Nuclear Excitation by Free Muon Capture

Efficient excitation of nuclei via exchange of a real or virtual photon has a fundamental importance for nuclear science and technology development. Here, we present a mechanism of nuclear excitation based on the capture of a free muon into the atomic orbits ($\mathrm{NE}\mu \mathrm{C}$). The cross section of such a proposed process is evaluated using the Feshbach projection operator formalism and compared to other known excitation phenomena, i.e., photoexcitation and nuclear excitation by electron capture (NEEC), showing up to 10 orders of magnitude increase in cross section. $\mathrm{NE}\mu \mathrm{C}$ is particularly interesting for MeV excitations that become accessible thanks to the stronger binding of muons to the nucleus. The binding energies of muonic atoms have been calculated introducing a state of the art modification to the Flexible Atomic Code. An analysis of experimental scenarios in the context of modern muon production facilities shows that the effect can be detectable for selected isotopes. The total probability of $\mathrm{NE}\mu \mathrm{C}$ is predicted to be $P\approx 1\times {10}^{-6}$ per incident muon in a beam-based scenario. Given the high transition energy provided by muons, $\mathrm{NE}\mu \mathrm{C}$ can have important consequences for isomer feeding and particle-induced fission.

Figure 1

Nuclear excitation by muon capture ($\mathrm{NE}\mu \mathrm{C}$): the capture of a free muon leads to a resonant excitation of the nucleus. The excited nucleus can subsequently decay towards lower levels reaching a long-lived state, i.e., isomer feeding. Another possibility is present if the excitation of the nucleus is in resonance with the giant dipole (GDR) or quadrupole resonances (GQR), and the latter is above the fission barrier: the nucleus can undergo a prompt fission induced by $\mathrm{NE}\mu \mathrm{C}$.

Figure 2

Isotopes matching the search criteria in case of $E2$ transition. Only the nuclear transitions with a $B\downarrow (E2)>10\mathrm{W}.\mathrm{u}.$ have been included in the plot. The color of the markers indicates the closest shell allowing $\mathrm{NE}\mu \mathrm{C}$. Vertical black lines group several isotopes of the same element.

Figure 3

Accuracy assessment of the fac. Muonic binding energies computed with the fac ($E_{\mathrm{FAC}}$) are compared with those of Ref. [43] ($E_{\mathrm{ref}}$). The color of the marker indicates the muonic state.