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It takes substantial energy - but it does happen, it's just difficult to achieve on earth.

However, the process of proton-proton fusion is one of the key reactions that takes place in the sun. 2 Hydrogen nuclei (protons) fuse to produce a deuterium nucleus (1 proton, 1 neutron) and a positron (positive electron). Subsequently, the deuterium nuclei can fuse with protons to form helium.

The electrostatic force provides substantial repulsion, hence the need for very high temperatures (about 15 million K). It is only at high temperatures that the KE of the protons is sufficient to overcome the electrostatic repulsion.

However, once you overcome electrostatics then the strong force will bind the 2 nucleons together - and produce a new nucleus. In the case of deuterium, and helium-3 and helium-4 the nuclei are stable. Tritium can also be produced, this is unstable and decays into helium-3.

There is a final catch - in that the temperatures of the sun aren't quite high enough to overcome the electrostatic repulsion between protons, so how can the reaction take place.

The solution is 'quantum tunneling' - A simple explanation: according to classical physics, if a particle doesn't has less energy than a barrier then the barrier acts like a brick wall - the particle can't cross it. In quantum mechanics, things are probability based - it's possible, for a particle to cross any barrier - the height of the barrier and the energy of the particle determine the probability that particle can cross. Occasionally, this means a particle can cross a barrier that is higher than its energy level - the particle appears to 'tunnel' through the barrier, instead of going over it. x TPS

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