Realistic Nuclear Density Distributions
The ?-function in the expression for the two-photon luminosity implies that the nuclei have sharp edges.
L?? = LAA ?? n(?1,b1) n(?2,b2) ?(?b1-b2?-2R) d2b1 d2b2
This ignores edge effects. A more realistic approach it to define
L?? = LAA ?? n(?1,b1) n(?2,b2) (1-Pint(?b1-b2?) d2b1 d2b2
Where Pint(b) is the hadronic interaction probability for a Nucleus-Nucleus Collision at impact parameter b. This can be calculated from (Glauber Model):
P(b) = 1 – EXP( – ?nn ?? TA(r) TB(b-r) d2r )
Where TA(r) is the thickness function.
Using a Woods-Saxon density distribution for TA(r) gives a
5-15% reduction in luminosity, depending on energy.