Higher virial coefficients in two and three dimensions: Planck-Larkin structure and Wigner-Kirkwood expansion

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Abstract
We derive three-particle higher-order sum rules in two dimensions in analogy with similar rules existing in three dimensions. We employ these rules to study the Planck-Larkin structure of the third cluster integral in the presence of three-particle processes like rearrangement scattering and breakup. In particular, in three dimensions we also show the cancellation between bound-state and continuum contributions at the Efimov point. As a byproduct we obtain a Wigner-Kirkwood-type expansion for the third virial coefficient in two and three dimensions.