Theory of Simultaneous Observation of Photoelectron and Emitted X-ray Photon in X-ray Emission Spectroscopy and Their Entanglement

We have theoretically investigated the character of entanglement between photoelectrons and emitted X-ray photons in XEPECS process which is a coincidence spectroscopy of photoelectrons and emitted X-ray photons. In the calculations, we used a three-electron sp-model consisting of an inner-shell 1s orbital and an outer-shell 2p orbital. We found that entanglement occurs between spin of photoelectrons and linear polarization of emitted X-ray photons, using the wavefunction of the whole system including the photon as well as the electron system. Furthermore, we calculated the degree of entanglement and found that it shows maximum at a particular angle of emitted X-ray photon.