two photon cross section

Mr Boom

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?

M Quack

E should be an energy

hv should proabably be [itex]h \nu = \hbar \omega[/itex] which is also an energy, so the fraction is unitless.

Mr Boom

Yes, the fraction has no units. It's just a large number. Thanks.

Any idea about the x-section units?

M Quack

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

I am not quite sure what units S is supposed to have.

Mr Boom

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.