Muon Capture in Gaseous Deuterium

We report the results of an experiment performed to measure the muon nuclear capture rate by free deuterons. The muons were slowed down in ultrapure gaseous hydrogen at 7.6 atm and 293 °K, containing 5% of deuterium. A special target was used, in which a system of gas proportional counters, working with the (${\mathrm{H}}_2$ + ${\mathrm{D}}_2$) gaseous mixture itself, was operating. Neutrons from the capture reactions were detected using liquid scintillation counters, and the $\gamma$-ray background was eliminated by pulse-shape discrimination. The experimental result is ${\Lambda }_{\exp }=(445\mathrm{}\pm 60)$ ${\sec }^{-1\mathrm{}}$, which is consistent with muon-electron universality and with the assumption that the nuclear capture proceeds from the doublet spin state of the $\mu d$ muonic atoms. Combining the present experimental value with a previous result obtained with a liquid-hydrogen deuterated target, one obtains a ratio between the axial-vector and vector coupling constants given by $\frac{g_{A,\mu }}{g_{V,\mu }}=-1.35\mathrm{}\pm 0.1$.