Scattering of Ions by Polarization Forces

Resonance and Threshold Phenomena in Low-Energy Electron Collisions with Molecules and Clusters

“…At very low energies the Wigner threshold behaviour (/ E lÀ1/2 ) is observed while towards high energies the respective unitary limit l ¼ (2lþ1)/k 2 is reached. It is interesting to note (see also Vogt and Wannier, 1954;Klots and Compton, 1996) that the total VW cross-section VW,tot (E) is found to agree with the classical Langevin cross-section Lang (E) ¼ 2 [ /(2E)] 1/2 (Langevin, 1905) to within 5% for energies above about 4 meV (more generally for E > 0.08 a.u.). Towards lower energies the ratio VW,tot (E)/ Lang (E) continuously rises towards the value 2 which is reached in the limit of zero energy, as illustrated in Fig.…”

“…(37) of Vogt and Wannier (1954), was derived from the theory of Mathieu functions. For the s-wave contribution Klots (1976) proposed a simple expression…”

Electron capture by finite-size polarizable molecules and clusters

“…Electron attachment to polarizable neutral molecules is often treated in terms of the Vogt-Wannier model for electron capture [1][2][3][4] in an interaction potential V(r) = Àe 2 a/2r 4 ( 1.1) where a is the polarizability of the neutral molecule and r is the center-of-mass distance between the molecule and the electron. Obviously, this potential is realistic only for large r. The accommodation of the incoming electron by the molecular electrons and the nuclear frame, through ''electron-phonon coupling'' or ''intramolecular vibrational redistribution (IVR)'', at small r requires a different treatment without separation of electronic and nuclear coordinates, e.g.…”

A New Nonrelativistic Investigation for the Lowest Excitations States of Interactions in One-Electron Atoms, Muonic, Hadronic and Rydberg Atoms with Modified Inverse Power Potential

“…[23,24,25]. This potential become useful for describes interactions in one-electron atoms, muonic, hadronic and Rydberg atoms; photo decay of excited states, when gaseous ions or electrons move through a gas whose molecules are not too large and we have also for Dirac equation for a spin 2 [23,24,25].…”