What is the joining of two small nuclei to form a larger nucleus known as?

The joining of two small nuclei to form a larger nucleus is known as nuclear fusion. This process occurs under conditions of extremely high temperature and pressure, such as in the core of stars, where hydrogen nuclei combine to form helium and release a significant amount of energy in the form of light and heat.

Nuclear fusion is distinct from other nuclear reactions; for instance, nuclear fission is the process where a large nucleus splits into smaller nuclei, which is the opposite of fusion. The term "splitting reaction" also reflects a misunderstanding of the fusion process, which is based on combining nuclei rather than breaking them apart. A controlled reaction typically refers to a self-sustaining nuclear fission reaction, such as those used in reactors, and is not applicable to the fusion process at this context. Therefore, nuclear fusion is the correct term for the process described in this question.