Using a free-running distributed-feedback quantum cascade laser (QCL) emitting at 9.54 $mu$m, the pressure shift parameters of four intense rovibrational transitions in the $ u_3$ fundamental band of ozone induced by oxygen (O$_2$), air and the noble gases helium (He), argon (Ar), and xenon (Xe) are obtained by employing second harmonic detection. The experimental analysis comprises a full uncertainty budget and provides line shift data which are traceable to SI. The high density of transitions in the $ u_3$ spectral region of ozone make this region particularly difficult to study with more commonly used techniques such as Fourier transform spectroscopy. The comparatively high spectral resolution of the QCL in the MHz range, on the contrary, allows to measure molecular shifts at relatively low pressures (from 2 to 70 hPa), thus reducing the impact of spectral congestion due to pressure broadening of molecular lines. The comparison of our results with published data shows that presently recommended values for the pressure shift are too low in this region. This observation is corroborated by semi-classical calculations using the Robert-Bonamy formalism. A slight negative $J$ dependence, already observed in other ozone vibrational bands, is predicted. Systematic use of our technique could be very useful to support this hypothesis and to make up for the lack of shift parameters for ozone $ u_3$ transitions in molecular spectral databases. A subsequent stabilization of the QCL onto an optical frequency comb will open up possibilities to perform metrological measurements of Doppler-free molecular lines.
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