Fano's theory on configuration mixing for many channel case has been applied to investigate the resonant vibrational excitation process of an oxygen molecule by low energy (less than 1 eV) electron impact. It has been shown that each channel width is proportional to the 5th power of the wave number of an incident or ejected electron. The energy integrated cross section for resonant vibrational 0→1 excitation via an intermediate vibrationally excited oxygen molecular ion state O 2 -* (υ'=6) is estimated to be 6.4×10 -3 a 0 2 eV. This is in fairly good agreement with the experimental results by Linder and Schmidt (Z. Naturforsch. 26a (1971) 1617): 9.0×10 -3 a 0 2 eV, and by Spence and Schulz (Phys. Rev. A 2 (1970) 1802): 1.4×10 -3 a 0 2 eV. It has been shown that the characteristic feature of branching ratio can also be explained by the k 5 rule.
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