The phenomenon of multi-photon ionization of atoms has been studied, both theoretically and experimentally, for several decades. Intense laser beam devices are the apparatuses used for the experimental study of this phenomenon.
QUESTION:
Would it be possible to use similar excitation processes with nuclei, using "low energy" $\gamma$-photons in order to manufacture nuclear isomers for industrial and medical applications?
Energy differences between nuclear excitation states are usually of the order of the MeV so you would need a photon beam with at least this photon energy. Also there are much fewer "fine structure" states with nuclei than there are with atoms, so you need photons with exactly the right (resonant) energies to induce the desired excitations. Furthermore, intermediate excitation states have lifetimes of the order of 10⁻¹² s, and I do not think you can achieve photon beam intensities so large that you have time to excite the nucleus further before it decays down to the ground state. These are all rather qualitative arguments as one would need to perform proper calculations to get the exact beam requirements, but they indicate that such a procedure would probably be highly impractical.
