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The Gamow peak is the peak of the probability density function (PDF) that relates the probability of fusing to the speed of atoms within a gas; the peak is at the speed at which the largest number atoms undergo fusion. The term Gamow window refers to the speed-regime near this peak within which basically all the fusion takes place. These are relevant to nucleosynthesis by fusion, such as that within stars. The probability distribution of fusion occurring at various relative speeds of colliding atoms is the combination (specifically, a convolution) of two probability distributions: the distribution of the probability that two colliding atoms have a particular speed relative to each other (assuming the Maxwell-Boltzmann distribution), and the distribution of the probability of quantum tunneling given that relative speed, a distribution that quantum mechanics provides. Fusion primarily takes place through quantum tunneling of a particle through the electric field of another (it being repelled by the Coulomb force), to get sufficiently close that the strong force holds them together.
The Gamow factor refers to a quantum-mechanical-derived expression worked out by George Gamow that is a factor of an exponent in the function mapping speed to the probability of quantum tunneling (which also depends upon particle masses, and can be characterized as a function of kinetic energy). The term is also sometimes seen labeling the resulting probability distribution.
The Gamow factor and Gamow peak of a gas are dependent upon its temperature as well as its constituents. Tunneling is more likely with higher the speed, but at a given temperature, above a certain speed, the higher the speed, the fewer atoms at that speed. The combination of the two probability distributions features a maximum probability of tunneling, the Gamow peak.