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The nucleus of deuterium, called a deuteron, contains one proton and one neutron. What is strong nuclear force between them?

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I'm having a hard time interpreting this question. Do we want the magnitude of the force. That's hard because it is hard to characterize the distance variation (but the binding energy is well measured at about 2.2 MeV). Or is there something else? – dmckee Jun 14 '12 at 22:23
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The solid state analogue of the force between a proton and a neutron is the Van der Waals forces between the molecules.

These forces are overflow forces from the central charges and the magnetic fields of the electrons and nuclei which comprise the electromgnetic environment of molecules. These are dipole and higher pole forces that can be attractive or repulsive creating the chemistry and solid state of the world around us.

The problem with nuclear forces is that in contrast to just electric and magnetic dipoles and quadrupoles etc, we have three colored quarks interacting with three colored quarks plus a large number of colored gluons in the sea. You can think of each color as a type of charge which will have its colored analogue of electric and magnetic fields. The complexity is enormous and the forces cannot be approximated simply as the case with electromagnetic forces.

Fortunately we have the quantum mechanical shell models which do not have to enter into the quark details and which work very well and precisely for nuclear physics problems, the analogue of the Van der Waals calculations.

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There's a good explanation of nuclear forces at The key thing to understand about them is it's really a force between the quarks that make up the proton and the neutron, so calculating the force is exceedingly complicated.

Despite much Googling I couldn't find a graph of the force between the proton and neutron in deuterium, but the binding energy (mentioned by dmckee in his comment) is actually pretty low. In fact it's so low that the first excited state of the nucleus isn't bound.

For a rough comparison I calculated the energy required to bring two protons to about the distance between the proton and neutron in a deuterium nucleus (I use $10^{-15}$m as the distance) and got a value of 1.4MeV, which is roughly the same as the binding energy in the deuteron. However the nuclear force is much shorter range than the electrostatic force, so while the potential energy is comparable the force due to nuclear forces will be much stronger than the electrostatic force.

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