Question: How many theoretical interaction between photons and atoms are there?
About the article "Photoelectric effect", section "Cross section".

Candidate passages:
Interactions between atoms and molecules: 
Gaseous rubidium atoms were pumped into a vacuum chamber.
The cloud was cooled using lasers to just a few degrees above absolute zero.
Using weak laser pulses, small numbers of photons were fired into the cloud of atoms.
As the photons entered the cloud, their energy excited atoms along their path, causing them to lose speed.
Inside the cloud medium the photons dispersively coupled to strongly interacting atoms in highly excited Rydberg states.
This caused the photons to behave as massive particles with strong mutual attraction (photon molecules).
Eventually the photons exited the cloud together as normal photons (often entangled in pairs).
The effect is caused by a so-called Rydberg blockade, which in the presence of one excited atom, prevents nearby atoms from being excited to the same degree.
In this case, as two photons enter the atomic cloud, the first excites an atom, but must move forward before the second can excite nearby atoms.
In effect the two photons push and pull each other through the cloud as their energy is passed from one atom to the next, forcing them to interact.
This photonic interaction is mediated by the electromagnetic interaction between photons and atoms. 
Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge.
Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons in spite of the fact that the electric charge structures of protons and neutrons are substantially different.
A theory called Vector Meson Dominance (VMD) was developed to explain this effect.
According to VMD, the photon is a superposition of the pure electromagnetic photon (which interacts only with electric charges) and vector meson.
However, if experimentally probed at very short distances, the intrinsic structure of the photon is recognized as a flux of quark and gluon components, quasi-free according to asymptotic freedom in QCD and described by the photon structure function.
A comprehensive comparison of data with theoretical predictions is presented in a recent review. 
The vast majority of photons that come anywhere near a particular atom are almost completely unaffected by that atom.
The atom is almost completely transparent to most frequencies (colors) of photons.
A few photons happen to "resonate" with the atom, in a few very narrow bands of frequencies (a single color rather than a mixture like white light).
When one of those photons comes close to the atom, the atom typically absorbs that photon (absorption spectrum) for a brief period of time, then emits an identical photon (emission spectrum) in some random, unpredictable direction.
(Other sorts of interactions between atoms and photons exist, but are not relevant to this article.
)The popular idea that lasers increase the thermal energy of matter is not the case when examining individual atoms.
If a given atom is practically motionless (a "cold" atom), and the frequency of a laser focused upon it can be controlled, most frequencies do not affect the atom — it is invisible at those frequencies.
There are only a few points of electromagnetic frequency that have any effect on that atom.
At those frequencies, the atom can absorb a photon from the laser, while transitioning to an excited electronic state, and pick up the momentum of that photon.
Since the atom now has the photon's momentum, the atom must begin to drift in the direction the photon was traveling.
A short time later, the atom will spontaneously emit a photon in a random direction, as it relaxes to a lower electronic state.
If that photon is emitted in the direction of the original photon, the atom will give up its momentum to the photon and will become motionless again.
If the photon is emitted in the opposite direction, the atom will have to provide momentum in that opposite direction, which means the atom will pick up even more momentum in the direction of the original photon (to conserve momentum), with double its original velocity.
But usually the photon speeds away in some "other" direction, giving the atom at least some sideways thrust.
Another way of changing frequencies is to change the positioning of the laser.
For example, using a monochromatic (single-color) laser that has a frequency that is a little below one of the "resonant" frequencies of this atom (at which frequency the laser will not directly affect the atom's state).
If the laser were to be positioned so that it was moving "towards" the observed atoms, then the doppler effect would raise its frequency.
At one specific velocity, the frequency would be precisely correct for said atoms to begin absorbing photons.
Something very similar happens in a laser cooling apparatus, except such devices start with a warm cloud of atoms moving in numerous directions at variable velocity.
Starting with a laser frequency well below the resonant frequency, photons from any one laser pass right through the majority of atoms.
However, atoms moving rapidly "towards" a particular laser catch the photons for that laser, slowing those atoms down until they become transparent again.
(Atoms rapidly moving "away" from that laser are transparent to that laser's photons — but they are rapidly moving "towards" the laser directly opposite it).
This utilization of a specific velocity to induce absorption is also seen in Mössbauer spectroscopy.
On a graph of atom velocities (atoms moving rapidly to the right correspond with stationary dots far to the right, atoms moving rapidly to the left correspond with stationary dots far to the left), there is a narrow band on the left edge corresponding to the speed those atoms start absorbing photons from the left laser.
Atoms in that band are the only ones that interact with the left laser.
When a photon from the left laser slams into one of those atoms, it suddenly slows down an amount corresponding to the momentum of that photon (the dot would be redrawn some fixed "quantum" distance further to the right).
If the atom releases the photon directly to the right, then the dot is redrawn that same distance to the left, putting it back in the narrow band of interaction.
But usually the atom releases the photon in some other random direction, and the dot is redrawn that quantum distance in the opposite direction.
Such an apparatus would be constructed with many lasers, corresponding to many boundary lines that completely surround that cloud of dots.
As the laser frequency is increased, the boundary contracts, pushing all the dots on that graph towards zero velocity, the given definition of "cold". 
In mathematical physics, scattering theory is a framework for studying and understanding the interaction or scattering of solutions to partial differential equations.
In acoustics, the differential equation is the wave equation, and scattering studies how its solutions, the sound waves, scatter from solid objects or propagate through non-uniform media (such as sound waves, in sea water, coming from a submarine).
In the case of classical electrodynamics, the differential equation is again the wave equation, and the scattering of light or radio waves is studied.
In particle physics, the equations are those of Quantum electrodynamics, Quantum chromodynamics and the Standard Model, the solutions of which correspond to fundamental particles.
In regular quantum mechanics, which includes quantum chemistry, the relevant equation is the Schrödinger equation, although equivalent formulations, such as the Lippmann-Schwinger equation and the Faddeev equations, are also largely used.
The solutions of interest describe the long-term motion of free atoms, molecules, photons, electrons, and protons.
The scenario is that several particles come together from an infinite distance away.
These reagents then collide, optionally reacting, getting destroyed or creating new particles.
The products and unused reagents then fly away to infinity again.
(The atoms and molecules are effectively particles for our purposes.
Also, under everyday circumstances, only photons are being created and destroyed.)
The solutions reveal which directions the products are most likely to fly off to and how quickly.
They also reveal the probability of various reactions, creations, and decays occurring.
There are two predominant techniques of finding solutions to scattering problems: partial wave analysis, and the Born approximation.