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

Theory of simultaneous observation of photoelectron and emitted X-ray photon in X-ray emission spectroscopy and their entanglement