Experimental study of $\mu$-atomic and $\mu$-molecular processes in pure helium and deuterium-helium mixtures

We present experimental results of $\mu$-atomic and $\mu$-molecular processes induced by negative muons in pure helium and helium-deuterium mixtures. The experiment was performed at the Paul Scherrer Institute (Switzerland). We measured relative intensities of muonic x-ray $K$ series transitions in ${\left(\mu {}^{3,4}\mathrm{He}\right)}^{*}$ atoms in pure helium as well as in helium-deuterium mixtures. The $d\mu {}^3\mathrm{He}$ radiative decay probabilities for two different helium densities in ${\mathrm{D}}_2+{}^3\mathrm{He}$ mixture were also determined. Finally, the $q_{1s}^{\mathrm{He}}$ probability for a $d\mu$ atom formed in an excited state to reach the ground state was measured and compared with theoretical calculations using a simple cascade model.

Figure 1

Scheme of the experimental setup. The view is that of the incoming muon.

Figure 2

Scheme of $\mu$-atomic and $\mu$-molecular processes in a ${\mathrm{D}}_2+{}^3\mathrm{He}$ mixture. Details for all processes and rates are found in Ref. 37.

Figure 3

Energy distribution of prompt events in run I without (a) and with coincidences with muon decay electrons (b).

Figure 4

Time distribution in run I without (a) and with coincidences with muon decay electrons (b).

Figure 5

Energy dependence of $q_{1s}^{\mathrm{He}}$ in the ${\mathrm{D}}_2+{}^3\mathrm{He}$ mixture calculated for runs III (curve a) and IV (curve b). Experimental values of $q_{1s}^{\mathrm{He}}$ measured in the present work [$q_{1s}^{\mathrm{He}}=(0.882\pm 0.018)$ and $q_{1s}^{\mathrm{He}}=(0.844\pm 0.020)$] are represented by hatched boxes.

Figure 6

Energy spectra of the prompt events in runs III (left) and IV (right).

Figure 7

Energy spectra of the delayed events in runs III (left) and IV (right).

Figure 8

Time distributions in runs III (left) and IV (right) within the energy range $5.74-7.50\mathrm{keV}$.

Figure 9

Density dependence of the $\gamma$-decay branching ratio ${\kappa }_{d\mu \mathrm{He}}$. Points with error bars are our experimental values. The solid line corresponds to the second mechanism with ${\lambda }_{\mathrm{Aug}}^{\mathrm{inn}}={10}^{12}{\mathrm{s}}^{-1}$ [34]. The dashed lines represents the first mechanism with ${\lambda }_{\mathrm{Aug}}^{\mathrm{ext}}=8.5\times {10}^{11}{\mathrm{s}}^{-1}$ [31], whereas the dotted lines is given for ${\lambda }_{\mathrm{Aug}}^{\mathrm{ext}}={10}^{10}{\mathrm{s}}^{-1}$ [32, 33].