José Paulo Santos

The theory of domain decomposition is described and used to divide the variable domain of a diatomic molecule into separate regions which are solved independently. This approach makes it possible to use fast Krylov methods in the broad interior of the region while using explicit methods such as Gaussian elimination on the boundaries. As is demonstrated by solving a number of model problems, these methods enable one to obtain solutions of the relevant partial differential equations and eigenvalue equations accurate to six significant figures with a small amount of computational time. Since the numerical approach described in this article decomposes the variable space into separate regions where the equations are solved independently, our approach is very well-suited to parallel computing and offers the long term possibility of studying complex molecules by dividing them into smaller fragments that are calculated separately.

Following our previous study on spin–rotation and shielding constants of the SF6 molecule, the rotational g factor and the magnetic susceptibility are calculated here, using ab initio methods to evaluate the electronic contribution to the nuclear hyperfine constants, and compared with experimental results. It is shown, for the first time, that the electronic component of the rotational g factor is proportional to a constant, which is given by a sum over electronic states. We also evaluate for the SF6 molecule the indirect, or electron-coupled spin–spin interaction, theoretically described by Ramsey, and show that it gives non-negligible corrections to direct coupling constants d1 and d2. The contributions of the terms included in this interaction (DSO, PSO, SD and FC) are also analysed.

Following our previous study on spin–rotation and shielding constants of the SF6 molecule, the rotational g factor and the magnetic susceptibility are calculated here, using ab initio methods to evaluate the electronic contribution to the nuclear hyperfine constants, and compared with experimental results. It is shown, for the first time, that the electronic component of the rotational g factor is proportional to a constant, which is given by a sum over electronic states. We also evaluate for the SF6 molecule the indirect, or electron-coupled spin–spin interaction, theoretically described by Ramsey, and show that it gives non-negligible corrections to direct coupling constants d1 and d2. The contributions of the terms included in this interaction (DSO, PSO, SD and FC) are also analysed.

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A new expression for the total K-shell ionization cross section by electron impact based on the rela- tivistic extension of the binary encounter Bethe (RBEB) model, valid from ionization threshold up to relativistic energies, is proposed. The new MRBEB expression is used to calculate the K-shell ionization cross sections by electron impact for the selenium atom. Comparison with all, to our knowledge, available experimental data shows good agreement.

A new expression for the total K-shell ionization cross section by electron impact based on the rela- tivistic extension of the binary encounter Bethe (RBEB) model, valid from ionization threshold up to relativistic energies, is proposed. The new MRBEB expression is used to calculate the K-shell ionization cross sections by electron impact for the selenium atom. Comparison with all, to our knowledge, available experimental data shows good agreement.

Two-photon decay of hydrogenlike ions is studied within the framework of second-order perturbation theory, based on the relativistic Dirac's equation. Special attention is paid to the effects arising from the summation over the negative-energy (intermediate virtual) states that occur in such a framework. In order to investigate the role of these states, detailed calculations have been carried out for the 2s1/2–>1s1/2 and 2p1/2–>1s1/2 transitions in neutral hydrogen H as well as for hydrogenlike xenon Xe53+ and uranium U91+ ions. We found that for a correct evaluation of the total and energy-differential decay rates, summation over the negative-energy part of Dirac's spectrum should be properly taken into account both for high-Z and low-Z atomic systems.

Two-photon decay of hydrogenlike ions is studied within the framework of second-order perturbation theory, based on the relativistic Dirac's equation. Special attention is paid to the effects arising from the summation over the negative-energy (intermediate virtual) states that occur in such a framework. In order to investigate the role of these states, detailed calculations have been carried out for the 2s1/2-->1s1/2 and 2p1/2-->1s1/2 transitions in neutral hydrogen H as well as for hydrogenlike xenon Xe53+ and uranium U91+ ions. We found that for a correct evaluation of the total and energy-differential decay rates, summation over the negative-energy part of Dirac's spectrum should be properly taken into account both for high-Z and low-Z atomic systems.