By studying the eigenvalue spectrum of the Faddeev kernel in a certain singular limit, we give an independent proof of an effect recently deduced by Efimov: When three identical particles interact via short-range pairwise potentials, the number of three-body bound states grows without limit when the pairwise scattering length a becomes large. [The number of bound states is then roughly (1/π)ln(Λ|a|), where Λ is a momentum cutoff]. We extend our proof to the case where only two particles are identical and show that Efimov's effect persists in the special limiting cases with two heavy and one light particle, and with two light and one heavy particle.
© 1972 The American Physical Society
http://prd.aps.org/abstract/PRD/v5/i8/p1992_1
Golldminer,
That abstract you linked (1972 ??) didn't convey much sense, and the article linked by me is nearly as pathetic because they are looking at events in dynamic three-dimensional space as a particulate two-dimensional math problem.
They are on the right
path with the concept of Three, imo, because even when the proposed theory is based on fixated bosonic/fermionic 'particles', at some point the math must always include (4)Wave mixing equations in order to have any meaning at all in the real world.
A "pair" of anything is initially a 2d abstraction. As soon as that pair is placed in real space, with real duration, you're into 3D~with motion.
In reality, one can't have T-waves without L-waves (or s-waves without p-waves in euroland).
Here's another tentative take on Efimov-
like effects:
For the description of 3-body systems it is helpful to use so-called dimer fields. Up to now such dimer fields were introduced by s-wave interactions and thus limited to spin 0. In order to enlarge its applicability we extend this formalism to p-wave interactions with resulting dimer fields of spin 1. Considering dimer-particle scattering it becomes evident that, analogous to s-wave interactions, an Efimov-like spectrum of 3-body bound states exists.
http://www.hiskp.uni-bonn.de/index.php? ... 4f177b346b