Angular Probability Distribution of Three Particles near Zero Energy Threshold

Details Angular Probability Distribution of Three Particles near Zero Energy Threshold Angular Probability Distribution of Three Particles near Zero Energy Threshold

2011-12-02

arxiv.org/abs/1112.0490v1

Physics

Mathematical Physics

Scientific paper

We study bound states of the 3--particle system in $\mathbb{R}^3$ described by the Hamiltonian $H(\lambda_n) = H_0 + v_{12} + \lambda_n (v_{13} + v_{23})$, where the particle pair $\{1,2\}$ is critically bound, and particle pairs $\{1,3\}$ and $\{2,3\}$ are neither bound nor critically bound. We prove the following: if $H(\lambda_n)\psi_n = E_n \psi_n$, where $E_n \to 0$ for $\lambda_n \to \lambda_{cr}$, and besides $\lim_{n \to \infty}\int_{|\zeta| \leq R} |\psi_n (\zeta)|^2 d\zeta = 0$ for any $R>0$, then the angular probability distribution of three particles determined by $\psi_n$ for large $n$ approaches the exact expression, which does not depend on pair--interactions. The result has applications in Efimov physics and in the physics of halo nuclei.

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