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Hyperfine dependent $gf$-values of Mn I lines in the 1.49 $-$ 1.80 $μ$m H-band

The three Mn I lines at 17325, 17339 and 17349 Å~are among the 25 strongest lines ($\log(gf)>0.5$) in the H-band. They are all heavily broadened due to hyperfine structure and the profiles of these lines have so far not been understood. Earlier studies of these lines even suggested that they were blended. In this work, the profiles of these three infra-red (IR) lines have been studied theoretically and compared to experimental spectra to assist in the complete understanding of the solar spectrum in the IR. It is shown that the structure of these lines can not be described in the conventional way by the diagonal $A$ and $B$ hyperfine interaction constants. The off-diagonal hyperfine interaction not only has large impact on the energies of the hyperfine levels, but also introduces a large intensity redistribution among the hyperfine lines, changing the line profiles dramatically. By performing large-scale calculations of the diagonal and off-diagonal hyperfine interaction and $gf$-values between the upper and lower hyperfine levels and using a semi-empirical fitting procedure, agreement between our synthetic and experimental spectra was achieved. Furthermore, we compare our results with observations of stellar spectra. The spectra of the Sun and the K1.5 III red giant star Arcturus were modelled in the relevant region, $1.73-1.74$ $μ$m using our theoretically predicted $gf$-values and energies for each individual hyperfine line. Satisfactory fits were obtained and clear improvements were found using our new data compared with the old available Mn I data. A complete list of energies and $gf$-values for all the $3d^54s({^7S})4d$ e$^{6}$D $-$ $3d^54s({^7S})4f$ w$^{6}$F hyperfine lines are available as supplementary material online, whereas only the stronger lines are presented and discussed in detail in this paper.