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arXiv:1105.4620 · Comptes Rendus Physique

Some applications of the Faddeev–Yakubovsky equations to the cold-atom physics

Jaume Carbonell, Arnoldas Deltuva, Rimantas Lazauskas

Published Jan 1, 2011• 6 citations
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Abstract

We present some recent applications of the Faddeev–Yakubovsky equations in describing atomic bound and scattering problems. We consider the scattering of a charged particle X by atomic hydrogen with special interest in X = p , e ± , systems of cold bosonic molecules and the bound and scattering properties of N = 3 and N = 4 atomic 4 He multimers.

DOI
10.1016/j.crhy.2010.12.001

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We present some recent applications of the Faddeev–Yakubovsky equations in describing atomic bound and scattering problems. We consider the scattering of a charged particle X by atomic hydrogen with special interest in X = p , e ± , systems of cold bosonic molecules and the bound and scattering properties of N = 3 and N = 4 atomic 4 He multimers.
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Cluster expansion of the many-body Schr\"odinger wave function is manifested through the projected Faddeev-Yakubovsky equations. It is shown that using these equations one can formulate a systematic expansion for the wave function of finite systems in a translational invariant manner. The solution of the N-body problem at a given order becomes equivalent to solving the few-body Faddeev-Yakubovsky equations. The first two orders in this expansion are given explicitly and then solved for the case of N bosons interacting through the nucleon-nucleon Afnan-Tang S3 and Malfliet-Tjon MT-V potentials.
This review examines the numerous studies performed in recent years on atomic processes involving cold hydrogen atoms in the gas phase and at a surface. The term cold atom denotes the range of relative collision energies E < 10 meV (correspondingly, ultracold atoms have E 1 meV). This corresponds to the temperature range of tens (or units) of kelvins. Three main fields of study in which extensive experimental programs have been realized are treated: the study of collision processes involving hydrogen atoms, which are of astrophysical interest; the study of elastic atom-molecule scattering at ultralow energies; and studies on the problem of condensed hydrogen. The fundamental technical means of realization and the results obtained from the studies are discussed.