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

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.