Ultra-low energy elastic scattering in a system of three He atoms

Published Jan 1, 2002• 0 citations

Abstract

Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold. 1

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Published Jan 1, 2002• 0 citations

OpenAlex

Abstract

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Four-body system of

{}^4\mathrm{He}

atoms: Dimer-dimer scattering

{}^4\mathrm{He}

atoms. The potential is gradually softened such that rigorous four-body equations for bound and scattering tates can be accurately solved in the momentum-space framework, and the results are extrapolated back to the limit of the original potential. Linear correlations between three- and four body quantities are observed, and the accuracy of the procedure is improved by extrapolating in one of the three-body quantities. Results for the

{}^4\mathrm{He}

tetramer ground and excited state binding energies and atom-trimer scattering agree well with at least some of earlier determinations and shed light on the existing disagreements. An additional case of the Phillips correlation line is established for the dimer-dimer scattering length. The trimer production rate via the ultracold two-dimer collisions is estimated, it exhibits significant finite-range effects despite the weak binding of the dimer.

a

and we compare our results to the universal zero-range form deduced by Efimov, $ak\mathrm{cot}\ensuremath{\delta}={c}_{1}(ka)+{c}_{2}(ka)\mathrm{cot}[{s}_{0}\mathrm{ln}({\ensuremath{\kappa}}_{*}a)+\ensuremath{\phi}(ka)]$, for selected values of the three-body parameter ${\ensuremath{\kappa}}_{*}$. Using the parametrization of the universal functions ${c}_{1},{c}_{2},\ensuremath{\phi}$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter ${\ensuremath{\kappa}}_{*}$.

{\mathit{e}}^{+}

), p+(p\ensuremath{\mu}), and d+(d\ensuremath{\mu}). A large negative value of the even-parity p+(p\ensuremath{\mu}) scattering length indicates the presence of a virtual state near threshold.