# Strong and Weak Nuclear forces at long ranges

• I
• jaumzaum

#### jaumzaum

A lot of articles I already read says the Strong and Weak Nuclear interactions have a very short range, the first one being ##10^{-15}m## and the second ##10^{-18}m##. My first question is how is this calculated? This leads me to 2 possibilities:\$
1. Both forces actually act with an infinite range, and someone defined the "range" to be the distance from which we could measure that force with a real apparatus, with a decent certainty and resolution. Is that the case? If so, what are the assumptions?
2. The forces really don't act after those distances, they are zero. This could be true if we consider the model in which the force is quantized and for some reason the bosons of those fields cannot travel further or they would break the Uncertainty principle

What is correct explanation?

and for some reason the bosons of those fields cannot travel further or they would break the Uncertainty principle

This sounds a lot like a personal theory.

The strength of these forces goes roughly as $e^{-r/r_0}/r^2$. The range you read about is $r_0$.

• mfb
To expand on Vanadium 50's answer: you can estimate ##r_0## via the formula ##r_0=\frac{\hbar}{mc}##. Plug in the values of the pion(*) and the W/Z masses (useful approximation: ##\hbar c\approx 200\,\rm{MeV}\,\rm{fm}##), and you will see that you'll get results of the order of the numbers that you quoted. That's where they come from.

(*) Due to confinement, the degrees of freedom of the strong interaction at long distances are not the quarks and the gluons, but hadrons. So think of this as an effective theory describing the (residual) strong force as an exchange of virtual pions instead of gluons.