Impact of the electron environment on the lifetime of the ${}^{229}{\mathrm{Th}}^m$ low-lying isomer

The question of the lifetime of the ${}^{229}{\mathrm{Th}}^m$ low-lying isomer is considered in light of current experimental research. A strong effect of the electron shell on lifetime is demonstrated, depending on the energy of the isomer. Calculations are performed within the framework of the multiconfiguration Dirac-Fock method. The calculated lifetime ranges from around 1 min down to ${10}^{-5}$ s. Prospects for further experimental research of the isomer are discussed.

Figure 1

Feynman graphs for the decay of the isomer via (a) the radiative decay and (b) BIC mechanisms. The ground and excited states of the nucleus are denoted by $g$ and ${\mathit{ex}}^{*}$, respectively. The initial, intermediate, and final atomic states are denoted by $i,\ell$, and $f$, respectively.

Figure 2

ICC ${\alpha }_{7s}^{M1}$ multiplied by the factor ${10}^{-8}$ for the $7s$ shell of the Th atom for the transition energy near the threshold. Calculations were made without regard for the hole in the $7s$ shell after conversion (solid line), with regard for the hole in the FO approximation (dashed line), and with regard for the hole in the SCF approximation (dot-dashed line).

Figure 3

Three types of interaction of the electron configurations: (a) mixing of the one-electron configurations due to the kinetic energy operator and Coulomb interaction with the nucleus, (b) one-electron mixing due to interaction with the electron core, and (c) interaction with multielectron configurations accompanied by the core excitation.

Figure 4

Spectrum of the primary photons.

Figure 5

Histogram for the spectrum of the primary photons.

Figure 6

Spectrum of the secondary photons.

Figure 7

Histogram for the spectrum of the secondary photons.

Figure 8

Resulting spectrum of the delayed photons.

Figure 9

Histogram for the resulting spectrum of the delayed photons.