Coexistence of Bound and Virtual-bound States in Shallow-core to Valence Spectroscopies

We develop the theory for shallow-core to valence excitations when the multiplet spread is larger than the core-hole attraction, e.g., if the core and valence orbitals have the same principal quantum number. This results in a cross-over from bound to virtual-bound excited states with increasing energy and in large differences between dipole and high-order multipole transitions, as observed in inelastic x-ray scattering. The theory is important to obtain ground state information from x-ray spectroscopies of strongly correlated transition metal, rare-earth and actinide systems.