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# 5.2 Electron capture

The second mechanism by which energy is absorbed in the iron core of a star is that of electron capture, allowing energy to be carried away by neutrinos. The conversion of protons (in nuclei) to neutrons by electron capture is possible if the gas is sufficiently dense for degenerate electrons to have an energy greater than the 1.29 MeV mass-energy excess of neutrons relative to protons (, while ). Actually, the energy excess required for electron capture by bound nuclear protons, rather than free protons, is usually somewhat higher and depends on the nucleus, but is nevertheless usually just a few MeV.

The general reaction may be written as

and is sometimes referred to as neutronisation.

At densities above about 1012 kg m-3, iron-56 nuclei will capture electrons in the following reaction which produces a neutron-rich manganese nucleus:

where is a neutrino. Following this, further electron-capture reactions occur in successive nuclei, converting more and more protons into neutrons.

Because electrons are rapidly used up by these reactions, the pressure support provided by degenerate electrons quickly disappears, and the core collapses rapidly, as noted earlier. The neutrinos produced by the electron-capture reactions carry away most of the energy. Although the passage of the neutrinos is hindered by the high densities in the core, which raises the likelihood of interactions, all of the neutrinos are still able to escape within a few seconds.

## Activity 9

If each neutrino produced in the reactions described above carries away 10 MeV of energy, how much energy (in joules) is removed by neutrinos if the whole core (comprising 1.4 M☉ of iron-56) undergoes neutronisation? (The mass of an iron-56 nucleus is 56u, where kg is the atomic mass unit.)

### Discussion

The number of nucleons contained in the stellar core is where u is the atomic mass unit. Because an iron-56 nucleus contains 26 protons (and 30 neutrons), the number of protons in the core is . This is evaluated as

Assuming charge neutrality, there will also be electrons. If every proton and electron undergoes neutronisation, this will produce neutrinos.

If each neutrino carries away 10 MeV of energy, then the amount of energy removed by each neutrino in joules is . So the total amount of energy removed is .

As the result of the previous activity shows, neutronisation, like nuclear photodisintegration, can also remove ~ 1045 J of energy from the collapsing stellar core within a few seconds!

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