Calculation of the resonant contribution to $Z_{eff}\left(k_0\right)$ using close-coupled equations for positron–molecule scattering

In a previous paper (2010 Phys. Rev. A 82 042702; 2014 Phys. Rev. A 89 069901(E)), one of us (EAGA) calculated the resonant contribution to $Z_{eff}\left(k_0\right)$, the effective number of electrons available for annihilation by a positron with wave number k ₀, in the scattering of a heavy positron by H₂. The mass of the positron was increased just sufficiently for a bound state to occur. This calculation was carried out using the Kohn variational method. An alternative method is to use the close-coupled equations for the system under consideration. We compare our results with those obtained by Gribakin and Lee (2006 Phys. Rev. Lett. 97 193201). There is a resonant contribution to $Z_{eff}\left(k_0\right)$ from the vibrationally excited quasibound state which may be described by a Breit–Wigner resonance formula arising naturally from the close-coupling analysis if a certain additional assumption is made. There is also a separate resonant contribution to $Z_{eff}\left(k_0\right)$ from the open channel function influenced by the quasibound state, and a cross term. It is shown that the contribution from the quasibound state is very similar to the expression for the resonant contribution obtained by Gribakin and Lee. Comparison is made with other treatments, for example, the close-coupling calculation of Nishimura and Gianturco (2003 Phys. Rev. Lett. 90 183201). (paper)