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The Efimov effect. Discrete spectrum asymptotics. (English) Zbl 0785.35070
A three-particle Schrödinger operator \(H\) with short-range pair potentials is considered. It is supposed that two-particle subsystems do not have negative eigenvalues and at least two of them have zero-energy resonances. In this case the discrete spectrum of \(H\) is infinite (this is called the Efimov’s effect).
It is shown that the number \(N(z)\) of bound states of \(H\) below \(z<0\) has the asymptotics \(N(z)\sim a|\ln| z| |\) where the coefficient \(a\) depends only on masses of particles.

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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