Mesotron production by nuclear bombardment with fast, heavy particles has been investigated theoretically in a semi-quantitative way to determine the expected threshold energies, the cross sections, and their energy dependence. Whereas a treatment in which the target nucleons are assumed to be at rest predicts a requisite incident energy of ∼210 Mev, the present treatment, based on the Fermi degenerate gas model, finds the threshold incident energy as ∼95 Mev. The threshold is somewhat higher for positive than for negative mesotrons. The cross section for single mesotron production, evaluated from the accessible volume in momentum space, is found to vary with the fractional excess energy, $\epsilon$, as ${\epsilon }^{3.5}$ in the scalar or axial-vector theories; at low values of $\epsilon$, a small difference in the energy dependence for negative and positive mesotrons arises from the necessity of giving the former a non-zero initial kinetic energy. For the pseudo-scalar and the polar-vector theories, the matrix element for mesotron emission is proportional to the momentum of the mesotron. This changes the power law to ${\epsilon }^{4.5}$.

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