How does the strong force loses its strength with distance?

[Giuseppino32]

The strong nuclear force keeps the protons together. The larger the number of protons, the larger the nucleus, but the weaker the bonds between the protons as the radius of the nucleus increases and more unstable is the element. However, since the strong nuclear force originates from within each proton, how do the bonds weaken with distance when the distance between two protons remains the same? How does it weaken as the nucleus increases?

 

[Orodruin]

You have set A-level for this thread, which indicates you expect an answer at graduate level. In this case this would mean at least an introductory understanding of quantum field theory. Is this correct?

 

[Giuseppino32]

You have set A-level for this thread, which indicates you expect an answer at graduate level. In this case this would mean at least an introductory understanding of quantum field theory. Is this correct?

That's correct

 

[Orodruin]

The beta function of SU(3) is negative due to the gauge self-interaction terms overcoming those terms that arise due to the quark content of the SM. This results in the strong interaction coupling constant growing as distance increases to such an extent that color charges confine - it is energetically favorable to create new particles than to separate two colored charges by a large distance - resulting in overall color neutral composite objects at low energies. These composite particles - baryons and mesons - can only interact via residual strong interactions similar to how electrically neutral particles would interact via van det Waal interactions. The residual strong force is effectively mediated by pions, which are massive, leading to the residual interactions essentially giving rise to a Yukawa-like potential, for which the range is exponentially suppressed by the pion mass.