Positronium cooling into nanopores and nanochannels by phonon scattering

We studied the acoustic phonon scattering of a positronium (Ps) atom emitted into and then confined in closed nanopores and open nanochannels of an insulating material at low temperature. Closed nanopores were approximated by a Cubic box, while nanochannels by a channel with square geometry. As a case study, calculations were carried out for nanopores and nanochannels in a silica matrix. First-order calculations allowed us to set a lower limit to the size of the pores and of the channels in order to achieve complete Ps thermalization. The Ps energy loss and the cooling time obtained from the Ps-phonon scattering model were compared to those obtained from the classical model considering Ps scattering with surface atoms with an effective mass.