Undergrad ?Measuring the Strong Force: Strength vs Distance

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Measurements of the strong force indicate that its strength varies with distance, but this relationship is complex due to the influence of particle orientation, necessitating a family of curves rather than a single representation. The strong force binds quarks in hadrons, while higher-order residuals of this force, which are comparable to gravitational tidal forces, bind nucleons in atomic nuclei. Simulating the strong force presents challenges, particularly at larger distances where calculations often diverge. Quasi-classical solutions suggest a long-range tail of the strong force can extend up to 20,000 femtometers before decaying exponentially, although in reality, hadrons are effectively shielded by virtual mesons, confining the force to a range of 1-2 femtometers. The mechanics of this shielding remain a topic of ongoing scientific discussion.
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Have there been any measurements of the strong force? Also its curve of the strength of the force vs distance
 
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It is possible to create such curve, but it will not be very useful, because the strong force also depends on particles orientation (spin), therefore you need to draw family of curves rather than single curve.
Also, you should distinguish between strong force itself (which binds quarks in hadrons), and the higher-order residuals of strong force (comparable to gravitational tidal forces - this part binding nucleons in atomic nuclei).
The force(distance) curve for strong force higher order residuals is below:
VTxIb.png

Actually, we have problems simulating strong force because calculations tends to easily diverge at larger distances. The quazi-classical solutions (based on matter wave made of pi-mesons) seems to suggest long-range tail of strong force can be as long as 20000 fm before exponentially decaying. In real world, hadrons strong force is very effectively shielded by their "shell" of virtual mesons, confining strong force to just 1-2 fm range. Details on how shielding works is still a subject of scientific debate, but within shield the strong force falls with distance slower than r-2
 

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Thank you so much.
 
Is there an equivalent charge value to elementary charge?
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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