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Asymptotic completeness for the impact parameter approximation to three particle scattering

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Asymptotic completeness for the impact parameter approximation to three particle scattering ANNALES DE L’I. H. P., SECTION A GEORGE A. HAGEDORN Asymptotic completeness for the impact parameter approximation to three particle scattering Annales de l’I. H. P., section A, tome 36, no 1 (1982), p. 19-40. <http://www.numdam.org/item?id=AIHPA_1982__36_1_19_0> © Gauthier-Villars, 1982, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A », implique l’accord avec les conditions générales d’utilisation (http://www. numdam.org/legal.php). Toute utilisation commerciale ou impression systé- matique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 19 Asymptotic completeness for the impact parameter approximation to three particle scattering George A. HAGEDORN (*) Department of Mathematics Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061 Ann. Inst. Henri Poincaré, Vol. XXXVI, n° 1, 1982, Section A : Physique théorique. ABSTRACT. - We prove a theorem of Yajima on the asymptotic complete- ness of the impact parameter model in three body scattering. The proof depends on developing suitable analogs of the Faddeev equations which allow one to study time dependent Hamiltonians directly. With these equations for the propagator, the physics of the problem is more trans- parent than it is in Yajima’s proof. As a corollary of our methods we show that for high impact velocities, the Faddeev-Watson multiple scattering series is convergent for the impact parameter approximation. 1. INTRODUCTION The impact parameter model in three body quantum scattering is supposed to approximate a system in which the masses of two of the three particles are very much greater than the mass of the third. The extremely massive particles ar

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