Nuclear Excitation by Two-Photon Electron Transition

A new mechanism of nuclear excitation via two-photon electron transitions (NETP) is proposed and studied theoretically. As a generic example, detailed calculations are performed for the $E1E1$ $1s2s{}^1{S}_0\to 1s^2{}^1{S}_0$ two-photon decay of a He-like ${}^{225}{\mathrm{Ac}}^{87+}$ ion with a resonant excitation of the $3/2+$ nuclear state with an energy of 40.09(5) keV. The probability for such a two-photon decay via the nuclear excitation is found to be $P_{\mathrm{NETP}}=3.5\times {10}^{-9}$ and, thus, is comparable with other mechanisms, such as nuclear excitation by electron transition and by electron capture. The possibility for the experimental observation of the proposed mechanism is thoroughly discussed.

Figure 1

The mechanism of the nuclear excitation by two-photon electron transition as here explained for a He-like ${}^{225}{\mathrm{Ac}}^{87+}$ ion. The initial state (left panel), which is characterized by the $1s2s{}^1{S}_0$ electronic state and nuclear GS, decays into the final state (right panel), where both the electrons and nucleus are in their ground states $1s^2{}^1{S}_0$ and GS, respectively, via the intermediate cascade state (middle panel) with the nucleus being in the ES. The emitted photons ${\gamma }_1$ (electron decay photon) and ${\gamma }_2$ (nuclear fluorescence photon) are depicted by wavy lines with arrows.

Figure 2

Feynman diagrams that represent the nuclear excitation during the two-photon electron transition from an initial state $a_2$ to a final state $a_1$. The double lines indicate the electron wave functions and electron propagator in the Coulomb field of the nucleus, the heavy lines denote the nucleus in its ground and excited states, and the internal wavy line stays for the photon propagator. The emission of the electron decay photon ${\gamma }_1$ is depicted by the wavy line with the outgoing arrow.

Figure 3

$1s2s{}^1{S}_0\to 1s^2{}^1{S}_0$ two-photon differential rate plotted as a function of the reduced energy (sharing fraction) $y$ for the He-like ${}^{225}{\mathrm{Ac}}^{87+}$ ion. The NETP resonances are emphasized by the dotted lines.

Figure 4

The overall intensity produced by the decay of the $1s2s{}^1{S}_0$ level (solid line) is compared with the intensity of nuclear fluorescence ${\gamma }_2$ photons (dashed line), which are plotted as functions of time in arbitrary units.