Before delving into the mathematical model, it is important to understand that pycnonuclear fusion, in its essence, occurs due to two main events:
* A phenomenon of quantum nature called quantum diffusion.
* Overlap of the wave functions of zero-point oscillations of the nuclei.
Both of these effects are heavily affected by screening. The term screening is generally used by nuclear physicists when referring to plasmas of particularly high density. In order for the pycnonuclear fusion to occur, the two particles must overcome the electrostatic repulsion between them - the energy required for this is called the Coulomb barrier. Due to the presence of other charged particles (mainly electrons) next to the reacting pair, they exert the effect of shielding - as the electrons create an electron cloud around the positively charged ions - effectively reducing the electrostatic repulsion between them, lowering the Coulomb barrier. This phenomenon of shielding is referred to as "screening", and in cases where it is particularly strong, it is called "strong screening". Consequently, in cases where the plasma has a strong screening effect, the rate of pycnonuclear fusion is substantially enhanced.
Quantum tunnelling is the foundation of the quantum physical approach to pycnonuclear fusion. It is closely intertwined with the screening effect, as the transmission coefficient  depends on the height of the potential barrier, the mass of the particles, and their relative velocity (since the total energy of the system depends on the kinetic energy). From this follows that the transmission coefficient is very sensitive to the effects of screening. Thus, the effect of screening not only contributes to the reduction of the potential barrier that allows for "classical" fusion to occur via the overlap of the wave functions of the zero-point oscillations of the particles, but also to the increase of the transmission coefficient, both of which increase the rate of pycnonuclear fusion.
On top of the other various jargon related to pycnonuclear fusion, the papers also introduce various regimes, that define the rate of pycnonuclear fusion. Specifically, they identify the zero-temperature, intermediate, and thermally-enhanced regimes as their main ones.