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A recombination rate of electron-ion in the strong-field atomic process is phenomenologically introduced into the ionization rate equation, and therefrom an ionization and recombination rates equation (IRRE) is obtained. By using the extended IRRE, the propagation equation of an intense femtosecond laser pulse in the gaseous medium is re-derived. Some new physical behaviors and characteristics caused by the introduced recombination rate are discussed in detail. (C) 2013 Optical Society of America
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