The phrase "nuclear reactions between atoms" may puzzle the educated reader. Nuclear reactions involve the transformation of nuclei, not atoms, and for this to occur, the nuclei must be close to one another. It has been shown that nuclear transformation is possible even when this requirement is not met. Such nuclear reactions, in which some nucleons from one nucleus are transferred to another similar nucleus located nearby, occurred deep within the Earth during the formation of the Earth's crust from interstellar matter. As a result of these reactions, the percentage of elements in the Earth's crust differs by tens and hundreds of times from the percentage of the same elements in interstellar matter. This circumstance provides experimental evidence for the existence of such reactions. The existence of such reactions fundamentally changes our understanding of the structure of matter, the prospects for generating nuclear energy, and nucleosynthesis in the Universe.