Coordinate-space Faddeev-Hahn-type approach to three-body charge-transfer reactions involving exotic particles

Abstract

Low-energy muon-transfer cross sections and rates in collisions of muonic atoms with hydrogen isotopes are calculated using a six-state close-coupling approximation to coordinate-space Faddeev-Hahn-type equations. In the muonic case satisfactory results are obtained for all hydrogen isotopes and the experimentaly observed strong isotopic dependence of transfer rates is also reproduced. A comparison with results of other theoretical and available experimental works is presented. The present model also leads to good transfer cross sections in the well-understood problem of antihydrogen formation in antiproton-positronium collision.

Integral–differential equations approach to atomic three-body systems

“…Recently, a few-body quantum-mechanical descriptions of charge-transfer reactions within modified Faddeev equations, specifically, Faddeev-Hahn (FH) equations, have been formulated [7]. In this previous study a close-coupling method was applied, which led to the expansion of the systemÕs wave function components into eigenfunctions of the subsystem (target) Hamiltonians providing us with a set of onedimensional integral-differential equations after partial-wave projection was applied.…”

Three-Body Protonium Formation in a Collision Between a Slow Antiproton ( $${\bar{\rm p}}$$ p ¯ ) and Muonic Hydrogen: $${{\rm H}_{\mu}}$$ H μ —Low Energy $${\bar{\rm p} + ({\rm p} \mu^-)_{1s} \rightarrow (\bar{\rm p} {\rm p})_{1s} + \mu^-}$$ p ¯ + ( p μ - ) 1 s → ( p ¯ p ) 1 s + μ - Reaction

“…Moreover, Ψ 1 (r 23 , ρ 1 ) is quadratically integrable over the variable r 23 , and Ψ 2 (r 13 , ρ 2 ) over the variable r 13 . To define |Ψ l , (l = 1, 2) a set of two coupled Faddeev-Hahn-type equations can be written [5][6][7]:…”

Low-energy direct muon transfer from H to Ne10+, S16+and Ar18+using the two-state close-coupling approximation to the Faddeev-Hahn-type equation

“…[20][21][22] which was used for the study of muon transfer from muonic hydrogen atoms to lighter charged nuclei H + , He 2+ , Li 3+ , C 6+ , and O 8+ . In the dynamical equations in Refs.…”