Resonant Electronic-Bridge Excitation of the ${}^{235}\mathrm{U}$ Nuclear Transition in Ions with Chaotic Spectra

Electronic-bridge excitation of the 76 eV nuclear isomeric state in ${}^{235}\mathrm{U}$ is shown to be strongly enhanced in the ${\mathrm{U}}^{7+}$ ion, potentially enabling laser excitation of this nucleus. This is because the electronic spectrum has a very high level density near the nuclear transition energy that ensures the resonance condition is fulfilled. We present a quantum statistical theory based on many-body quantum chaos to demonstrate that typical values for the electronic factor increase the probability of electronic bridge in ${}^{235}{\mathrm{U}}^{7+}$ by many orders of magnitude. We also extract the nuclear matrix element by considering internal conversion from neutral uranium. The final electronic-bridge rate is comparable to the rate of the ${\mathrm{Yb}}^{+}$ octupole transition currently used in precision spectroscopy.

Figure 1

Feynman diagram of the considered electronic-bridge process. The double line represents the nucleus, while the dashed line is the hyperfine-$E3$ interaction. In our excitation scheme the electronic state $t$ is the lowest $6p^{4}5f[5/2{]}^{-}$ level and $i$ is the $6p^5[3/2{]}^{-}$ ground state.

Figure 2

$G_2$ calculated using Eq. (8) and a configuration interaction spectrum generated using ambit. For comparison, the value calculated with the statistical theory of many-body quantum chaos Eq. (12) is shown: $G_2=8.0\times {10}^6$ (dashed line).

Figure 3

Cumulative distribution function for ${\mathrm{\Gamma }}_{\mathrm{EB}}$ extracted from Fig. 2. Dashed line, the estimate of ${\mathrm{\Gamma }}_{\mathrm{EB}}$ from MBQC [Eq. (13)]; dotted line, linewidth of $E3$ clock transition in ${\mathrm{Yb}}^{+}$ [53].