SIMPLE SPECTRAL WIDTH ESTIMATION FORMULA EXTRACTED FROM REAL ENERGY SHAPE RESONANCE WAVE-FUNCTIONS

A formula for estimating spectral widths of narrow or moderately broad isolated shape resonances is established, by simple arguments based o n the three-turning point WKB theory. This formula enables one to hand le all resonances of the potential at one go, by only using as input r eal-energy wavefunctions obtained from a standard Hamiltonian-matrix d iagonalization. For its derivation, the ratio between the probability amplitude computed near the equilibrium position and that defined asym ptotically, both referring to maxima of the (unnormalized) resonance w avefunction, is of major importance. The performance of the formula is demonstrated on the unimolecular dissociation of the ground electroni c state of the exotic BeH2+. Comparison is made with results from a co mplex-energy propagation and a previous WKB analysis.