Electric-dipole-forbidden transitions of nuclei interacting with super-intense laser fields are investigated by considering stable isotopes with suitable low-lying first excited states. Different classes of transitions are identified, and all magnetic sublevels corresponding to the near-resonantly driven nuclear transition are included in the description of the nuclear quantum system. We find that large transition matrix elements and convenient resonance energies qualify nuclear M1 transitions as good candidates for the coherent driving of nuclei. We discuss the implications of resonant interaction of intense laser fields with nuclei beyond the dipole approximation for the controlled preparation of excited nuclear states and important aspects of possible experiments aimed at observing these effects.
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