  Compact obscured nuclei (CONs) are mainly found in local U/LIRGs. In the
local Universe, these sources are generally selected through the detection of
the HCN-vib (3-2) emission line at submillimetre wavelengths. In this work, we
present a diagnostic method to select deeply buried nuclei based on
mid-infrared (mid-IR) polycyclic aromatic hydrocarbons (PAHs) and continuum
ratios. Using Spitzer/IRS spectra of a representative sample of local ULIRGs
(z<0.27), we examine their PAH and underlying continuum emission ratios. For
deeply embedded sources, we find that the 9.7 micron silicate absorption band
has a particularly pronounced effect on the 11.3 micron PAH feature. The low
flux level in the nuclear silicate absorption band enhances the 11.3 micron PAH
feature contrast (high PAH equivalent width) compared to that of the other PAH
features. The technique has been extended to include the use of the continuum
ratios. However, the latter are affected both by the extinction coming from the
host galaxy as well as the nuclear region, whereas the foreground extinction is
cancelled out when using the PAH equivalent width ratios. We apply our method
to the HERUS and GOALS samples and classify as CON candidates 14 ULIRGs and 10
LIRGs, corresponding to 30% of ULIRGs and 7% of LIRGs from these samples. We
find that the observed continuum ratios of CON-dominated sources can be
explained by assuming torus models with a tapered disk geometry and a smooth
dust distribution. This suggests that the nuclear dusty structure of CONs has
an extremely high dust coverage. We also demonstrate that the use of mid-IR
color-color diagrams is an effective way to select CON-dominated sources at
different redshifts. In particular, the combination of filters of the JWST/MIRI
will enable the selection of CONs out to z~1.5. This will allow extending the
selection of CONs to high redshifts where U/LIRGs are more numerous.
