Electronic K x rays emitted from muonic atoms: An application of relativistic density-functional theory

Abstract

We develop a method using relativistic density-functional theory with a self-interaction correction, which is simple and fast yet has reasonable accuracy. A comparison with measured $K\ensuremath{\alpha}$ lines and their hypersatellites of several atoms, from low $Z$ to high $Z$, reveals that the relativistic local density approximation is suitable for $K\ensuremath{\alpha}$ lines. In contrast, the relativistic local spin density approximation with a self-interaction correction is better for ${K}^{h}\ensuremath{\alpha}$ hypersatellites. Compared with the nonrelativistic density-functional theory, we found that the relativistic effect is significant (about 100 eV) even for middle-$Z$ atoms, such as Cu. The screening effects, from inner shell to outer shell, and the conduction band, are also discussed. The present paper provides all the transition lines of muonic atoms, which can be used to narrow down the possible transitions by comparing them with the measurements.