Can Two Protons Exist in an Atom's Nucleus Without Neutrons?

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Hi, I am a young physics student who wonders a lot about the atom, especially it's nucleus. I thought about the atom and realized that there could never be a nucleus of two protons because they both would reject each other. I have made some calculations and realized that the gravitational force is far lower than the electric force, so both protons would reject each other. Is there an element with only two protons in it's nucleus? or does it needs neutrons to bring the protons together? Thanks.
 
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2 protons in the nucleus, Helium 2, is not (practically) possible. There needs to be at least one neutron in the nucleus for the strong force to overcome the electrostatic-repulsion of the Protons.

For further information on diprotons, see the wikipedia article: http://en.wikipedia.org/wiki/Diproton (also see references provided)

The force that keeps the atom together is the Strong force, not the gravitational force (which is far too weak).
 
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