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A theoretical approach is proposed to deal with the detuning between the atom and cavity field in the one-photon mazer. Our starting point is to find a conserved quantity, which is characteristic of the atom plus field system.Resorting to this characteristic conserved quantity, we separate the Hamiltonian into two independent parts and then solve the Schrodinger equation of quantum scattering of an incident cold atom. We investigate the detuning effects on the one-photon induced emission probability and obtain some distinct results in contrast to the previous work.