AVOIDING LONG PROPAGATION TIMES IN WAVE-PACKET CALCULATIONS ON SCATTERING WITH RESONANCES - A NEW ALGORITHM INVOLVING FILTER DIAGONALIZATION

We present a new and more efficient implementation of a hybrid approac h to computing the solution of scattering problems affected by resonan ces. In the computationally expensive part of the calculation, wave pa cket propagation is used to obtain the time-dependent wave function Ps i(t) up to some time tau at which direct scattering is over. This part is made efficient by using a recently introduced modification for the absorbing boundary conditions evolution operator which allows the use of real operator algebra if the initial wave function is chosen real. In the second part of the calculation, filter diagonalization is used to efficiently obtain the energies, widths, and expansion coefficient s of resonances needed to describe the long time behavior of the scatt ering wave function. This part is made efficient by using a recently i ntroduced algorithm which avoids the storage of energy-dependent basis functions. We demonstrate the application of the method to a two-dime nsional reactive scattering problem. (C) 1997 American Institute of Ph ysics.