In this paper, we generalize and improve the derivation of photoionization rate formula for one-electron atoms proposed by Keldysh [Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)]]. More exact expressions of the photoionization rate in the tunneling regime have been obtained. In addition, we extend the derivation to photoionization rates of randomly oriented diatomic molecules.
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Mishima et al. (2002) studied this question.