Existence and Born-Oppenheimer asymptotics of the total scattering cross-section in ion-atom collisions. - Archive ouverte HAL Access content directly
Book Sections Year : 2001

Existence and Born-Oppenheimer asymptotics of the total scattering cross-section in ion-atom collisions.

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Abstract

We prove the finitness of the total scattering cross-section for ion-atom collisions with an initial channel given by a simple eigenvalue of the internal Hamiltonian describing the neutral cluster, i.e. the atom. Under more restrictive assumptions, we show that some effective interaction in the Born-Oppenheimer approximation is precisely of order O(|x|^{-4}) in the distance between the mass centers of the two clusters. We then extract the leading term of the scattering cross-section in the Born-Oppenheimer limit. Paper published in: "Long time behaviour of classical and quantum systems", proceedings of the Bologna AP-TEX international conference, sept. 1999, edité par A. Martinez et S. Graffi.
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hal-03213428 , version 1 (30-04-2021)

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Thierry Jecko, Markus Klein, Xue Ping Wang. Existence and Born-Oppenheimer asymptotics of the total scattering cross-section in ion-atom collisions.. Long Time Behaviour of Classical and Quantum Systems: Proceedings of the Bologna Aptex International Conference, Bologna, Italy 13-17 September 1999, 2001, Series on Concrete and Applicable Mathematics, ⟨10.1142/4640⟩. ⟨hal-03213428⟩
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