New variants of many-particle Faddeev equations

B.E. Grinyuk

Hiroyuki Kamada, J. Golak

Willy Bierter

Vladimir M. Krasnopolsky, V. I. Kukulin

R. M. Adam, S. A. Sofianos

We use the assumption that the potential for the $A$-boson system can be written as a sum of pairwise acting forces to decompose the wave function into Faddeev components that fulfill a Faddeev type equation. Expanding these components in terms of potential harmonic (PH) polynomials and projecting on the potential basis for a specific pair of particles results in a two-variable integro-differential equations suitable for $A$-boson bound-state studies. The solution of the equation requires the evaluation of Jacobi polynomials ${P}_{K}^{\ensuremath{\alpha},\ensuremath{\beta}}(x)$ and of the weight function $W(z)$ which give severe numerical problems for very large $A$. However, using appropriate limits for $A\ensuremath{\rightarrow}\ensuremath{\infty}$ we obtain a variant equation which depends only on the input two-body interaction, and the kernel in the integral part has a simple analytic form. This equation can be readily applied to a variety of bosonic systems such as microclusters of noble gasses. We employ it to obtain results for $A\ensuremath{\in}(10\ensuremath{-}100)$ $^{87}\mathrm{Rb}$ atoms interacting via interatomic interactions and confined by an externally applied trapping potential ${V}_{\mathrm{trap}}(r)$. Our results are in excellent agreement with those previously obtained using the potential harmonic expansion method (PHEM) and the diffusion Monte Carlo (DMC) method.

Jaume Carbonell, Arnoldas Deltuva, Rimantas Lazauskas

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.