Toward an energy measurement of the internal conversion electron in the deexcitation of the ${}^{229}\mathrm{Th}$ isomer

The first excited isomeric state of Th-229 has an exceptionally low energy of only a few eV and could form the gateway to high-precision laser spectroscopy of nuclei. The excitation energy of the isomeric state has been inferred from precision $\gamma$ spectroscopy, but its uncertainty is still too large to commence laser spectroscopy. Reducing this uncertainty is one of the most pressing challenges in the field. Here we present an approach to infer the energy of the isomer from spectroscopy of the electron which is emitted when the isomer de-excites through internal conversion (IC). The experiment builds on U-233, which $\alpha$-decays to Th-229 and populates the isomeric state with a 2% branching ratio. A film of U-233 is covered by a stopping layer of few-nm thickness and placed between an $\alpha$ detector and an electron detector, such that the $\alpha$ particle and the IC electron can be detected in coincidence. Retarding field electrodes allow for an energy measurement. In the present design, the signal of the Th-229m IC electrons is masked by low-energy electrons emitted from the surface of the metallic stopping layer. We perform reference measurements with U-232 and U-234 to study systematic effects, and we study various means to reduce the background of low-energy electrons. Our study gives guidelines to the design of an experiment that is capable of detecting the IC electrons and measuring the isomer energy.

Figure 1

(a) Experimental setup: A thin uranium layer is sandwiched between two gold layers and placed between a Si detector ($\alpha$ particles) and an MCP detector (electrons). (b) A typical time trace of the MCP signal, triggered by an $\alpha$ decay that is registered by the Si detector. The counts are integrated over bins of 500 ns length and normalized to the number of detected $\alpha$ decays (“sweeps”). This data set represents an average over $5\times {10}^7$ sweeps, it is taken with the U-233 sample at zero retarding field.

Figure 2

Simulation of the experiment. (a) Probability distribution $p_H\left(H\right)$ for a Th-229 recoil nucleus to be emitted into the upper hemisphere and stopped at a depth $H$ from the outer surface, simulated with the help of the SRIM package for the configuration presented in Sec. 3. (b) Probability $\eta$ that the decay ${}^{233}\mathrm{U}\to {}^{229m}\mathrm{Th}+\alpha$ is accompanied by the emission of an $\alpha$ particle into the lower hemisphere, the recoil nucleus is stopped within the source, and the conversion electron leaves the source toward the upper hemisphere, as a function of the inelastic mean free path ${\lambda }_e$ of the electron. The solid black curve corresponds to the calculation according to Eq. (3) for the SRIM-simulated distribution of recoil nuclei presented in (a), and styled colored curves correspond to approximate estimations of recoil nuclei (see the Appendix) for different thicknesses $D_{\mathrm{Au}}$ of the stopping layer. (c) Probability $\eta$ in dependence of the stopping layer thickness.

Figure 3

$\alpha$ spectra of (a) the U-233 sample and (b) the U-234 sample. The thickness of the uranium layer is 1.6 nm for U-233 and 1.1 nm for U-234. In both cases, the sample is sandwiched in between 4 nm of gold. The U-233 sample contains a 19.3 ppm contamination of U-232 (4.5% in activity), and the U-234 sample contains 1.4% of U-233 contaminations. The decay chains are clearly visible, where superscripts ${}^{a,b,c}$ denote the U-233, U-232, and U-234 decay chains, respectively.

Figure 4

Time dependence of electron emission registered by the MCP, in dependence of the energy of the $\alpha$ particle that triggered the detection. For this data set, the U-233 sample was used, and the retarding field was set to 0 V. The signal is recorded in time bins of 500 ns, and the energy is recorded in bins of 0.86 keV width. The signal at about 4800 keV (5300 keV) corresponds to the decay of U-233 (U-232). The MCP counts are normalized to the number of sweeps; highest count rates are measured in the first few $\mu \mathrm{s}$ of each sweep.

Figure 5

Fitting a single exponential decay to the U-233 data, where the dataset is subdivided into bins of 25 keV width. (a) Fraction of the total number of sweeps in each energy bin. (b) Amplitude and (c) decay constant of the exponential fit to the data; lines are only a guide to the eye.

Figure 6

The observed signal for U-233 (solid black line) is orders of magnitude stronger than the expected isomer signal (dotted red line). Also the difference signal between measurements with U-233 and U-234 is considerably larger than the expected signal (dashed green line). Inset: Difference signal between U-233 and U-232; see the text for details.

Figure 7

Comparison of the exponential decay of the electron signal for U-233 (black squares) and U-232 (red dots). We plot the amplitudes of the single exponentials fitted to the data: within the error bars, they are identical for the two isotopes. Inset: Same data on a linear scale.

Figure 8

Schematic drawing of the paths of the $\alpha$ particle, the recoil nucleus, and the conversion electron.