A direct method for determining time delays for scattering processes is developed using theRhyphen;matrix propagation method. The procedure involves the simultaneous generation of the globalRmatrix and its energy derivative. The necessary expressions to obtain the energy derivative of theSmatrix are relatively simple and involve many of the same matrix elements required for theRhyphen;matrix propagation method. This method is applied to a simple model for a chemical reaction that displays sharp resonance features. The test results of the direct method are shown to be in excellent agreement with the traditional numerical differentiation method for scattering energies near the resonance energy. However, for sharp resonances the numerical differentiation method requires calculation of theShyphen;matrix elements at many closely spaced energies. Since the direct method presented here involves calculations at only a single energy, one is able to generate accurate energy derivatives and time delays much more efficiently and reliably.
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