Manifestation of Universality in the Asymmetric Helium Trimer and in the Halo Nucleus $^{22}$C

TL;DR

This paper demonstrates that certain three-body systems, like the asymmetric Helium trimer and halo nucleus $^{22}$C, exhibit universal corner angle distributions when the pair interactions have a zero-energy virtual state and the system is weakly bound.

Contribution

It derives explicit universal formulas for corner angle distributions in three-body systems, linking atomic and nuclear physics through universality principles.

Findings

Asymmetric Helium trimer $^3$He$^4$He$_2$ shows universal features.

Halo nucleus $^{22}$C exhibits universal corner angle distributions.

Derived formulas depend only on mass ratios, not on specific interactions.

Abstract

We prove that the corner angle distributions in the bound three-body system AAB, which consists of two particles of type A and one particle of type B, approach universal form if the pair AA has a virtual state at zero energy and the binding energy of AAB goes to zero. We derive explicit expressions for the universal corner angle distributions in terms of elementary functions, which depend solely on the mass ratio m(A)/m(B) and do not depend on pair interactions. On the basis of experimental data and calculations we demonstrate that such systems as the asymmetric Helium trimer $^3$He$^4$He$_2$ and the halo nucleus $^{22}$C exhibit universal features. Thus our result establishes an interesting link between atomic and nuclear physics through the few-body universality.