two photon cross section

Hello. I was hoping someone could help me understand some units. In several papers, I have seen the two photon LIF signal written as:

S = n*(Ω/4π)*T*G*σ*(E/hv)^2*η*a

where the units are

n (density of measured atom): #/cm3
Ω/4π (solid angle fraction): unitless
T (optical transmission fraction): unitless
G (statistical factor): unitless
E/hv (total photons): photons2 to photons4
η (detector conversion): unitless

So that leaves σ, which I've only seen defined in cm4*s. However, that leaves cm on top as well as square photons, which doesn't make sense. What am I not getting?
 E should be an energy hv should proabably be $h \nu = \hbar \omega$ which is also an energy, so the fraction is unitless.
 Yes, the fraction has no units. It's just a large number. Thanks. Any idea about the x-section units?

two photon cross section

Normally cross sections are given in (length)^2, e.g. barn

I am not quite sure what units S is supposed to have.
 The units of S can be photons, counts, or electrons depending if you put those conversions in. This is a two photon cross section so the tabulated values I see are cm4*s. Not sure where the seconds come from unless it is supposed to be multiplied by a power rather than energy.

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