Strong and Weak Nuclear forces at long ranges

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SUMMARY

The discussion centers on the range of Strong and Weak Nuclear forces, which are defined as approximately 10-15 m and 10-18 m, respectively. The range is calculated using the formula r0 = ħ/(mc), where ħ is the reduced Planck constant, m is the mass of the particle, and c is the speed of light. The effective theory for the strong interaction at long distances involves hadrons and virtual pions rather than quarks and gluons due to confinement. This understanding clarifies the limitations of these forces and their quantized nature.

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  • Understanding of quantum mechanics principles, particularly the Uncertainty Principle.
  • Familiarity with particle physics concepts, including bosons, hadrons, and quarks.
  • Knowledge of the reduced Planck constant (ħ) and its significance in quantum calculations.
  • Basic grasp of force interactions and their mathematical representations in physics.
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  • Research the derivation and implications of the formula r0 = ħ/(mc) in particle physics.
  • Explore the concept of confinement in quantum chromodynamics (QCD) and its effects on strong interactions.
  • Study the role of virtual particles in mediating forces, focusing on pions in the context of the strong force.
  • Investigate the Uncertainty Principle and its implications for particle behavior at quantum scales.
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Physicists, students of quantum mechanics, and anyone interested in understanding the fundamental forces of nature and their mathematical foundations.

jaumzaum
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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?
 
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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.
 
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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.
 

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