# Strong and Weak Nuclear forces at long ranges

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• jaumzaum
In summary, the Strong and Weak Nuclear interactions have a very short range of ##10^{-15}m## and ##10^{-18}m## respectively. This range is calculated using the formula ##r_0 = \frac{\hbar}{mc}## and is the distance from which we can measure the force with a certain level of certainty and resolution. There are two possible explanations for this short range: either the forces have an infinite range, but we can only measure them up to a certain distance, or the forces truly cease to act after these distances due to the quantization of the force and the Uncertainty Principle. The strength of these forces decreases with distance according to the formula ##e^{-r/r_0}/r^
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?

jaumzaum said:
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.

## 1. What are strong and weak nuclear forces?

The strong and weak nuclear forces are two of the four fundamental forces of nature that act on subatomic particles. The strong nuclear force is responsible for binding protons and neutrons together in the nucleus of an atom, while the weak nuclear force is involved in radioactive decay.

## 2. How do strong and weak nuclear forces differ from each other?

The main difference between strong and weak nuclear forces is their range. Strong nuclear forces act only on particles that are extremely close together, within the size of an atomic nucleus. Weak nuclear forces, on the other hand, have a much shorter range and only act on particles that are within the size of an atom.

## 3. Can strong and weak nuclear forces act at long ranges?

No, strong and weak nuclear forces are only effective at extremely short distances. As particles move further apart, the forces become weaker and eventually become negligible.

## 4. How do strong and weak nuclear forces contribute to the stability of atoms?

The strong nuclear force is responsible for holding the nucleus of an atom together, preventing it from breaking apart due to the repulsive forces between positively charged protons. The weak nuclear force helps to stabilize the nucleus by causing certain types of radioactive decay, which can reduce the number of protons and neutrons in the nucleus to a more stable configuration.

## 5. Are there any other forces that act at long ranges?

Yes, in addition to strong and weak nuclear forces, there are two other fundamental forces that act at long ranges: electromagnetism and gravity. Electromagnetic forces are responsible for the interactions between charged particles, while gravity is the force that governs the interactions between massive objects.

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