Yes, there is a specific temperature range at which protons and neutrons can combine to form atomic nuclei. This temperature range is commonly referred to as the "nuclear binding energy regime" or the "nuclear reaction temperature regime."
At extremely high temperatures, such as those found in the early universe or in the core of a massive star, the thermal energy is so high that it can overcome the electrostatic repulsion between positively charged protons. This allows for nuclear reactions to occur and for protons and neutrons to combine to form atomic nuclei.
The reason for this temperature dependence is related to the nature of the strong nuclear force, one of the fundamental forces of nature that binds protons and neutrons together within the atomic nucleus. At low temperatures, the electrostatic repulsion between protons dominates, making it difficult for them to come close enough to each other to experience the attractive strong nuclear force.
However, as the temperature increases, the kinetic energy of the particles also increases, and they move with higher speeds. This enhanced thermal motion leads to more frequent and energetic collisions between protons and neutrons. Consequently, there is a higher likelihood that they will overcome the electrostatic repulsion and get close enough for the strong nuclear force to act.
In the early universe, during a phase known as Big Bang nucleosynthesis, the temperature was high enough for the formation of light atomic nuclei such as helium-4, deuterium, and helium-3. In the core of massive stars, temperatures can reach millions of degrees Celsius, enabling nuclear fusion reactions that produce heavier elements.
It's important to note that the exact temperature at which nuclear reactions become significant depends on various factors, including the densities of protons and neutrons, the presence of other particles, and the specific isotopes involved. Detailed nuclear physics models and experiments are used to study these temperature regimes and understand the processes involved in nucleosynthesis and nuclear reactions.