By Yu.N. Demkov, V.N. Ostrovskii
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Additional resources for Zero-Range Potentials and Their Applications in Atomic Physics
Example text
L .. M .. c. (Z. ) L i,j ~] ] ~ ~] ~ ~] s .. 7) we have used the following notations: K.. z 2 ¢. ~ ¢. z ¢. ¢. 8) M.. ¢. s .. dr. ~] ~] ~ ~K ~K ¢. dr ]K - ]K - All these integrals can be solved in terms of elementary functions. 7) for the polarizability of a molecule has been obtained for arbitrary positions of the centers. We shall point out that in earlier calculations of the polarizability, which used a a-function model for the atomic potentials, i t was essential to assume one-dimensional motion of the electron in the molecule (for references, see (63)).
This state is not stable and, under the influence of small perturbation, it becomes a resonance (quasi-stationary state) as shown by Beregi et al. (38). As v + ± 00, the poles can move asymptotically to fixed points in the complex k plane. Pairs of the poles moving in the lower half-plane may describe semi-circular trajectories symmetric with respect to the imaginary axis (similar trajectories were obtained by Ferreira and Teixeira (53) for £ = 2 states in the cutoff Coulomb field). Chapter 3 ZERO-RANGE POTENTIALS FOR MOLECULAR SYSTEMS.
For large all poles move to infinity. This result is different from the previous one, where a was fixed and R was changing, since then the trajectories could tend to finite point (K = a" K = 0) as R + 00. The trajectories of the poles are in agreem~nt with the general picture obtained earlier in Chapter 2. Even for a relatively simple problem of scattering on a system of two ZRPs the S-matrix is of a complicated structure. We shall emphasize here that the existence of this structure is entirely due to multiple scattering of the projectile on the ZRPs (for multiple scattering see Sec.