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-/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 _X(r) = l/4·A_nx·r^X·e^–ar. Thus the validity of selecting a test variation positron wave function (r) = l/4·A·r·e^–ar is demonstrated for the potential V_eff = at r = 0 and V_eff = –/r for r > 0 (Gol'danskii-Prokop'ev optical positron model, Fiz. Tverd. Tela,8, 515 (1966)), belonging to the class of functions _X(r). Having the wave function _X(r) and Slater wave functions _ns,p(r) of the electrons, annihilation photon angular distribution (APAD) curves are calculated, together with halfwidths of the APAD curves and positron lifetimes _ns,p.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 52–56, May, 1990.