An example is forming of Cooper pairs in metals at very low temperatures: electrons with opposite spins and impulses attract each other and form correlated pairs. It is a quantum effect. Due to it metals become superconductive.

@ A. Uryson

In Cooper pairs, those electrons are spin vectors side by side (parallel). What I'm looking for, is an experiment where spin vectors are introduced head-on. My model predicts particle annihilation in such experiment (if opposite spins).

Actually, I'm quite confident that such experiment will be conducted in near future.

Not quite clear to me what you have in mind. Head-on collisions of polarized particles with anti-paralel spins ? Some experiments with polarized targets and/or beams have been done in the past , see for example: http://www.umich.edu/~mctp/SciPrgPgs/events/2010/Spin/Talks/Marshak-zgs_polarized_beams_14nov2009.pdf

In any case no annihilation can be expected due to a particular spin configuration of colliding particles. Except of colliding particles with anti-particles, but then it has nothing to do with the spins.

@Adam Spin axis poles head-on. Naturally that requires the hypothesis that there exists such an axis. I do know what contemporary physics thinks about that hypothesis, so save me from a lecture ;-)

One other thing Adam, you guys should conduct the experiment at CERN pretty quickly. At least before some not so responsible country/lab. I really do mean that.

Measurement of the differences in the total cross-section for antiparallel and parallel longitudinal spins and a measurement of parity nonconservation with incident polarized protons and anti-protons at 200-GeV/c

E581/704 Collaboration (D.P. Grosnick (Argonne) et al.). May 1996. 98 pp.

Published in Phys.Rev. D55 (1997) 1159-1187

That's behind a paywall... longitudinal spins? For example, spin up parallel to a velocity vector?

This one is very interesting also http://arxiv.org/abs/1001.0790

@Hideto What I'm looking for is an experiment where spins are anti-parallel on axis connecting incident particles.

Sorry about my confusion, I meant spins antiparallel on axis perpendicular to the line connecting incident particles (in contemporary particles physics terms).

It's kind of tricky thing to describe spins in contemporary terms and in ToEbi terms at the same time :-)

The RHIC collider has produced a lot of polarized-proton research, including lots of collisions with the spin vectors pointing toward each other as the particles collide (as well as other configurations). See, eg, http://arxiv.org/abs/hep-ex/0701048 . Although the protons are destroyed in this process, it isn't generally described as 'annihilation', since at every point in time there are quarks present.

Similar polarized electron-electron experiments have also been run, and these definitively show that the electrons do not annihilate regardless of the directions of their spin vectors during the collision.

If you'd like to learn more, the term for spin vectors that are pointed along their velocity vector is "Longitudinally Polarized". There are countless papers on the subject of these collisions.

@Ross Mm... that arXiv paper is about longitudinal spins. I'm looking for an answer to this question http://physics.stackexchange.com/questions/117342/whats-the-outcome-of-two-polarized-electrons-beam-collide-head-on

Transverse-transverse case.

@kimmo RHIC has also done a lot of transverse-transverse research (the collider is very flexible), eg http://arxiv.org/abs/0801.2990 . Although both beams are transversely polarized (with each beam containing a pattern of differently-polarized bunches), that particular paper combines the statistics from up-up and up-down collisions (and separately combines down-up and down-down) for its particular goal.

For electrons themselves, the theory has long been established, with quantum mechanics providing descriptions that match measurement (note that if two electrons collide, there is some frame in which the collision is head-on). http://rspa.royalsocietypublishing.org/content/126/801/259.full.pdf (1930!)

If a spin-up electron were the antiparticle of a spin-down electron (and could hence annihilate), it would be difficult to explain the stability of a helium atom, which has two electrons with differing spins in the same orbital, and does not spontaneously ionize itself.

@Ross In helium case those different spin electrons lack the needed orientation what I'm looking for http://www.toebi.com/blog/theory-of-everything-by-illusion/experiment-setup/

don't they?

I'll read those two other links tomorrow! Thanks!

@Ross Do you mean this kind of setup (at RHIC) with protons? http://arxiv.org/pdf/nucl-ex/0612020.pdf ?

Those beams are not in the same line.

@Ross I have now studied many transverse double spin papers and concluded that I was hoping too much from those kind of experiments. There won't be any annihilation processes. Thanks for the guidance!