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Functional Analysis and Its Applications

On Efimov's effect in a system of three identical quantum particles

Saidakhmat Norzhigitovich Lakaev

Published Jul 1, 1993• 96 citations
Publisher
DOI
10.1007/bf01087534

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In this note we discuss the Efimov effect emerging in a three-particle quantum system with zero-range interactions. In particular, we consider two non-interacting identical bosons plus a different lighter particle such that the interaction between a boson and the light particle is resonant. We also assume the validity of the Born-Oppenheimer approximation. Under these conditions, we show that the three-particle system exhibits infinitely many negative eigenvalues which accumulate at zero and satisfy the universal geometrical law characterising the Efimov effect. The result we find is a generalisation of previous results recently obtained in [13, 24].