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Nucleons (neutrons and protons) can be regarded as composed of three massless relativistic quarks freely moving inside a spherical volume with radius r and uniform energy per unit volume B inside the sphere. (The energy density outside the sphere is zero). Given that the experimentally measured rest energy of a nucleon is M ~ 1000 MeV and the radius of a nucleon is ~ 1 fm (10-15m), estimate the magnitude of B in MeV/m3.
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Answer
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The quarks are confined with radius r, so
(1)$\partial E/ \partial r = 0$ implies that
(2)$\hbar c = 1.97 \times 10^{-13}$ MeV-m so
$B=\frac{1.97 \times 10^{-13}}{\left ( 10^{-15} \right )^4} = 1.97 \times 10^{47}$ MeV/m3
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