Muon Reactions in Liquid Hydrogen and Liquid Deuterium

Abstract

The reactions of muons in liquid hydrogen containing a low concentration of deuterium, $p\mu +d\to d\mu +p\to {\left(d\mu p\right)}^{+}\to {\mathrm{He}}^3+{\mu }^{-}\left(\mathrm{a}\right) or {\left({\mathrm{He}}^3\mu \right)}^{+}+\gamma \left(\mathrm{b}\right)$, and in liquid deuterium containing a low concentration of hydrogen, $d\mu +p\to {\left(d\mu p\right)}^{+}\to {\mathrm{He}}^3+{\mu }^{-}\left(\mathrm{c}\right) or {\left({\mathrm{He}}^3\mu \right)}^{+}+\gamma \left(\mathrm{d}\right)$, and $d\mu +d\to {\left(d\mu d\right)}^{+}\to {\mathrm{He}}^3+n+{\mu }^{-}\left(\mathrm{e}\right) or p+t+{\mu }^{-}\left(\mathrm{f}\right)$, have been investigated using the Chicago 9-in. bubble chamber. Using previously determined values for the formation and fusion rates of the ${\left(d\mu p\right)}^{+}$ ion in hydrogen in conjunction with a theoretical determination of the population of the various hyperfine levels in the ${\left(d\mu p\right)}^{+}$ ion, reaction (a) is found to occur in (15±1.5)% of all ${\left(d\mu p\right)}^{+}$ fusion reactions. The formation rate of the ${\left(d\mu d\right)}^{+}$ ion in liquid deuterium is found to be ${\lambda }_{\mathrm{dd}}=(3.6\mathrm{}\pm 1.3)\times {10}^5$ ${\sec }^{-1\mathrm{}}$. The fusion rate of the ${\left(d\mu d\right)}^{+}$ is ${\lambda }_{\mathrm{df}}=(2.5\mathrm{}\pm 0.04)\times {10}^5$ ${\sec }^{-1\mathrm{}}$, and the fraction of muons which, having catalyzed reaction (e), are subsequently bound in a ${\left({\mathrm{He}}^3\mu \right)}^{+}$ muonic ion is (0.31±0.0034). The rate of de-excitation to the lower hyperfine level of the $d\mu$ muonic atom via the reaction $d\mu \left(\frac{3}{2}\right)+d\to d+d\mu \left(\frac{1}{2}\right)$ has been investigated and found to be $(7.9\mathrm{}\pm 2.8)\times {10}^5 invsec<{\lambda }_{(\frac{3}{2}-\frac{1}{2})}<(1.35\mathrm{}\pm 0.48)\times {10}^6 invsec$. The interference of reactions (c), (d), (e), and (f) in the investigation of the spin-independent capture reaction ${\mu }^{-}+d\to n+n+\nu$ is discussed.