Lorentz Transformation for pairs generated with headon collision

Momentum and energy in headon collsions;

a = half the crossing angle ( in horizontal direction)

Lorentz transformation in x-direction

betax = P*sin(a)/E
gamx = sqrt(1./(1.-betax)/(1.+betax))

Px' = gamx * (Px - betax * E )
E'  = gamx * ( E - betax * Px )

if a << 1;  betax=a and gamx=1
Px' = Px - a * E 
E'  = E - a * Px