The physical processes behind the production of light nuclei in heavy ion collisions are unclear. The nice theoretical description of experimental yields by thermal models conflicts with the very small binding energies of the observed states, being fragile in such a hot and dense environment. Other available ideas are delayed production via coalescence, or a cooling of the system after the chemical freeze-out according a Saha equation, or a `quench instead of a thermal freeze-out. A recently derived prescription of an (interacting) Hagedorn gas is applied to consolidate the above pictures. The tabulation of decay rates of Hagedorn states into light nuclei allows to calculate yields usually unaccessable due to very poor Monte Carlo statistics. Decay yields of stable hadrons and light nuclei are calculated. While the scale-free decays of Hagedorn states alone are not compatible with the experimental data, a thermalized hadron and Hagedorn state gas is able to describe the experimental data. Applying a cooling of the system according a Saha-equation with conservation of nucleons and anti-nucleons in number leads to (nearly) temperature independent yields, thus a production of the light nuclei at temperatures much lower than the chemical freeze-out temperature is possible.
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