This reaction is actually connected to a branch of Chemistry, called Nuclear Chemistry. Nuclear Chemistry does not deal in quarks and/or all the substructure of matter that is found in particle accelerator data. Nuclear Chemistry stops at the basic model of the atom at ambient conditions; protons, neutrons and electrons. Nature also shows natural radiation at room temperature; Uranium and half lives of isotopes. These observation adds some other ambient particles, to nuclear chemistry, like neutrinos.
Once you add lots of energy and smash particles together, in ways not found on earth at natural ambient conditions, this is where Nuclear Chemistry ends and Nuclear Physics begins. Ironically, the new fusion process with lasers, is based on Nuclear Chemistry and not Nuclear Physics. Nuclear physics did not work very well for fusion; magnetic containment. The Nuclear Chemistry that works with the lasers is based on 1950's knowledge.
If there were no particle accelerators, Nuclear Chemistry could still do fusion. One problem with Nuclear Physics is it does not take into consideration the phases of matter. In chemistry, the same matter, under different amounts of temperatures and pressure, can form different phases. Water at very high temperature and pressure will form a metal. If we lower this to ambient conditions, we get a liquid phase.
Particle Physics uses extreme temperature; extreme energy, but the pressure is not very high; sustained. Their data is more like an isotherm on a much larger phase diagram, that should include extreme gravitational pressures to be more complete simulation of all type of star cores. They are at the wrong part of the full diagram, which was not useful for fusion.
Physics does not think in terms of phases of matter, but seems to assume one phase for all conditions. This is not found in chemical and nuclear chemical nature. The neutron star, for example, will not allow the proton and electron phases to exists, freely, due to the extreme pressures; neutron only phase. This is a different place on the phase diagram of Nuclear Chemistry. Nuclear Physics would need sustained pressure to maintain this neutron phase, stating with protons and electrons, which they then atom smash. They would need a secondary pressure zone, to induce the primary substructure, into the correct phase. This may be beyond current technology.
