How to Determine the Range of Strong and Weak Interaction

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Discussion Overview

The discussion centers on how to determine the ranges of strong and weak interactions, exploring both theoretical predictions and experimental measurements. Participants consider the implications of scattering cross sections and various models related to these fundamental forces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the range can be estimated using the rest-mass energy of the mediating boson in relation to the Heisenberg Uncertainty Principle (HUP).
  • Another participant provides specific estimates for the ranges of weak and strong interactions, citing approximately 0.02 fm for weak interactions and about 1 fm for strong interactions between baryons and quarks.
  • A different viewpoint emphasizes the distinction between theoretical predictions and experimental determinations of interaction ranges, particularly noting that the strong interaction between nucleons and quarks may be modeled differently.
  • One participant mentions the liquid drop model as a method to establish an upper limit on the range of the strong force between nucleons, suggesting that the range is small compared to the size of nuclei.
  • Another participant raises a question about defining what is meant by the "range" of an interaction and how it can be measured, particularly in the context of weak interactions.

Areas of Agreement / Disagreement

Participants express differing views on the methods for determining interaction ranges, with some focusing on theoretical models and others on experimental approaches. There is no consensus on how to define or measure the range of these interactions.

Contextual Notes

Participants highlight the complexity of measuring interaction ranges, noting that definitions and models may vary significantly between different contexts, such as between nucleons and quarks. There are unresolved questions regarding the implications of these definitions on the understanding of strong and weak interactions.

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How can we determine the ranges of strong interactions and weak interactions?
Can calculations of relevant scattering cross sections do this?
Thanks.
 
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The ballpark-range can be worked out by putting the rest-mass energy of the mediating boson into the HUP relations.

It can be checked impirically by working out the crossection as a function of range.
 
The range of weak interactions is of the order of 1/M_W~.02 fm.
The range of strong interactions between baryons is of the order of 1/m_pi~1 fm.
The range of strong interactions between quarks is due to gluon-gluon interactions,
leading to a confining potential with a range of about 1 fm.
 
I think the OP was asking how to determine these things experimentally, not how to predict them theoretically.

The answers to these questions are completely different depending on whether you're talking about the strong interaction between two nucleons and the strong interaction between two quarks. The latter interaction is usually modeled with an interaction that is of infinite range, and that gets *stronger* with distance.

A very simple way to put an upper limit on the range of the strong force between nucleons is from the liquid drop model. The liquid drop model contains a surface tension term, and the fact that the liquid drop model does a good job of fitting nuclear binding energies tells us that this surface tension term is physically accurate. This implies that the range of the strong force is small compared to the diameter of nuclei.

Re the question of how to put a lower limit on the range of the strong force, I'm not sure what it would even mean to hypothesize that the range of the strong force between two nucleons was less than about 1 fm, since nucleons themselves are fuzzy and about 1 fm in size.
 
Someone interested in the experimental foundation of the strong force should probably start with Hideki Yukawa (Nobel Prize 1935).
http://www.nobelprize.org/nobel_prizes/physics/laureates/1949/yukawa-facts.html
Somewhat accessible discussion:
http://www.applet-magic.com/yukawa.htm

Weak interaction is eluding me - it looks like it was more the accumulated general success of the model rather than any direct measurement.

I think the key here would be to define what one would mean by the "range" of an interaction - i.e. what are you actually going to measure?
 

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