Positron annihilation in ionic media and an optical model of the positron

It is proposed that positron motion in quasiatomic positron + anion systems formed in anionic media can be described by a potential of the form V_eff(r) = Z_eff/r²-η/r, where Z_eff is the "effective" charge of the nucleus, and n is the effective charge of the anion. It is shown that the positron wave function of the ground state of the quasiatomic positron + anion system in the field of such a potential is ψ_X(r) = l/√4π·A_nx·r^X·e^-ar. Thus the validity of selecting a test variation positron wave function ψ(r) = l/√4π·A·r·e^-ar is demonstrated for the potential V_eff = ∞ at r = 0 and V_eff = -η/r for r > 0 (Gol'danskii-Prokop'ev optical positron model, Fiz. Tverd. Tela, 8, 515 (1966)), belonging to the class of functions ψ_X(r). Having the wave function ψ_X(r) and Slater wave functions ψ_ns,p(r) of the electrons, annihilation photon angular distribution (APAD) curves are calculated, together with halfwidths of the APAD curves and positron lifetimes τ_ns,p.