  The Gas Pixel Detector belongs to the very limited class of gas detectors
optimized for the measurement of X-ray polarization in the emission of
astrophysical sources. The choice of the mixture in which X-ray photons are
absorbed and photoelectrons propagate, deeply affects both the energy range of
the instrument and its performance in terms of gain, track dimension and
ultimately, polarimetric sensitivity. Here we present the characterization of
the Gas Pixel Detector with a 1 cm thick cell filled with dimethyl ether (DME)
at 0.79 atm, selected among other mixtures for the very low diffusion
coefficient. Almost completely polarized and monochromatic photons were
produced at the calibration facility built at INAF/IASF-Rome exploiting Bragg
diffraction at nearly 45 degrees. For the first time ever, we measured the
modulation factor and the spectral capabilities of the instrument at energies
as low as 2.0 keV, but also at 2.6 keV, 3.7 keV, 4.0 keV, 5.2 keV and 7.8 keV.
These measurements cover almost completely the energy range of the instrument
and allows to compare the sensitivity achieved with that of the standard
mixture, composed of helium and DME.
