Proposal for observation of transitions induced by external magnetic fields mixing in the lower states: With an example from Fe X

It is normally assumed that induced transitions, by e.g. hyperfine, magnetic field or spin interaction, arise due to mixing in the upper levels. In this paper we discuss an example when mixing in the lower levels through an externally applied magnetic field gives rise to a magnetic field induced transition. We discuss the theory for such a transition and give an example from Fe X, which is relevant for the determination of the magnetic field of the solar corona. To make this possible, it is important to determine the energy difference between the 3p ⁴3d ⁴ D _5/2 and ⁴ D _7/2, which are accidentally very close in energy in Fe X. The splitting of these levels is expected to be around 3.5 cm^-1 whereas their excitation energies are about 388 709 cm^-1. We discuss how this fine structure can be determined, by observing transitions from levels that decay into this pair which have a longer wavelength than the resonance transition. Finally we discuss an experimental scenario based on an electron beam ion trap and a Fabry-Perot interferometer, to perform the measurement of this interval.