Lifetime and population of the $2S$ state in muonic hydrogen and deuterium

Radiative deexcitation (RD) of the metastable $2S$ state of muonic hydrogen and deuterium atoms has been observed. In muonic hydrogen, we improve the precision on lifetime and population (formation probability) values for the short-lived $\mu p\left(2S\right)$ component, and give an upper limit for RD of long-lived $\mu p\left(2S\right)$ atoms. In muonic deuterium at 1 hPa, $3.1\pm 0.3$% of all stopped muons form $\mu d$($2S$) atoms. The short-lived $2S$ component has a population of $1.35{}_{-0.33}^{+0.57}$% and a lifetime of ${\tau }_{2S}^{\mathrm{short}}\left(\mu d\right)=138{}_{-34}^{+32}$ ns. We see evidence for RD of long-lived $\mu d\left(2S\right)$ with a lifetime of ${\tau }_{2S}^{\mathrm{long}}\left(\mu d\right)=1.15{}_{-0.53}^{+0.75}\mu \mathrm{s}$. This is interpreted as formation and decay of excited muonic molecules.

Figure 1

Energy spectrum of all prompt x rays in the muonic deuterium data. The plot is split to give a better overview over the contributions with low statistics.

Figure 2

Time spectra and fits for muonic hydrogen (top) and deuterium (bottom). Note the break in the horizontal time axis. The stop time is given by the $\mu \mathrm{N}$ and $\mu \mathrm{O}$ (not shown) time spectra. The $K\ge \gamma$ spectrum is the stop time, convoluted with an (exponential) cascade time distribution. The $K\alpha$ spectrum in $\mu p$ shows a short-lived exponential component from radiative quenching of fast $\mu p$($2S$) atoms. In $\mu d$, an additional long-lived component is visible which we consider as evidence for radiative deexcitation of long-lived $\mu d$($2S$) atoms after formation of excited molecular ions ${\left[{\left(dd\mu \right)}^{+}\right]}^{*}$. The $2S$ components are constructed by the convolution of the $K\ge \gamma$ distribution with exponential lifetimes (see text). In $\mu p$ ($\mu d$), the prompt $K\alpha$ peak contains 881k (412k) events, and the fast component contains 11.6k (4.2k) events. The long-lived component in $\mu d$ contains 440 events. The fit region starts at 0.1 $\mu \mathrm{s}$ to exclude early-time beam-correlated background.

Figure 3

Centroid energy of the $K\ge \gamma$ component as obtained by the fit of the $\mu p$ dataset between 0.1 and 0.4 $\mu$s after muon entry.