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Positronium decay in a circular polarized laser field

We calculate the lifetime of both the o-Ps and the p-Ps positronium annihilation decay $ Ps\toγγ$ in the strong circular polarized laser field. We take a strategy of the factorization to separate the effects caused by the Coulomb interaction and the strong laser field interaction. It is factorized in the time direction but not in the space direction. Our results show that in the laser with long wavelength and high intensity, the lifetimes of those Ps states are dramatically increased. For $\rm CO_2$ laser with $10\, μm$ wavelength and $10^{13} W/cm^2$ intensity, lifetime of the spin-single positronium is increased by $10^8$ times. Our result is consistent with those obtained by solving the Sch{ö}dinger equation. This effect may be useful for the high harmonic generation(HHG) effects provided with the Ps\cite{keitel2004}.