Neutron drip line

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The neutron drip line is a concept in particle and nuclear physics. An unstable atomic nucleus beyond the neutron drip line will leak free neutrons. In other words, the neutron drip line is the line on the Z, N plane (see table of nuclides) where the neutron separation energy is zero; the neutron drip line serves as a boundary for neutron-rich nuclear existence. This phenomenon may be contrasted with the proton drip line, as these concepts are similar, but occurring on opposite sides of nuclear stability.

We can see how this occurs by considering the energy levels in a nucleus. The energy of a neutron in a nucleus is its rest mass energy minus a binding energy. In addition to this, however, there is an energy due to degeneracy: for instance a neutron with energy $E 1$ will be forced to a higher energy $E 2$ if all the lower energy states are filled. This is because neutrons are fermions and obey Fermi-Dirac statistics. The work done in putting this neutron to a higher energy level results in a pressure which is the degeneracy pressure. So we can view the energy of a neutron in a nucleus as its rest mass energy minus an effective binding energy which decreases as we go to higher energy levels. Eventually this effective binding energy has become zero so that the highest occupied energy level, which is the Fermi energy, is equal to the rest mass of a neutron. At this point adding a neutron to the nucleus is not possible as the new neutron would have a negative effective binding energy — i.e it is more energetically favourable (system will have lowest overall energy) for the neutron to be created outside the nucleus. This is the neutron drip point.

In astrophysics, the neutron drip line is important in discussions of nucleosynthesis or neutron stars. In neutron stars, neutron heavy nuclei are found as relativistic electrons penetrate the nuclei and we get inverse beta decay, wherein the electron combines with a proton in the nucleus to make a neutron and an electron-neutrino:

$p^+ + e^- \rightarrow n + \nu_e \,$

As more and more neutrons are created in nuclei the energy levels for neutrons get filled up to an energy level equal to the rest mass of a neutron. At this point any electron penetrating a nucleus will create a neutron which will "drip" out of the nucleus. At this point we have:

$E_F^n=m_n c^2 \,$

And from this point the equation

$E_F^n=\sqrt{(p_F^n)^2c^2 + m_n^2 c^4} \,$

applies, where $p_F^n$ is the Fermi momentum of the neutron. As we go deeper into the neutron star the free neutron density increases, and as the Fermi momentum increases with increasing density, the Fermi energy increases, so that energy levels lower than the top level reach neutron drip and more and more neutrons drip out of nuclei so that we get nuclei in a neutron fluid. Eventually all the neutrons drip out of nuclei and we have reached the neutron fluid interior of the neutron star.