Nonperturbative calculation of energies and widths of predissociative states of diatomic molecules

摘要

A nonperturbative theory of predissociation based upon an effective Hamiltonian is presented. For a model diatomic system in which a (boundhyphen;state) Morse potentialhyphen;energy curve is crossed by an (unboundhyphen;state) exponential potentialhyphen;energy curve, the exact effective Hamiltonian may be obtained in high precision for any well behaved interaction potential. The real and imaginary parts of the eigenvalues of the effective Hamiltonian give the (shifted) energies and widths, respectively, of the predissociative states. Numerical results are obtained and compared with both a semiclassical approximation and those derived from solutions of coupled Schrouml;dinger equations. In the weakhyphen;coupling regime the agreement between the present method and semiclassical results is good, and better in general than the coupledhyphen;equations results, which apparently suffer from instability problems. For couplings of intermediate strength, the semiclassical method breaks down, as do fully quantumhyphen;mechanical firsthyphen;order perturbation approximations, as is demonstrated by comparison with the converged nonperturbative results. Fixed points of the spectrum appear at lsquo;lsquo;resonancersquo;rsquo; values of the coupling strength which bring the exact energy eigenvalue into resonance with one of the adiabatic levels so that the imaginary part (level width) of the former vanishes. Thus beyond a critical coupling strength, stronger coupling enhances the stability of a resonance.