Abstract. Multiconfiguration wave function expansions combined with configuration interaction methods are a method of choice for complex atoms where atomic state functions are expanded in a basis of configuration state functions. Combined with a variational method such as the multiconfiguration Hartree-Fock (MCHF) or multiconfiguration Dirac-Hartree-Fock (MCDHF), the associated set of radial functions can be optimized for the levels of interest. The present review updates the variational MCHF theory to include MCDHF, describes the multireference single and double (MRSD) process for generating expansions and the systematic procedure of a computational scheme for monitoring convergence. It focuses on the calculations of energies and wave functions from which other atomic properties can be predicted such as transition rates, hyperfine structures and isotope shifts, for example.PACS numbers: 31. 31.15ag, 32.70.Cs

The J \ 0 ] J@ \ 0 radiative transitions, usually viewed as allowed through two-photon decay, may also be induced by the hyperÐne (HPF) interaction in atoms or ions having a nonzero nuclear spin. We compute new and review existing decay rates for the transitions in ions of the Be nsnp 3PJ o ] ns2 1S J{/0 (n \ 2) and Mg (n \ 3) isoelectronic sequences. The HPF induced decay rates for the J \ 0 ] J@ \ 0 transitions are many orders of magnitude larger than those for the competing two-photon processes, and when present are typically 1 or 2 orders of magnitude smaller than the decay rates of the magnetic quadrupole (J \ 2 ] J@ \ 0) transitions for these ions. Several HPF induced transitions are potentially of astrophysical interest in ions of C, N, Na, Mg, Al, Si, K, Cr, Fe, and Ni. We highlight those cases that may be of particular diagnostic value for determining isotopic abundance ratios and/or electron densities from UV or EUV emission-line data. We present our atomic data in the form of scaling laws so that, given the isotopic nuclear spin and magnetic moment, a simple expression yields estimates for HPF induced decay rates. We examine some UV and EUV solar and nebular data in light of these new results and suggest possible applications for future study. We could not Ðnd evidence for the existence of HPF induced lines in the spectra we examined, but we demonstrate that existing data have come close to providing interesting upper limits. For the planetary nebula SMC N2, we derive an upper limit of 0.1 for 13C/12C from Goddard High-Resolution Spectrograph data obtained by Clegg. It is likely that more stringent limits could be obtained using newer data with higher sensitivities in a variety of objects.

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The present work illustrates the potential of a new diagnostic technique that allows the measurement of the coronal magnetic field strength in solar active regions by utilizing a handful of bright Fe x and Fe xi lines commonly observed by the high-resolution Hinode/EUV Imaging Spectrometer (EIS). The importance of this new diagnostic technique is twofold: (1) the coronal magnetic field is probably the most important quantity in coronal physics, being at the heart of the processes regulating space weather and the properties of the solar corona, and (2) this technique can be applied to the existing EIS archive spanning from 2007 to 2020, including more than one full solar cycle and covering a large number of active regions, flares, and even coronal mass ejections. This new diagnostic technique opens the door to a whole new field of studies, complementing the magnetic field measurements from the upcoming DKIST and UCoMP ground-based observatories, and extending our reach to active regions observed on the disk and until now only sampled by radio measurements. In this work, we present a few examples of the application of this technique to EIS observations taken at different times during the EIS mission, and we discuss its current limitations and the steps to improve its accuracy. We also present a list of EIS observing sequences whose data include all of the lines necessary for the application of this diagnostic technique, to help the solar community navigate the immense set of EIS data and to find observations suitable for measuring the coronal magnetic field.