Exciting inner shell electrons to a higher energy state is indeed possible through core-level photoemissions and Auger spectroscopy. The rarity of these transitions is explained by the Fermi Golden Rule, which indicates that the probability of such transitions is determined by a matrix element divided by the energy difference. Selection rules for atomic transitions do not prohibit these processes, allowing for their occurrence under specific conditions.
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so-crates said:Is it possible to excite the inner shell electrons to higher energy state? If not, why not? I'm aware of selection rules for atomic transitions and haven't come across anything that would indicate that those transitionss are forbidden