Large Hi-E cross-sections from Lorentz contraction?

[Widdekind]

Total cross-sections measure the overall strength of an interaction. At low energies total cross-sections for strongly interacting particles show peak due to resonances, and in many instances, an overall drop as the collision energy rises. At larger energies, however, a new feature comes into play, first noticed by experimenters at the Serpukhov proton synchrotron 90km south of Moscow, back in 1971. There's an across-the-board rise -- in proton-proton, pion-nucleon, kaon-nucleon collisions, and more besides -- in cross-section, with increasing collision energy. It's as though particles expand and become more opaque at high energies.

 

Watson. Quantum Quark, pg. 367.

 

Please ponder the low-energy limit. There, the wave functions of the collision particles are relatively de-localized & diffuse. As the two diffuse probability "clouds" come together, and begin to merge & overlap, at any given moment, the total Transition Matrix Element (TME), computed from the overlap integral as [math]| <\Phi | \Psi > |^2[/math], is low.

 

But, at high-energy, the Lorentz contraction "pancakes" the wave functions, into "dense disks" perpendicular to the direction of motion. When these "dense disks" of probability collide, like "lead plates", the overlap integrals automatically "max out", making for larger TMEs.

 

Moreover, at higher & higher energies, the colliding wave functions "bore into" the other particle's electrostatic potential well more & more easily, having less & less time to "adapt" and "deflect away", so that interactions are more & more "intimate", "immediate", at "point blank", w/ more wave function overlap (lead plate on lead plate), and less wave function dispersion, away from the intervening area of high potential.

 

Is this what explains the phenomena?