Abstract
We study a three-particle Schrödinger operatorH for which none of the two-particle subsystems has negative bound states and at least two of them have zero energy resonances. We prove that under this condition the numberN(z) of bound states ofH belowz<0 has the asymptotics\(N(z) \sim \mathfrak{A}_0 |\log |z||\) asz→-0, where the coefficient\(\mathfrak{A}_0 \) depends only on the ratio of masses of the particles.
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Communicated by B. Simon
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Sobolev, A.V. The Efimov effect. Discrete spectrum asymptotics. Commun.Math. Phys. 156, 101–126 (1993). https://doi.org/10.1007/BF02096734
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DOI: https://doi.org/10.1007/BF02096734