BOUND POLARON IN A NARROW-BAND POLAR CRYSTAL

The ground-state energy of a bound polaron in a narrow-band polar crys tal (such as a metal oxide) is studied using variational wave function s. We use a Frohlich-type Hamiltonian on which the effective mass appr oximation has not been effected and in which a Debye cutoff is made on the phonon wave vectors. The wave functions that are used are general enough to allow the existence of a band state and of a self-trapped s tate and are reliable in the nonadiabatic limit. We find that three gr ound states are possible for this system. First, for small electron-ph onon coupling, moderate bandwidth, and shallow impurities, the usual e ffective-mass hydrogenic ground state is found. For a narrow bandwidth and a deep defect, a collapsed state is predicted in which the polaro n coincides with the position of the defect. Finally, for moderate ele ctron-phonon coupling, narrow bandwidth, and a very weak defect, a sel f-trapped polaron in a hydrogenic state is predicted. Our conclusions are presented as asymptotic expansions and as phase diagrams indicatin g the values of the parameters for which each phase can be found.