The protonated Argon ion, $^{36}$ArH$^{+}$, has been identified recently in the Crab Nebula (Barlow et al. 2013) from Herschel spectra. Given the atmospheric opacity at the frequency of its $J$=1-0 and $J$=2-1 rotational transitions (617.5 and 1234.6 GHz, respectively), and the current lack of appropriate space observatories after the recent end of the Herschel mission, future studies on this molecule will rely on mid-infrared observations. We report on accurate wavenumber measurements of $^{36}$ArH$^{+}$ and $^{38}$ArH$^{+}$ rotation-vibration transitions in the $v$=1-0 band in the range 4.1-3.7 $mu$m (2450-2715 cm$^{-1}$). The wavenumbers of the $R$(0) transitions of the $v$=1-0 band are 2612.50135$pm$0.00033 and 2610.70177$pm$0.00042 cm$^{-1}$ ($pm3sigma$) for $^{36}$ArH$^{+}$ and $^{38}$ArH$^{+}$, respectively. The calculated opacity for a gas thermalized at a temperature of 100 K and a linewidth of 1 km.s$^{-1}$ of the $R$(0) line is $1.6times10^{-15}times N$($^{36}$ArH$^+$). For column densities of $^{36}$ArH$^+$ larger than $1times 10^{13}$ cm$^{-2}$, significant absorption by the $R$(0) line can be expected against bright mid-IR sources.
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