbative Za approach (in terms of the electron nucleus interaction) is irrelevant. The reason is not only that the most precise numerical methods developed for the one-electron contributions [34] encounter serious numerical accuracy problems for high angular momentum values but also that, even for two-electron atoms or ions, the standard QED prescription [35] is unable to deal with quasi-degenerate levels. Recent developments [36-37] open new perspectives for getting accurate estimates in two-electron systems without any restriction on the nuclear charge. 

The main goal of data treatment in conventional mass spectrometry (MS) is to facilitate identification and quantification of analytes. The focus of time-resolved mass spectrometry (TRMS) is to track variations of identities and quantities of analytes and products over time. In many chemical reactions, the concentrations of reactants decrease and those of products increase with time. In more complex reactions, reaction intermediates exist and their concentrations may increase and decrease within certain periods of time. The evolution of reaction intermediates is distinct from that of reactants and products. TRMS provides an insight into the progress of reactions by identifying molecules based on their mass-to-charge (m/z) ratios. It also determines concentrations of molecules based on signal intensities of ions. Thus, it is important for TRMS to interpret MS data on highly complex and dynamic systems correctly. This chapter will first introduce definitions of various technical terms, and then discuss how to predict molecular compositions of complex mixtures based on the information contained in mass spectra. 

Rosene and Manes studied the effect of pH on the total adsorption from aqueous solutions of sodium benzoate + benzoic acid by activated charcoal. They interpreted their data in terms of the Polanyi potential theory applied to bisolute adsorption (see later p. 117), in which the concentrations of neutral benzoic acid and benzoate anions depend on the pH of the solution (activity coefficient corrections were ignored). They confirmed that, at constant total equilibrium concentration, the adsorption dropped from a relatively high plateau for pH <2 down to a small adsorption at pH >10. The analysis of results is somewhat more complex than with essentially non-electrolyte adsorption, and in this case there were additional effects involving chemisorption of benzoate ion by residual ash in the carbon which had, therefore, to be eliminated. Even with ash-extracted carbon there was evidence of some residual chemisorption. The theoretical analysis correlated satisfactorily with the experimental data on the basis that at pH >10 sodium benzoate is not physically adsorbed and that the effect of pH is completely accounted for by its effect on the concentration of free acid. In addition the theory explains successfully the increase in pH (called by the authors hydrolytic adsorption ) when solutions of sodium benzoate are treated with neutral carbon. However, no account is taken in this paper of the effect of pH on the surface charge of the carbon. 

---