μ-Mesonic Molecules. II. Molecular-Ion Formation and Nuclear Catalysis

The methods developed in the preceding paper are applied to the study of the behavior of $\mu$ mesons in liquid hydrogen. Numerically evaluated energy eigenvalues for the bound states of the various molecular-ion configurations are presented. Phase shifts and cross sections for the scattering of mesonic atoms from hydrogen and deuterium are given. It is shown that in the neighborhood of 0.2 ev the scattering of ($d\mu$) atoms from protons exhibits a Ramsauer-Townsend effect with an anomalously small cross section occurring in this region. The existence of this effect provides an explanation for the appearance of "gaps" in the experimental observation of the catalytic process. The rate of exchange of mesons from protons to deuterons in pure deuterium is calculated along with the rates of formation of the ${\left(p\mu p\right)}^{+}$, ${\left(p\mu d\right)}^{+}$, and ${\left(d\mu d\right)}^{+}$ molecular ions. It is shown that the predominant mechanism for the formation of the molecular ions is dipole electron ejection. These results are shown to be in agreement with available experimental data. A semiphenomenological treatment of the ($\mathrm{pd}$) nuclear reaction is also given. A rough estimate of the $\gamma$-emission process indicates that the dominant mode of emission is from the singlet proton spin states.