Ordinary muon capture studies for the matrix elements in $\beta \beta$ decay

High-purity germanium (HPGe) detectors were used to make a precise measurement of the $\gamma$-ray spectrum produced following ordinary (nonradiative) capture of negative muons by natural Se, Kr, Cd, and Sm. The measurement was repeated for isotopically enriched ${}^{48}\mathrm{Ti}, {}^{76}\mathrm{Se}, {}^{82}\mathrm{Kr}, {}^{106}\mathrm{Cd}$, and ${}^{150}\mathrm{Sm}$ targets. By investigating energy and time distributions, the lifetime of negative muons in the different isotopes was deduced. A detailed analysis of the intensity of the $\gamma$ lines enabled the extraction of the relative yields of several daughter nuclei. The partial rates of $({\mu }^{-},\nu )$ capture to numerous excited levels of the ${}^{48}\mathrm{Sc}, {}^{76}\mathrm{As}, {}^{82}\mathrm{Br}, {}^{106}\mathrm{Ag}$, and ${}^{150}\mathrm{Tc}$ isotopes (considered to be virtual states of the intermediate odd-odd nuclei in the $\beta \beta$ decay of ${}^{48}\mathrm{Ca}, {}^{76}\mathrm{Ge}, {}^{82}\mathrm{Se}, {}^{106}\mathrm{Cd}$, and ${}^{150}\mathrm{Nd}$, respectively) were also extracted. These rates are important as an experimental input for the theoretical calculation of the nuclear matrix elements in $\beta \beta$ decay.

Figure 1

Schematic representation of $\beta \beta$ decay of an (even, even) nucleus as two consequent virtual transitions via excited states of an intermediate (odd, odd) nucleus. OMC on a target consisting of the $(A,Z+2)$ daughter nucleus could provide information about the right virtual transition. Any admixture of the heavier $(A+1,Z+2)$ isotope would cause intensive population of the same intermediate states, and would thus be a background to the measurement.

Figure 2

An example of U spectrum measured with a HPGe detector and the ${}^{76}\mathrm{Se}$ target. Some of $\gamma$ lines follow decay of the OMC products: ${}^{74m}\mathrm{As},{}^{75}\mathrm{As},{}^{76}\mathrm{As}$.

Figure 3

(a) A simplified scheme of the transitions in a muonic atom. (b) Correlated P- and D-spectra measured with enriched ${}^{76}\mathrm{Se}$ target. Some of the identified $\gamma$-ray transitions are indicated. “DE” and “SE” denote the double and single escape peaks. The $\mu \text{X}$ ray transitions for carbon and oxygen are indicated as $\mu \mathrm{X}$(C) and $\mu \mathrm{X}$(O).

Figure 4

$K{\alpha }_1$ and $K{\alpha }_2 \mu \mathrm{X}$-ray doublet measured with enriched and natural Cd targets.

Figure 5

$(E,t)$ distribution of the correlated events measured with the ${}^{76}\mathrm{Se}$ target.

Figure 6

Schematic layout of the $\mu$ beam line and the target arrangement: the aperture defining veto counters C0, the trigger counters C1 and C2, the target area, the veto counter C3, and the HPGe $\gamma$ detectors around the target area. The target enclosure was constructed to accommodate solid (like in this figure) as well as gaseous materials.

Figure 7

Typical relative efficiency ($\eta$) of the $\gamma$ detection system. In the low-energy region (0.03–0.08 MeV) the efficiency drops because of absorption in various dead layers. The energy region 0.17–3.2 MeV is dominated by Compton scattering, whereas above 3–4 MeV the radiation length becomes larger than the crystal dimensions.

Figure 8

Distribution of the instrumental delay $\mathrm{\Delta }t$ between the $\mu$ stop and registration of prompt $\mu \mathrm{X}$ rays of different energies measured with a big HPGe detector. Time resolution below 200 keV deteriorates due to slow charge collection near the surface edges of the Ge crystal.

Figure 9

Time evolution of the spectrum fragment: 227 keV $\gamma$ line following OMC in ${}^{48}\mathrm{Ti}$. (1) Integral of central part of the fragment (line itself + background under it). (2) Area of the background around the line. (3) Integral of the $\gamma$ line fitted with a five-parameter Gaussian for each time slice.

Figure 10

Time evolution of the intensities of some of the strongest $\gamma$ lines produced after $\mu$ stop in ${}^{48}\mathrm{Ti}$. Note, the isomer of ${}^{47}\mathrm{Sc}$ ($J^{\pi }=3/2^{+}$, 767.1 keV) decays with its own characteristic lifetime $\approx 272$ ns.

Figure 11

Evolution of $\gamma$ lines intensity with time after $\mu$ stop in Se targets. The figure shows two separate measurements, one with an enriched ${}^{76}\mathrm{Se}$ target (top graphs) and one with a natural Se target. In the latter the main components of the initial Se isotopes are indicated. The identification is based on the different lifetimes and the isotopic abundances. The deterioration of the time resolution below $\approx 200$ keV $\gamma$-ray energy is clearly observed.

Figure 12

Evolution of $\gamma$-line intensity with time after $\mu$ stop in Cd targets. The two upper plots correspond to the enriched target; the three lower plots, to the natural target. In the latter, the main components of the initial Cd isotopes are indicated. The identification is based on the different lifetimes and the isotopic abundances.

Figure 13

Measured $\mu$ capture rates on Kr isotopes and ${}^{150}\mathrm{Sm}$. The measurements for ${}^{82}\mathrm{Kr}$ were performed with an isotopically enriched material, while those for ${}^{84}\mathrm{Kr}$ and ${}^{86}\mathrm{Kr}$ used the natural composition of Kr gas. The total rates from the various Kr isotopes exhibit significant differences. The total rate on ${}^{150}\mathrm{Sm}$ (yield scale to the left) is about a factor of 2 larger than for the Kr cases. Note, ${}^{82}\mathrm{Kr}$ and ${}^{150}\mathrm{Sm}$ are the final nuclei in the ${}^{82}\mathrm{Se}$ and ${}^{150}\mathrm{Nd} \beta \beta$ decays.