Theory of Hyperspherical Sturmians for Three-Body Reactions

G GASANEO; D MITNIK; A L FRAPICCINI; F D COLAVECCHIA; J M RANDAZZO

JOURNAL OF PHYSICAL CHEMISTRY A

AMER CHEMICAL SOC

Año: 2009 p. 14573 - 14582

1089-5639

In this paper we present a theory to describe three-body reactions. Fragmentation processes are studied bymeans of the Schro¨dinger equation in hyperspherical coordinates. The three-body wave function is written asa sum of two terms. The first one defines the initial channel of the collision while the second one describesthe scattered wave, which contains all the information about the collision process. The dynamics is ruled byan nonhomogeneous equation with a driven term related to the initial channel and to the three-body interactions.A basis set of functions with outgoing behavior at large values of hyperradius is introduced as products ofangular and radial hyperspherical Sturmian functions. The scattered wave is expanded on this basis and thenonhomogeneous equation is transformed into an algebraic problem that can be solved by standard matrixmethods. To be able to deal with general systems, discretization schemes are proposed to solve the angularand radial Sturmian equations. This procedure allows these discrete functions to be connected with thehyperquatization algorithm. Finally, the fragmentation transition amplitude is derived from the asymptoticlimit of the scattered wave function.