As part of the CALIFA survey, we conducted a thorough 2D analysis of the ionized gas in two E/S0 galaxies, NGC6762 and NGC5966, aiming to shed light on the nature of their warm ionized ISM. We present optical IFS obtained with the PMAS/PPAK spectrophotometer. To recover the nebular lines, we subtracted the underlying stellar continuum from the observed spectra using the STARLIGHT code. In NGC6762, the ionized gas and stellar emission display similar morphologies, while the emission line morphology is elongated in NGC5966, spanning ~6 kpc, and is oriented roughly orthogonal to the major axis of the stellar continuum ellipsoid. Whereas gas and stars are kinematically aligned in NGC6762, the gas is kinematically decoupled from the stars in NGC5966. A decoupled rotating disk or an ionization cone are two possible interpretations of the elongated ionized gas structure in NGC5966. The latter would be the first ionization cone of such a dimension detected within a weak emission-line galaxy. Both galaxies have weak emission-lines relative to the continuum [EW(Ha)< 3 A] and have low excitation, log([OIII]5007/Hb) < 0.5. Based on optical diagnostic ratios ([OIII]5007/Hb,[NII]6584/Ha,[SII]6717,6731/Ha,[OI]6300/Ha), both objects contain a LINER nucleus and an extended LINER-like gas emission. The emission line ratios do not vary significantly with radius or aperture, which indicates that the nebular properties are spatially homogeneous. The gas emission in NGC6762 can be best explained by photoionization by pAGB stars without the need of invoking any other excitation mechanism. In the case of NGC5966, the presence of a nuclear ionizing source seems to be required to shape the elongated gas emission feature in the ionization cone scenario, although ionization by pAGB stars cannot be ruled out.(abridged)
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