Li-like ions

The values of F are given at Z = 10 -110, nlj = s,2s,2,2 These results are here modified for the 7/ nlj states of Li-like ions. It is assumed that for any ion with an nlj electron over the core of closed shells the searched value may be presented in the form ... 

The parameters X, X, X2,X are determined hy four especially chosen reference points. The energies of the states of Li-like ions were calculated twice with the real value of the fine structure constant a = 1/137 and with the smaller value a = a/lOOO. The results of these latter calculations were considered as non-relativistic. This helped the isolation of Ej and. A detailed evaluation of their accuracy may be made only after a complete calculation of Z,nlj). It may be stated that the above extrapolation... 

TABLE 2. QED corrections (in cm ) to the energy of Li-like ions in linlj- states. 

Detailed analysis of the VP and SE energy eontributions shows that for ions with small Z the QED eontribution is not signifieant, but with growth of Z (Z > 40) the QED contribution becomes very important. Moreover, for heavy and superheavy ions its role is of main importance. Now let us consider the role of the nuelear finite-size effeet. As calculations show, for multicharged ions with Z < 20 its contribution is very small, but for ions with Z > 70 it can equal the vacuum polarization contribution. In Table 3 there are displayed the results of calculations for the nuelear eorrection to the energy of low transitions for Li-like ions. Our calculations also show that a variation of the nuelear radius by a... 

TABLE 3. Nuclear finite-size correction to the energy (in cm ) for the low transitions of Li-like ions, and values of the effective nuclear radius (in 10 cm). 

We have also performed the calculation of hyperfine coupling constants the electric quadrupole constant B and magnetic dipole constant A, with inclusion of nuclear finiteness and the Uehling potential for Li-like ions. Analogous calculations of the constant A for ns states of hydrogen-, lithium- and sodiumlike ions were made in refs [11, 22]. In those papers other bases were used for the relativistic orbitals, another model was adopted for the charge distribution in the nuclei, and another method of numerical calculation was used for the Uehling potential. 

In Tables 5 and 6 there are displayed the results for the hyperfine coupling constants in the lowest excited states of Li-like ions. In Table 5 we compare the results of our calculations with those from papers [11, 22] for magnetic dipole coupling constants in the ground state ls 2s of a few lithium-like ions. 

The methods described in Sect. 3 for the calculation of accurate nonrelativistic wave functions and energies can in principle be applied to more complex atoms and molecules. The principal difficulties are that the number of terms required in the basis set to reach a given level of accuracy grows extremely rapidly with the number of particles, and the correlated integrals become much more difficult to evaluate. Only in the case of lithium (and Li-like ions) have results of spectroscopic accuracy been obtained (see Ref. [69] for a review). However, the demand on computer resources increases by about a factor of 6000 to reach the same level of accuracy. 

The information on the relative abundances of ionization stages is found by detailed modeling of the spectra. The density of Li-like ions is obtained from the intensity of doubly excited satellites, which are predominately populated by collisional inner-shell excitation with small contributions of dielec-... 

The k and j satellites are the strongest dielectronic satellites to the He-like lines, the q, r, s and t satellites have strong contributions due to inner-shell excitation from the Li-like ground state. Besides the dominant collisional excitation of He-like ions in the ground state, recombination processes (radiative, dielectronic and charge exchange) of H- and He-like ions, inner-shell excitation of the Li-like ions and, in the case of the z line, also inner-shell ionization process contribute to the intensity of the He-like lines. We will discuss these processes in detail. 

Inner-shell excitation of the Li-like ion core is the second mechanism to populate the doubly excited levels. For the three electron system, the cascade effect between doubly excited levels is negligible compared to dielectronic recombination. This is justified by the fact that for highly charged ions the states with higher n, n > 3, have large initial populations, so therefore the contribution due to the cascade is negligible. The emission of the satellite line is then ... 

In addition, inner-shell ionization contributes to the intensity of the z line. The removal of an inner-shell electron leads directly to the ls2s excited level of the He-like system. The contribution of this process is proportional to the concentration of the Li-like ions and should be taken into account at low electron temperatures or if the charge state distribution differs from ionization equilibrium. 

The determination of plasma parameters using He-like spectra is based on a self-consistent modeling of the theoretical spectra. The following variables take part in the variation procedure based on least-squares fitting electron and ion temperatures, toroidal plasma velocity, concentrations of H-, He-and Li-like ions. In addition, a background function was used to subtract the plasma background from the experimental spectra. The background consists of continuum radiation from the plasma and detector noise. 

Fig. 8.3. (a) Radial profiles of argon density in TEXTOR point line H-like, dashed line He-like solid line Li-like ions. Emissivity profiles of the different argon stages presented in (b) point line H-like, dashed line He-like, solid line Li-like ions... 

In contrast to the density measurements of Li-like ions by means of inner-shell excitation, the spectra provide information not directly on the density... 

The authors are glad to thank many scientists, who have contributed to the results. The TEXTOR team, where the measurements were performed and highly reproducible plasmas were provided, especially to Dr. W. Biel, who did the experiments on the transport properties of TEXTOR, Prof. L. Vainshtein, Dr. A. Urnov and F. Goryaev provided us with the results of atomic data calculation. Dr. N. Badnell trained one of us (O. M.) to get the results on dielectronic recombination using atomic codes. Dr. S. Fritzsche put our attention to the cascades within the Li-like ions and Prof. R. Janev discussed the charge exchange recombination processes. Princeton Plasma Physics Laboratory supported the measurements on TEXTOR, both by cooperation with Dr. M. Bitter, and loan of X-ray detectors. 

State selective dielectronic recombination rate coefficients from Li-like ions to Be-like ions (C, O, Ne, Fe ions) and for carbon L-shell ions have been calculated [10-13]. These data are used to develop collisional-radiative models including dielectronic recombination to excited states [14-17]. The population kinetics of L-shell ions and atoms have been developed and their results have been applied to plasma diagnostics. 

In Table 10, RCI [76] and MBPT [85] energies on the 2s—2pi/2 and Is — lpoji transitions in Li-like ions are compared with experiment. For these low- to imd-Z ions, higher-order Breit corrections are quite negligible and RCI and MBPT are in very good agreement... 

Table 4.6 compares the Bethe logarithms for the two lowest S-states of lithium with those for fhe Li-like ions Li+(ls S) and Li++(ls S). The comparison emphasizes again thaf fhe Befhe logarithm is determined almost entirely by the hydro-genic value for fhe Is elecfron, and is almosf independenf of fhe sfafe of excifation of the outer electrons, or the degree of ionization. 

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