Feshbach projection operator approach to positron annihilation

We present a theory of vibrationally enhanced positron annihilation on molecules based on the Feshbach projection operator formalism. A key aspect of the present approach is the fact that no direct vibrational excitation is assumed, i.e., the attachment mechanism is electronic in nature, arising from positron-electron correlation-polarization forces, and energy transfer to the nuclei essentially follows from the difference between the potential-energy surfaces of the isolated target and the positron-molecule compound; moreover, no a priori assumption is made on the character of the transient (bound or virtual state). An approximate relation between the annihilation parameter Z_eff and the vibrationally summed cross section is presented, as well as a hierarchy of approximations that may allow for elaborate model calculations. We also discuss how important aspects of the annihilation process are taken into account in the present theory, such as isotope effects, vibrational energy redistribution and relative strengths among vibrational resonances. For completeness, semiempirical model calculations for acetylene and ethylene are presented. Despite the stringent approximations employed in this simplest version of the theory, fair agreement with experimental data was obtained in the vicinity of 0→1 thresholds.