  We propose a general method to cool the translational motion of molecules.
Our method is an extension of single photon atomic cooling which was
successfully implemented in our laboratory. Requiring a single event of
absorption followed by a spontaneous emission, this method circumvents the need
for a cycling transition and can be applied to any paramagnetic or polar
molecule. In our approach, trapped molecules would be captured near their
classical turning points in an optical dipole or RF-trap following an
irreversible transition process.
