Muonic Molecules and Nucleon-Deuteron Capture

Abstract

Variational wave functions have been computed for all $S$ states of muonic molecules involving hydrogen isotopes. Results for the $p\ensuremath{\mu}d$ ground state have been used to compare nucleon-deuteron capture cross sections with $p\ensuremath{\mu}d$ fusion rates. Using our molecular wave functions and the results of muonic-molecule experiments, we estimate the low-energy $S$-wave cross section for the reaction $\mathrm{D}(p, \ensuremath{\gamma}){\mathrm{He}}^{3}$. Our result is in disagreement with measurements in the tens-of-kilovolts region, but is consistent with thermal neutron-deuteron capture data when Coulomb effects are taken into account by means of the usual penetration factor. Finally, we reexamine the usual assumption that proton-deuteron capture occurs only from the doublet state and show how the doublet and quartet matrix elements could both be determined from a new measurement of the total yield of gamma rays from $p\ensuremath{\mu}d$ fusion in liquid hydrogen.