Complex coordinate calculations of resonances in N-electron atoms

✍ Scribed by B. R. Junker

• Publisher: John Wiley and Sons
• Year: 1978
• Tongue: English
• Weight: 554 KB
• Volume: 14
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560140406

✦ Synopsis

Abstract

We present a discussion of the functional dependences of the wave functions for bound, resonant, and scattering states on the radial coordinate ρ and the rotation angle α in the complex coordinate method. We conclude that for bound states and resonances, ρ and α are constrained to appear in the wave functions only in the for ρ exp(__i__α). On the other hand, this constraint is not obtained for the scattering states since the energy of the scattering states depends on α. In addition we suggest a partitioning of the resonant wave function into two parts—a boundlike or “Q‐space” part and a scattering like or “P‐space” part. With these concepts one can incorporate physical insight into the choice of configurations as one does in other methods and can apply the complex coordinate method to many electron systems with an expected rate of convergence similar to other techniques. Its advantages are that a single calculation yields the position and width of the resonance, only square integrable functions are used, only a solution of a straightforward eigenvalue problem is required unlike some methods, arbitrarily accurate target states are easily incorporated, and polarization terms can easily be explicitly included. Variational calculations for the position and width of the lowest ^2^S resonance in the negative helium ion are reported using trial wave functions containing 39, 43, 55, 24, and 32 “P‐space” configurations, respectively. Values of 19.387 eV and 12.13 meV are obtained for the position and width, respectively, for the resonance over a range in the rotation angle of almost two orders of magnitude. One also finds that inclusion of free‐particle‐like basis functions improves the representation of the scattering states.