Mechanisms of positron annihilation on molecules

The aim of this work is to identify the mechanisms responsible for very large rates and other peculiarities observed in low-energy positron annihilation on molecules. The two mechanisms considered are the following: (i) Direct annihilation of the incoming positron with one of the molecular electrons. This mechanism dominates for atoms and small molecules. I show that its contribution to the annihilation rate can be related to the positron elastic scattering cross section. This mechanism is characterized by a strong energy dependence of $Z_{\mathrm{eff}}$ at small positron energies and high $Z_{\mathrm{eff}}$ values (up to ${10}^3)$ for room-temperature positrons, if a low-lying virtual level or a weakly bound state exists for the positron. (ii) Resonant annihilation, which takes place when the positron undergoes resonant capture into a vibrationally excited quasibound state of the positron-molecule complex. This mechanism dominates for larger molecules capable of forming bound states with the positron. For this mechanism $Z_{\mathrm{eff}}$ averaged over some energy interval, e.g., due to thermal positron energy distribution, is proportional to the level density of the positron-molecule complex, which is basically determined by the spectrum of molecular vibrational states populated in the positron capture. The resonant mechanism can produce very large annihilation rates corresponding to $Z_{\mathrm{eff}}\sim {10}^8.$ It is highly sensitive to molecular structure, and shows a characteristic ${\varepsilon }^{-1/2}$ behavior of $Z_{\mathrm{eff}}$ at small positron energies $\varepsilon .$ The theory is used to analyze calculated and measured $Z_{\mathrm{eff}}$ for a number of atoms and molecules.