A Momentum transfer perpendicular to velocity of proton?

rjseen
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An assumption in deducing the Bethe equation is that the momentum transfer is perpendicular to the direction of the particle.

ALSO

In Allison & Cobb (1980), just after eq. 28, they state that the first two terms of the Photoabsorption Ionization model arise from the magnetic vector potential in the Coulomb gauge, for which the electric field is transverse to the direction of 3-momentum transfer.

I know that the magnetic vector potential A is in units of momentum per charge, so ignoring hard collisions, how does the justification of this look?
 
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