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{{Unreferenced|date=March 2008}} {{Unreferenced|date=March 2008}}
The '''neutron drip line''' is a concept in ] and ]. The line is found on a graph of Z (] or number of protons) vs N (number of neutrons). Such a graph is called a ]. In ] and ], the '''neutron drip line''' is found on a graph of ''Z'' (] or number of protons) versus ''N'' (number of neutrons). Such a graph is called a ]. The physics of ] dictates that nuclei with excess ]s will ] free neutrons. The neutron drip line serves as the neutron-rich boundary in the table of nuclides. The ], in contrast, serves as the opposite boundary of nuclear stability.
The physics of ] dictates that nuclei with excess neutrons will ] free ]. The neutron drip line serves as the neutron-rich boundary in the table of nuclides. The ], in contrast,
serves as the opposite boundary 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 <math>E_1</math> will be forced to a higher energy <math>E_2</math> if all the lower energy states are filled. This is because neutrons are ] and obey ]. The work done in putting this neutron to a higher energy level results in a pressure which is the ]. 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 ], 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 &mdash; 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. 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''<sub>1</sub> will be forced to a higher energy ''E''<sub>2</sub> if all the lower energy states are filled. This is because neutrons are ] and obey ]. The work done in putting this neutron to a higher energy level results in a pressure which is the ]. 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 ], 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 &mdash; 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 ] or ]s. In neutron stars, neutron heavy nuclei are found as relativistic electrons penetrate the nuclei and we get ], wherein the electron combines with a proton in the nucleus to make a neutron and an electron-neutrino: In astrophysics, the neutron drip line is important in discussions of ] or ]s. In neutron stars, neutron heavy nuclei are found as relativistic electrons penetrate the nuclei and we get ], wherein the electron combines with a proton in the nucleus to make a neutron and an electron-neutrino:
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: <math> E_F^n=\sqrt{(p_F^n)^2c^2 + m_n^2 c^4} \,</math> : <math> E_F^n=\sqrt{(p_F^n)^2c^2 + m_n^2 c^4} \,</math>


applies, where <math>p_F^n</math> is the ] 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 ] 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. applies, where ''p''<sub>''F''</sub><sup>''n''</sup> is the ] 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 ] 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.


==Known values== ==Known values==
The values of the neutron drip line are only known for the first eight elements, hydrogen to oxygen.<ref>http://www.sciencedaily.com/releases/2007/10/071024130508.htm</ref> For Z=8, the maximal number of neutrons is 16, resulting in the (still-undiscovered) O-24 as the heaviest possible oxygen isotope.<ref>http://www.sciencedaily.com/releases/2007/09/070913170108.htm</ref> The values of the neutron drip line are only known for the first eight elements, hydrogen to oxygen.<ref>http://www.sciencedaily.com/releases/2007/10/071024130508.htm</ref> For ''Z''&nbsp;=&nbsp;8, the maximal number of neutrons is 16, resulting in the (still-undiscovered) O-24 as the heaviest possible oxygen isotope.<ref>http://www.sciencedaily.com/releases/2007/09/070913170108.htm</ref>


==See also== ==See also==

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In particle and nuclear physics, the neutron drip line is found on a graph of Z (atomic number or number of protons) versus N (number of neutrons). Such a graph is called a table of nuclides. The physics of atomic nuclei dictates that nuclei with excess neutrons will leak free neutrons. The neutron drip line serves as the neutron-rich boundary in the table of nuclides. The proton drip line, in contrast, serves as the opposite boundary 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 E1 will be forced to a higher energy E2 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
 		 → 
n
 		 + 
ν
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 {\displaystyle E_{F}^{n}=m_{n}c^{2}\,}

And from this point the equation

E F n = ( p F n ) 2 c 2 + m n 2 c 4 {\displaystyle E_{F}^{n}={\sqrt {(p_{F}^{n})^{2}c^{2}+m_{n}^{2}c^{4}}}\,}

applies, where pF 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.

Known values

The values of the neutron drip line are only known for the first eight elements, hydrogen to oxygen. For Z = 8, the maximal number of neutrons is 16, resulting in the (still-undiscovered) O-24 as the heaviest possible oxygen isotope.

See also

Proton drip line

References

  1. http://www.sciencedaily.com/releases/2007/10/071024130508.htm
  2. http://www.sciencedaily.com/releases/2007/09/070913170108.htm
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