  We present a joint analysis of the four most prominent sodium-sensitive
features (NaD, NaI8190, NaI1.14, and NaI2.21), in the optical and Near-Infrared
spectral range, of two nearby, massive (sigma~300km/s), early-type galaxies
(named XSG1 and XSG2). Our analysis relies on deep VLT/X-Shooter long-slit
spectra, along with newly developed stellar population models, allowing for
[Na/Fe] variations, up to 1.2dex, over a wide range of age, total metallicity,
and IMF slope. The new models show that the response of the Na-dependent
spectral indices to [Na/Fe] is stronger when the IMF is bottom heavier. For the
first time, we are able to match all four Na features in the central regions of
massive early-type galaxies, finding an overabundance of [Na/Fe], in the range
0.5-0.7dex, and a bottom-heavy IMF. Therefore, individual abundance variations
cannot be fully responsible for the trends of gravity-sensitive indices,
strengthening the case towards a non-universal IMF. Given current limitations
of theoretical atmosphere models, our [Na/Fe] estimates should be taken as
upper limits. For XSG1, where line strengths are measured out to 0.8Re, the
radial trend of [Na/Fe] is similar to [Mg/Fe] and [C/Fe], being constant out to
0.5Re, and decreasing by 0.2-0.3dex at 0.8Re, without any clear correlation
with local metallicity. Such a result seems to be in contrast with the
predicted increase of Na nucleosynthetic yields from AGB stars and TypeII SNe.
For XSG1, the Na-inferred IMF radial profile is consistent, within the errors,
with that derived from TiO features and the Wing-Ford band, presented in a
recent paper.
