A Novel Method to Determine Magnetic Fields in low-density Plasma e.g. Solar Flares Facilitated Through Accidental Degeneracy of Quantum States in Fe$^{9+}$

We propose a new method to determine magnetic fields, by using the magnetic-field induced electric dipole transition $3p^43d\,^4\mathrm{D}_{7/2}$ $\rightarrow$ $3p^5\, ^2\mathrm{P}_{3/2}$ in Fe$^{9+}$ ions. This ion has a high abundance in astrophysical plasma and is therefore well-suited for direct measurements of even rather weak fields in e.g. solar flares. This transition is induced by an external magnetic field and its rate is proportional to the square of the magnetic field strength. We present theoretical values for what we will label the reduced rate and propose that the critical energy difference between the upper level in this transition and the close to degenerate $3p^43d\, ^4\mathrm{D}_{5/2}$ should be measured experimentally since it is required to determine the relative intensity of this magnetic line for different magnetic fields.

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