Journal of Luminescence 31 & 32(1984) 45-49 45 North-Holland, Amsterdam TWO-CENTER OPTICAL TRANSITIONS IN CONDENSED MATTER Michael STAVOLA AT&T Bell Laboratories, Murray Hill, New Jersey 07974 D. L. Dexter’s contributions to the theory of two-center electronic and vibronic transitions are reviewed. Experimental results are presented which illustrate the main features of the theoretical ideas. The use of two-center vibronic transitions as a local infrared spectroscopy is also described. In 1960 Varsanyi and Dieke 1 observed that in PrCl 3, two Pr 3~ ions could absorb a single photon with an energy equal to the sum of the single ion transition energies. This is surprising because the 4f electrons of the rare earth ions are well shielded and therefore, a product wave function, ~8a4b for ions A and B, is a good approximation. The radiative dipole moment operator, because it is a sum of one electron operators, must give a pair transition matrix element of zero for such product wave functions. The ground work for the solution to this puzzle had been laid in Dexter’s earlier work on energy transfer.2 Dexter explained Varsanyi, and Dieke’s observation by correcting the product wave functions with perturbation theory to include the electron-electron Coulomb interactions between ions.3 The radiative dipole matrix element between the corrected wave functions is then non-zero for ion-pair transitions. The corrected wave function for the doubly excited state, for example, would be <a”b”IHAB lab’> (1) ~ bb ~ — C~’÷ C~ — e2 where HAB — — ~ r,(A) — — Here a’b’ denotes the doubly excited state, a”b” denotes an intermediate state, the C’s are the energies of these states, r,(A) are the electronic coordinates for the rare earth ion A; and similarly for i~(B). Typically the interaction Hamiltonian is expanded in a multipole expansion, the first term of which is the dipole-dipole interaction. One term of the radiative dipole matrix element (there are four such terms) would be, ~ <a’I~e?(A)Ia’><O0lHABIa”b”>/(e~+eb). (2) The dipole-dipole interaction falls off like hR6 where R is the separation between centers so that the interaction between ions is short ranged. 0022—2313/84/$03.00© Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)