Fe3+ paramagnetic ion in {\alpha}-Al2 O3 energy levels revisited.   Application to a 31 GHz Maser proposal
  The molecular structure of a 3d 5 configuration ion in a trigonal ligand field is theoretically established on the basis of the 252\times252 complete energy matrice. The optical absorption and the electron paramagnetic resonance spectra of the Fe3+ ion in the sapphire crystal ({\alpha}-Al2 O3) have been studied by diagonalizing the complete energy matrice. The calculated results are in very good agreement with previous experimental observations. The strength of the transition probabilities between pairs of the energy levels have been calculated to determine the possibility to achieve a population inversion in the ground state by applying optical pumping to the crystal. Preliminary results based on the computed transition parameters and on the maser rate equations model show that a 31 GHz maser signal can be effectively generated depending on the cryogenic resonator design. 
M. Mrad, P. Y. Bourgeois, Y. Kersal\'e and V. Giordano
physics.chem-ph physics.atom-ph