Attempt to optically excite the nuclear isomer in ${}^{229}\mathrm{Th}$

We aim to perform direct optical spectroscopy of the ${}^{229}\mathrm{Th}$ nuclear isomer to measure its energy and lifetime, and to demonstrate optical coupling to the nucleus. To this end, we develop ${}^{229}\mathrm{Th}$-doped ${\mathrm{CaF}}_2$ crystals, which are transparent at the anticipated isomer wavelength. Such crystals are illuminated by tunable VUV undulator radiation for direct excitation of the isomer. We scan a $\pm 5\sigma$ region around the assumed isomer energy of 7.8(5) eV and vary the excitation time in sequential scans between 30 and 600 seconds. Suffering from an unforeseen strong photoluminescence of the crystal, the experiment is sensitive only to short radiative isomer lifetimes. In our data analysis, we assume that radiative decay is the dominant de-excitation channel. Further, we suppose that the luminescence background has a super-Poissonian character and may be represented as a sum of a constant term and several decaying exponents whose time constants do not depend on the wavelength of the excitation. With these assumptions, we can exclude an isomer with lifetime between 0.2 and 1.1 s and energy between 7.5 and 10 eV at the 95% confidence level.

Figure 1

The experimental setup, shown here as a cut in the horizontal plane, which includes the path of the excitation beam (dotted line).

Figure 2

Wavelength-dependent parameters of the experiment. (a) Photon flux on the crystal, measured with a Cs-I photocathode and normalized to a beam current of 100 mA. As a conservative estimate (dashed line), we assume a value of $4\times {10}^{14}$ photons per second and 100 mA beam current across the entire scan range of our study, which covers 124–242 nm. (b) Spectral line shape of the excitation light measured at five different nominal wavelengths (dots) and fit functions according to Eq. (2) (lines). (c) Quantum efficiencies of the PMT models used in the experiment. (d) Transmission through a 4.1-mm thick ${\mathrm{CaF}}_2$ crystal; adapted from Ref. [33]. (e) Number of Cherenkov photons emitted per disintegration of ${}^{229}\mathrm{Th}$; adapted from Ref. [33].

Figure 3

A typical data set showing the light emission of the crystal after excitation. For this specific data set, we used a Cs-I PMT model R10454, an excitation wavelength of ${\lambda }_0=148\mathrm{nm}$, excitation and detection times of 300 s, and 100 ms bin length. An exponential decay fitted to the long-term component is shown as well. Inset: Magnification of the short-term decay on a linear scale.

Figure 4

Contour plots representing cross sections of the confidence region for ${\tau }_1$, ${\tau }_2$, and ${\tau }_3$ by several planes with fixed ${\tau }_3$. Here, $\alpha$ describes the confidence level at which the combination $({\tau }_1,{\tau }_2$, ${\tau }_3)$ lies outside the respective contour. We used the basic model (7) for these estimations with fixed ${\tau }_L=68.75\text{s}$. The procedure of estimation of the confidence region in the $({\tau }_1,{\tau }_2$, ${\tau }_3)$-space is similar to the one described in Sec. 4e for the $({\lambda }_{is},{\mathrm{\Gamma }}_{sp})$ space.

Figure 5

Coefficients $C_{i,\alpha }$ for various decay curves corresponding to the best fits with model (7) with three nonzero short-term decay constants ${\gamma }_{\alpha }$ given in (11), one long-term component ${\gamma }_L$, and one time-independent term, as a function of the nominal wavelength ${\lambda }_0$ of the excitation light. The example curves shown here are obtained with a Cs-I photocathode, where red diamonds (black circles) show a data set with time bins of 1 s (100 ms).

Figure 6

A contour plot of the parameter $\alpha$ in the plane of isomer wavelength ${\lambda }_{is}$ and bare decay rate ${\mathrm{\Gamma }}_{sp}$. The parameter $\alpha$ describes the level at which a pair of parameters $({\lambda }_{is},{\mathrm{\Gamma }}_{sp})$ is excluded by our measurements, see the text for details. To give an example, the innermost region can be excluded at the 99.9% level.