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Critical stability of few-body systems

Abstract : When a two-body system is bound by a zero-range interaction, the corresponding three-body system -- considered in a non-relativistic framework -- collapses, that is its binding energy is unbounded from below. In a paper by J.V. Lindesay and H.P. Noyes it was shown that the relativistic effects result in an effective repulsion in such a way that three-body binding energy remains also finite, thus preventing the three-body system from collapse. Later, this property was confirmed in other works based on different versions of relativistic approaches. However, the three-body system exists only for a limited range of two-body binding energy values. For stronger two-body interaction, the relativistic three-body system still collapses. A similar phenomenon was found in a two-body systems themselves: a two-fermion system with one-boson exchange interaction in a state with zero angular momentum J=0 exists if the coupling constant does not exceed some critical value but it also collapses for larger coupling constant. For a J=1 state, it collapses for any coupling constant value. These properties are called "critical stability". This contribution aims to be a brief review of this field pioneered by H.P. Noyes.
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Submitted on : Monday, January 6, 2014 - 2:47:03 PM
Last modification on : Wednesday, September 16, 2020 - 4:07:55 PM

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V. A. Karmanov, J. Carbonell. Critical stability of few-body systems. John C Amson, Louis H Kauffman. Scientific Essays in Honor of H Pierre Noyes on the Occasion of His 90th Birthday, 54, pp.148-168, 2014, 978-981-4579-36-0. ⟨10.1142/9789814579377_0010⟩. ⟨in2p3-00924191⟩

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