Efimov states in general
Efimov states are special states of three praticle systems. Their existence is a purely quantum effect, because "size" (i.e. cross-section) of these states can be much greater than the range of underlying particle-particle interaction. (1,2)
For each system having an <PERSON> state there are in fact infinitely many of such states. Some properties of Efimov states are universal and do not depend on the nature of underlying particle-particle interaction: (1,2)
1) size of $n$-th <PERSON> state is $s_0 \approx 22.7$ times the size of $(n-1)$-th state
2) energy of $n$-th <PERSON> state is $s_0^2$ times the energy of $(n-1)$-th state
$s_0$ is the solution of the following transcedental equation (3):
$s_0 \cosh(\pi s_0/2) = \frac{8}{\sqrt{3}} \sinh(\pi s_0/6) $
There can be <PERSON> states, so bound three particle states, when there are no bound dimer states. This is often depicted with borromean rings, since if we take one of the praticles away, the resulting two particle state will be unbound.
<PERSON> states and halo nuclei
The original <PERSON> work treated three identical bosons. 469
However, the particles need not be identical, they can have different mases. The <PERSON> theory can also be extended to describe fermions. (2)
Halo nuclei, that can be viewed as <PERSON> states, are the nuclei with two-neutron halos:
A two-neutron halo is exhibited by ${}^6He$, ${}^{11}Li$, ${}^{17}B$, ${}^{19}B$ and ${}^{22}C$. Two-neutron halo nuclei break into three fragments, never two, and are called Borromean because of this behavior (referring to a system of three interlocked rings in which breaking any ring frees both of the others). (Atomic nucleus-Wikipedia)
The two neutrons in the halo "do not stick together", so we indeed have a three-particle system. It is interesting, that
[lithium-11] has an exceptionally large cross-section of 3.16 fm, comparable to that of ${}^{208}Pb$. (4)
For an introduction to halo nuclei and Efimov states see the presentation Halo world: The story according to <PERSON>,<PERSON> and <PERSON> by <PERSON>: http://www.boseinst.ernet.in/capss/talks/2011/IndranilMazumder.ppt
I also advertise the freely available Physics.APS.org article on <PERSON> states: http://physics.aps.org/articles/v3/9 1020