Inverse beta decay ( ) becomes possible once the electrons' Fermi energy (total…
PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Relativity & Gravitation · Quantum statistical mechanics and quantum gases
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Problem
Inverse beta decay (p+e−→n+ν) becomes possible once the electrons' Fermi energy (total relativistic energy, including rest mass) reaches EF=1.29MeV, the neutron-proton mass difference. The threshold density found in the text is for an idealised gas of free protons and electrons, with one electron per baryon (Ye=1). Consider instead a hypothetical patch of symmetric nuclear matter with equal numbers of protons and neutrons, so that there is one electron for every two baryons (Ye=0.5). Treating the electrons as a degenerate relativistic Fermi gas and the baryons as each carrying one atomic mass unit mu, find the mass density at which inverse beta decay starts in this matter.