  Tree amplitudes of the production of two kinds of scalar particles at
threshold from one virtual particle are calculated in a model of two scalar
fields with $O(2)$ symmetric quartic interaction and unequal masses. These
amplitudes exhibit interesting factorial and exponential behaviour at large
multiplicities. As a by-product we observe that the kinematically allowed decay
of one real particle into $n$ real particles of another kind, all at rest, has
zero tree amplitude in this model for $n>2$.
