The fixed core stochastic variational method is used to investigate positro
n binding to a model alkali atom with a continuously adjustable ionization
potential. Positron binding is possible for model atoms which have ionizati
on potential (IP) ranging from 0.1767 to 0.479 Hartree (corresponding to di
pole polarizabilities ranging from 209 to 23.5 a(0)(3)) Results of the mode
l indicate that positron binding is likely for gold, but not for potassium,
rubidium or caesium. The annihilation rate was largest (1.97 x 10(9) s(-1)
)when the IP is smallest and smallest (0.07 x 10(9) s(-1)) when the TP is l
argest. The presence of a positronium (Ps) cluster configuration in the wav
efunction is found to be important for an accurate estimate of the annihila
tion rate even in circumstances when the positron and electron are located
large distances apart.