Study of the Zeeman Structure and the Gyromagnetic Ratios of the 2p4f and 3p4f Configurations of the Carbon and Silicon Atoms

摘要

The present article is a continuation of the authors works devoted to the theoretical study of the fine structure parameters, and other atom characteristics, for which there are no experimental data except for energies of levels of the fine structure. The authors have studied Zeeman structure of the 2p4f and 3p4f configurations and revealed its particular features — crossings and anticrossings of the magnetic sublevels. From splittings of levels in the assured linear range, the authors have calculated gyromagnetic ratios and compared them with their counterparts in the absence of the field. The study of the Zeeman structure is interesting in its own right. Furthermore, through Zeeman splitting in the linear domain of the magnetic field, one can determine the gyromagnetic ratios -- one of the most important characteristics of the atoms. Calculation of the Zeeman structure is correct, if in the absence of the field, during the diagonalisation of the energy operator matrix, one obtains the calculated energies, practically coinciding with experimental values (zero energy residuals). To this effect it is necessary to know the numerical values of fine structure parameters. Their exact calculation is possible, if in the energy operator matrix one takes into account not only the electrostatic interaction and the spin-own orbit interaction, where the majority of authors are limited, but also the magnetic interactions, namely: spin-other-orbit, spin-spin, and also the orbit-orbit interactions. Consideration of these interactions is very important for the obtaining null residuals in energy. It is known that, by increasing the role of the magnetic interactions, a deviation from LS-coupling is observed. This is realize in the studied 2p4f C I and 3p4f Si I systems. Authors executed calculations in the jK-coupling approximation taking into account the doublet character of the energy spectra of the considered systems. Later the numerical value of fine structure parameters were introduced in the energy operator matrix; written in the LK and LS-coupling approximations. This was very useful, as gyromagnetic ratios, calculated by intermediate coupling coefficients in different basis, do not always coincide with each other. The comparison of g-factors, determined by different bases in the absence of the field, with the gyromagnetic ratios, calculated by Zeeman splitting was necessary.