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When a star becomes a neutron star, it says that the gravity is so large that it exceed the electron degeneracy pressure then electron combine with atomic nucleus to give neutrons.

Is there known/verified microscopic processes for the above process, like a electron scattering with a proton to give a neutron plus some other particles for a given chance? For example, when talking about normal stars, there are a lot of nuclear reaction equations for the microscopic processes in the stars, but I can't find one online for this.

There is electron capture process which is based on weak interaction, but I think it is the process that happens in some special atoms, not plasma in the star.

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$$ p + e \rightarrow n + \nu_e$$ is a weak interaction that conserves baryon and lepton number. Often known as neutronisation or inverse beta decay.

It also occurs for protons inside nuclei with atomic mass $A$ and atomic number $Z$. $$ (A,Z) + e \rightarrow (A,Z-1) + \nu_e$$

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