Picture the proton

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Particle Physics, Ch Isospin: a symmetry used as bookkeeping

Problem

Picture the proton, crudely, as a charge

+e

smeared over a sphere of radius

r \approx 0.8\,\mathrm{fm}

(its measured charge radius). Taking the fact that two unit charges

1\,\mathrm{fm}

apart store

1.44\,\mathrm{MeV}

of electrostatic energy, estimate the electromagnetic self-energy scale of the proton on this size. Compare your estimate with the measured proton-neutron mass difference of

1.293\,\mathrm{MeV}/c^2

(the neutron is the heavier one), and explain, in terms of the two competing contributions to isospin breaking, why the sign of the observed splitting is not the sign this electromagnetic estimate alone would suggest.

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