Treatment of resonances in the scattering of a heavy positron byH2that are due to interaction with vibrationally excited quasibound states

Abstract

For a positron with wave number $k$, the rate of annihilation when scattered by an atom or molecule is proportional to ${Z}_{\mathrm{eff}}(k)$, the effective number of electrons in the target that are available to the positron for annihilation. There is currently great interest in the very large positron annihilation rates, and hence values of ${Z}_{\mathrm{eff}}(k)$, that have been observed in low-energy positron scattering by some molecules. These are observed experimentally to occur at energies just below the energies of excited vibrational states of the molecule concerned. This has been explained by Gribakin [Phys. Rev. A 61, 022720 (2000)] and Gribakin and Lee [Phys. Rev. Lett. 97, 193201 (2006)] as being due to Feshbach resonances involving excited quasibound vibrational states. These treatments make skilful use of approximate methods. It is of interest to determine how the expression obtained for the resonant contribution to ${Z}_{\mathrm{eff}}(k)$ from a quasibound state using a very accurate method is related to the expressions obtained in the previously mentioned articles. In view of this, in this article I carry out a detailed ab initio theoretical treatment of positron scattering by ${\mathrm{H}}_{2}$ using the Kohn variational method. ${\mathrm{H}}_{2}$ is the simplest molecule, which makes it easier to take into account all the interactions involved. However, a positron does not form a bound state with ${\mathrm{H}}_{2}$. To investigate resonant behavior in ${Z}_{\mathrm{eff}}(k)$, I increase the mass ${m}_{p}$ of the positron so that it forms a weakly bound state with ${\mathrm{H}}_{2}$. This gives rise to excited quasibound vibrational states. The expression I obtain for the resonant contribution to ${Z}_{\mathrm{eff}}(k)$ has some similarity with the expressions obtained by Gribakin and Lee. This gives some support to their explanation of the very large values of ${Z}_{\mathrm{eff}}(k)$. However, they make no explicit mention of corrections to the Born-Oppenheimer (BO) approximation. These play a key role in my treatment as they couple the quasibound states to the continuum. I am able to show how the BO corrections are taken into account implicitly in calculating the expressions obtained by Gribakin and Lee. The most important difference between my treatment and their treatments is that in my treatment ${Z}_{\mathrm{eff}}(k)$ may be infinite at the resonant energy, whereas in the other treatments it is likely to be large, but can never be infinite. Further investigation is necessary to determine the origin of this infinity in my treatment. My treatment could be applied to positron scattering by molecules such as methyl halides in which very high ${Z}_{\mathrm{eff}}(k)$ values are observed, though using the Kohn variational method would be considerably more complicated than in the case of ${\mathrm{H}}_{2}$.