The deexcitation process of an atom in an optically allowed excited state by a collision with an axially symmetric molecule is considered. In order to make a precise comparison with experimental data that have recently been obtained, we extend previous work for a Penning ionization process [T. Watanabe and K. Katsuura, J. Chem. Phys. 47, 800 (1967)]. Using the straight-line trajectory impact parameter method, the probability of deexcitation in the incident atom is described by a discrete-continuum excitation transfer mechanism. The effects of the ionization yield eta in molecular target and of the molecular anisotropic property of the optical transition dipole are considered. The cross-section formula sigma is presented by a similar formula for Penning ionization of the atomic target by introducing a stereo factor C(lambda) as sigma = C(lambda)[e(4)mu(2)mu(E, perpendicular)/(4piepsilon(0))(2) (2)hv](2/5). Here, v is the relative velocity of the colliding system and lambda is given by the ratio lambda =(mu(E||)/mu(E perpendicular)), where mu, mu(E perpendicular), mu(E||) are the transition dipole moments of an excited atom, A-->A(*), those of a molecule at energy E for the perpendicular component and the parallel component with respect to molecular axis. Applications to He(*)(2(1)P)+H(2) (or D(2)), Ne(*)[2p(5)((2)P(1/2))3 s (1)P(1)]+ H(2) (or D(2)) systems and systems of the same projectiles on C(6)H(6), (or C(6)D(6)) molecules are made. The results for hydrogen molecules are compared with the experimental data.
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