Measurement of the ${}^{229}\mathrm{Th}$ Isomer Energy with a Magnetic Microcalorimeter

We present a measurement of the low-energy (0–60 keV) $\gamma$-ray spectrum produced in the $\alpha$ decay of ${}^{233}\mathrm{U}$ using a dedicated cryogenic magnetic microcalorimeter. The energy resolution of $\sim 10\mathrm{eV}$, together with exceptional gain linearity, allows us to determine the energy of the low-lying isomeric state in ${}^{229}\mathrm{Th}$ using four complementary evaluation schemes. The most precise scheme determines the ${}^{229}\mathrm{Th}$ isomer energy to be 8.10(17) eV, corresponding to 153.1(32) nm, superseding in precision previous values based on $\gamma$ spectroscopy, and agreeing with a recent measurement based on internal conversion electrons. We also measure branching ratios of the relevant excited states to be $b_{29}=9.3(6)\%$ and $b_{42}<0.7\%$.

Figure 1

(a) Partial nuclear level scheme of the ${}^{229}\mathrm{Th}$ nucleus with relevant decay paths and energies. The nuclear states are grouped into two rotational bands, which are labeled by their bandheads: $5/2$ [633] (ground state) and $3/2$ [631] (isomeric state). The total spectrum in the energy range up to 60 keV is shown in the bottom. (b) Schematic of a magnetic microcalorimeter. A $\gamma$ ray is absorbed in a gold absorber. The heat is then transferred and measured by a $\mathrm{Ag}:{\mathrm{Er}}^{3+}$ paramagnetic sensor. A weak thermal link to the heat bath enables thermalization. (c) A persistent current $(I_p)$ circulates in the superconducting meander-shaped pickup coil polarizing the magnetic moment in the sensor. As the flux in a superconducting loop is conserved, a change of flux $\mathrm{\Delta }\mathrm{\Phi }$ driven by a temperature-induced change of magnetization induces an additional screening current ($\delta I$), which is read out as a voltage drop over the dc-SQUID.

Figure 2

Residual uncertainty of the calibration lines with respect to the literature values (see Table 1) before the quadratic correction. The residuals follow the quadratic polynomial, indicating that quadratic correction is sufficient. Inset: residual energy differences after the quadratic correction. The standard deviation of the residual error is 0.76 eV.

Figure 3

Line shape of the 29.2 keV doublet. The red curve represents the fit of the 29 190 eV line, and the blue curve represents the fit of the 29 182 eV line. The branching ratio $b_{29}$ and the isomer energy ($E_{\mathrm{is}}$) can be extracted directly from this fit. The inset shows a two-dimensional plot of ${\chi }^2$ as a function of branching ratio and the isomer energy. The white dashed lines point to the fitted $E_{\mathrm{is}}$ and $b_{29}$ values.

Figure 4

MMC spectra of the 29 and 42 keV doublets. The ${}^{237}\mathrm{Np}$ contamination leads to a weak signal [29378.6(18) eV] which overlaps the 29.4 keV line (see the Supplemental Material [35]).

Figure 5

Isomer energies $E_{\mathrm{is}}$ measured in this study compared to previous experiments using $\gamma$ spectroscopy. The green and red faded areas represent the isomer energy reported in [22, 24], respectively, with their corresponding uncertainties. Error bars for our $E_{\mathrm{is}}$ represent the root sum square of statistical and systematic uncertainty.