When is a transition radiationless? I am reading the english wiki article about population inversion, to understand the laser. However the authors described different energy level transitions of the atom. But not all transitions emit photons. So I am wondering what determines if a specific energy transitions will result in the emission of a photon or not? What field of physics deals with those kind of calculations? 
Thank you in advance.
 A: Radiationless transitions occur when the timescale for radiative decay is much longer than that for de-excitation by interactions/collisions with other atoms and molecules.
What you need to look at is the physics of forbidden transitions. The rate at which spontaneous emission occurs is ordinarily proportional to the square of the "electric dipole matrix" elements between the final and initial states.
$$A_{ji}\propto \left[\int \psi_f (-er) \psi^{*}_i\ d^3r \right]^2$$
Transitions governed by magnetic dipole or electric quadrupole transitions occur much more slowly - by roughly a factor of $\sim l^2/\lambda^2$, where $l$ is the size of the atom or molecule.
However, for certain combinations of the initial and final states, the electric dipole matrix element is exactly zero; this is possible for symmetric potentials with eigenstates that have definite parities. These forbidden transitions are identified by the electric dipole selection rules and are unlikely to occur radiatively unless in a very rarefied environment, such that a slower magnetic dipole or electric quadrupole transition has time to occur before a collisional de-excitation. Ordinarily, a radiative transition is never seen and de-excitation occurs by collision.
A: The energy of an excited state has to go somewhere, so it is either lost by emitting a photon or some other mechanism must transfer the energy away. The most common of these mechanisms is collisional de-excitation (that Wikipedia article is for collisional excitation, but de-excitation is the same process in reverse). The difference in the energy of the two states ends up as kinetic energy of the molecules/atoms involved.
In a solid the energy can also be lost to lattice vibrations, i,e, heat, which is generally known as quenching.
If the excited atom/molecule is isolated the only mechanism available is to emit a photon, so whether a collisional de-excitation occurs depends on the collision frequency with other atoms/molecules and de-excitation probability per collision.
A: The electron simply slides over from a low vibrational state of the excited electronics state to a high vibrational state of the electronic ground.
