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The three Mn I lines at 17325, 17339 and 17349 \AA~are among the 25 strongestlines ($\log(gf)>0.5$) in the H-band. They are all heavily broadened due tohyperfine structure and the profiles of these lines have so far not beenunderstood. Earlier studies of these lines even suggested that they wereblended. In this work, the profiles of these three infra-red (IR) lines havebeen studied theoretically and compared to experimental spectra to assist inthe complete understanding of the solar spectrum in the IR. It is shown thatthe structure of these lines can not be described in the conventional way bythe diagonal $A$ and $B$ hyperfine interaction constants. The off-diagonalhyperfine interaction not only has large impact on the energies of thehyperfine levels, but also introduces a large intensity redistribution amongthe hyperfine lines, changing the line profiles dramatically. By performinglarge-scale calculations of the diagonal and off-diagonal hyperfine interactionand $gf$-values between the upper and lower hyperfine levels and using asemi-empirical fitting procedure, agreement between our synthetic andexperimental spectra was achieved. Furthermore, we compare our results withobservations of stellar spectra. The spectra of the Sun and the K1.5 III redgiant star Arcturus were modelled in the relevant region, $1.73-1.74$ $\mu$musing our theoretically predicted $gf$-values and energies for each individualhyperfine line. Satisfactory fits were obtained and clear improvements werefound using our new data compared with the old available Mn I data. A completelist 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 supplementarymaterial online, whereas only the stronger lines are presented and discussed indetail in this paper.

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