Excitation of the 3.071mm Hyperfine Line in Li-Like 57-Fe in Astrophysical Plasmas

As noted first by Sunyaev & Churazov (1984), the 3.071 mm hyperfine line from $^{57}Fe^{+23}$ might be observable in astrophysical plasmas. We assess the atomic processes which might contribute to the excitation of this line. We determine the intensity of the hyperfine line from an isothermal, coronal plasma in collisional ionization equilibrium and for a coronal plasma cooling isobarically due to its own radiation. Comparisons of the hyperfine line to other lines emitted by the same ion, Fe$^{+23}$, are shown to be useful for deriving the isotopic fraction of $^{57}$Fe. We calculate the ratios of the hyperfine line to the 2s--2p EUV lines at 192 \AA and 255 \AA, and the 2s--3p X-ray doublet at 10.6 \AA.