A spectrum of Sn in the region around 135 Å arises from transitions in Sn ions with the 4d electrons in the ground configuration. Because of the very complex structure of these transitions, the spectrum is largely unknown. Only four lines were identified in Sn XIV, where the ground configuration is 4p64d. We made calculations of the energy levels and transition probabilities in the Sn VI–XV spectra using the Flexible Atomic Code (FAC). Some results of similar calculations made with the aid of the Cowan code also can be found in Chapter 5. The spectrum of Sn excited in a low-inductance vacuum spark was recorded on a high-resolution grazing-incidence spectrograph in the region 100–200 Å and compared with the results of the calculations. Due to the large uncertainty of the calculations, the straightforward identification of the experimental spectrum is impossible; but some general features can be traced.
4.2 Theoretical Approach
The FAC authored by Ming Feng Gu has been chosen for the calculations of energy levels and transition probabilities of Sn ions. The FAC is a publicly available complete software package for the computation of various atomic data. The choice was caused by the following advantages of the FAC:
• It combines the strengths of existing atomic codes [CIV3, SUPERSTRUCTURE, multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Fock (MCDF) codes, and the HULLAC package] with modifications to numerical procedures made to extend the capability and improve the efficiency and robustness.
• It has a uniform, flexible, and easy-to-use user interface for accessing all computational tasks and performing bulk-scale calculations.
• A fully relativistic approach based on the Dirac equation is used throughout the entire package, which allows its application to ions with large nuclear charge.
The bound states of the atomic system are calculated in the configuration-mixing approximation with convenient specification of mixing schemes; the radial orbitals for the construction of the basis states are derived from a modified self-consistent Dirac-Fock-Slater iteration on a fictitious mean configuration with fractional occupation numbers, representing the average electron cloud of the configurations included in the calculation.
The mean configuration in the construction of the potential is used in order to take into account the screening of more than one configuration involved in the physical processes to be calculated. This mean configuration is usually obtained by distributing the active electrons in the initial and final states. Therefore, the potential obtained is not optimized to a single configuration; rather, it is a compromise to accommodate different configurations. To reduce the error of level energies due to the use of this less than optimized potential, a special correction procedure is applied. Before the potential for the mean configuration is calculated, an optimized potential for each configuration is obtained, and the average energy of the configuration using this potential is calculated. The average energy of each configuration is then recalculated using the potential optimized for the mean configuration. The difference of the two average energies is then applied as a correction to the states within that configuration after the Hamiltonian is diagonalized.
The radiative transition rates are calculated in the single-multipole approximation. This means that the interference between different multipoles is not taken into account, although rates corresponding to arbitrary multipoles can be calculated.