A new method, using the finite-difference boundary value method, is proposed for finding the wavefunctions and energies of shape-resonance states in atomic collisions. A numerical illustration is presented for the l = 50 states of OH (X2Π).
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Knowledge of the resonant states of two-body systems is important for understanding two-body col-hsions (since the phase shift changes rapidly as a function of energy at a resonance state \[1 \]) and for treating three-body collisions \[2\].O ther applications have been summarized by Dickinson and Bernstein \[3\]. Recently Jackson and Wyatt \[4\] reported a new method and reviewed previous methods for finding wavefunctions and energies of shape resonances** in atomic collisions, and since then new methods for calculating the energies of shape resonances have been proposed and illustrated by Johnson et al. \[5\] and Bain and Bardsley \[6\].A new method for finding wavefunctions and energies of shape resonances is presented in this article. This method combines the finite-difference boundary value method \[7\]* ** for solving the radial eigenvalue equation with ideas used * Supported in part by National Science Foundation grant no. GP 28684. ** Shape resonances (also called potential resonances and single-particle resonances) arise in a single-channel treat-ment of the scattering problem, whereas compound-state resonances (also called Feshbach resonances and core-excited resonances) require a multichannel treatment. In this note we are concerned only with the former. *** A program, written by the author, for performing cal-culations by the method of this reference is available as program no. 203 from Quantum Chemistry Program Ex-change, Chemistry Department, Indiana University.
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