  The latest Micromesh Gas Amplification Structures (Micromegas) are achieving
outstanding energy resolution for low energy photons, with values as low as 11%
FWHM for the 5.9 keV line of $^{55}$Fe in argon/isobutane mixtures at
atmospheric pressure. At higher energies (MeV scale), these measurements are
more complicated due to the difficulty in confining the events in the chamber,
although there is no fundamental reason why resolutions of 1% FWHM or below
could not be reached. There is much motivation to demonstrate experimentally
this fact in Xe mixtures due to the possible application of Micromegas readouts
to the Double Beta Decay search of $^{136}$Xe, or in other experiments needing
calorimetry and topology in the same detector. In this paper, we report on
systematic measurements of energy resolution with state-of-the-art Micromegas
using a 5.5 MeV alpha source in high pressure Ar/isobutane mixtures. Values as
low as 1.8% FWHM have been obtained, with possible evidence that better
resolutions are achievable. Similar measurements in Xe, of which a preliminary
result is also shown here, are under progress.
