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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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##### References:
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