, Volume 156, Issue 1, pp 101-126

The Efimov effect. Discrete spectrum asymptotics

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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.

Communicated by B. Simon