  A method is proposed to manipulate the annihilation dynamics of a dense gas
of positronium atoms employing superradiance and subradiance regimes of the
cooperative spontaneous emission of the system. The annihilation dynamics is
controlled by the gas density and by the intensity of the driving strong
resonant laser field. In particular, the method allows to increase the
annihilation lifetime of an ensemble of positronium atoms more than hundred
times by trapping the atoms in the excited state via collective radiative
effects in the resonant laser and cavity fields.
