What I Learned Today

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Posts in the mathematics category

The three Borromean rings.

The three Borromean rings.

There are some properties of few-body systems that are "Universal", so shared between all few-body systems that feel an attractive interaction (with certain boundary properties for defining eventual spin-orbit and isospin).

An example of this behavior are the Efimov states of three-body systems: when an interaction loosely bound two bodies, the three-body system have a precise spectrum of excitation. This spectrum is observed in three nucleons systems like Helium-3 and Triton, since the two-body system, the deuteron, is loosely bound (for nuclear scales).

Moreover Efimov states can predict that even when two-body subsystems are unbound, three-body counterpart can form bound states. This is the so-called Borromean systems, from the coat of arms of Borromeo family of the lake Maggiore, where three rings interweave such as to take one out you have to break the whole system.

There is no bound 5-nucleons nucleus (Litium-5 or Helium-5 are unbound systems). Is that an Universal property of the nuclear force that make impossible to form 5-body systems, or is just an accident?

Today I learned from J. Kirscher that seems just an accident and there are no Efimov-like properties expected from the properties of non-existent 5-body systems.