Relaxation and decay of an atom with a core-hole

Relaxation of an atom in which a core electron has been excited or removed into the continuum can lead to a fully relaxed core-hole state. This process competes with core-hole decay from an unrelaxed atom. The competition is studied here by treating excitation and decay in a uniform manner. It is shown that a resonantly excited core-hole state and a corehole shakeup state which relaxes and subsequently undergoes radiationless decay produces an Auger electron spectrum which is identical with the spectrum from decay of a fully relaxed core-hole state.