# Estimation nuclear force between proton and neutron in deuteron

Is there an estimation of nuclear force between proton and neutron in deuteron to say What is the strong nuclear force between them? 1N? 10N? 100N? 1000N?

It's about 10-100 times stronger than the electromagnetic repulsive force between two "nearly touching" protons because the dimensionless "strong coupling constant" is of order one while the corresponding "fine-structure constant" is $1/137.036$.

The electrostatic force is $$F = \frac{e^2}{4\pi\varepsilon_0\cdot (1\,{\rm fm})^2} = \frac{(1.602\cdot 10^{-19})^2}{4\pi\cdot 8.85\times 10^{-12}\cdot 10^{-30}} {\rm N} = 230\,{\rm N}$$ Amusingly enough, it's a reasonable force we know from the everyday life. The strong force could be 10,000 newtons, still reasonable – like the weight of one ton. But one must realize how extreme the force is in the proportion: the whole force doesn't act on a car but it acts on one elementary particle.

• I've found an unpublished theory that would account for the strong nuclear force. my calculation is close to your estimation
– Neo
Commented Dec 1, 2012 at 6:36

I have a formula able to calculate the binding energy of the deuteron: it needs only to apply the electric and magnetic Coulomb's laws to the deuteron. The formula is the same as above, but with the potential instead of the force, needing the empirical radius:

A better theory, e.g. electromagnetic, gives the correct result by using only the fundamental laws and constants shown in my paper:

http://www.aemjournal.org/index.php/AEM/article/view/218/