The primary atomic reaction that occurs within the Sun to convert hydrogen atoms into helium atoms is called nuclear fusion. Specifically, it's a process called the proton-proton chain reaction.

Here's a simplified explanation:

1. Proton-Proton Collision: Two protons (hydrogen nuclei) collide with enough energy to overcome their electrostatic repulsion.

2. Weak Interaction: One proton undergoes a weak interaction, transforming into a neutron, emitting a positron (anti-electron) and a neutrino.

3. Deuterium Formation: The neutron and the remaining proton combine to form deuterium (an isotope of hydrogen with one proton and one neutron).

4. Deuterium Capture: Deuterium captures another proton, forming helium-3 (two protons and one neutron).

5. Helium-3 Fusion: Two helium-3 nuclei collide and fuse, producing a helium-4 nucleus (two protons and two neutrons) and releasing two protons.

The net reaction is:

4 protons -> 1 helium-4 nucleus + 2 positrons + 2 neutrinos + energy

This process releases a tremendous amount of energy, which is what powers the Sun and other stars. It's important to note that this is a simplified explanation, and the proton-proton chain reaction involves several intermediate steps and variations.