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The enclosed graph shows the number of Protons on the x-axis (Z), and the number of Neutrons on the y-axis for all elements (N). Stable combinations are marked by black squares, whereas unstable ones are marked by grey squares. I understand why there is a grey "line" located above the black "line", as adding electrically positive, mutually repelling, protons would make the nucleus less stable. However, I do not understand why there is a grey "line" to the right of the black "line": isn't adding neutrons supposed to make a nucleus more stable (as a result of the additional Strong Force and greater distance between the protons)?

Can anyone help out?

Thank you!

enter image description here from Yoram Kirsh, Fundamentals of Physics B, Tel Aviv, 1998, p. 111.

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    $\begingroup$ Please don't cut and paste stuff on the internet without attribution to the author. It's rude. $\endgroup$ – Ben Crowell Oct 4 '18 at 13:26
  • $\begingroup$ So you think one should be able to add an infinite number of neutrons? The simple answer to the question is that nuclear physics is more complicated than that. $\endgroup$ – Jon Custer Oct 4 '18 at 14:06
  • $\begingroup$ @BenCrowell You're right: sorry, it totally slipped my mind… I have edited the question accordingly. $\endgroup$ – Pregunto Oct 4 '18 at 15:11
  • $\begingroup$ @JonCuster No, I do not think that, but that does little to reveal the underlying mechanisms. $\endgroup$ – Pregunto Oct 4 '18 at 15:12
  • $\begingroup$ @Pregunto, note: protons (atomic number) are on the y-axis and neutrons are on the x-axis. $\endgroup$ – David White Oct 4 '18 at 18:14
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What your analysis is missing is that the nuclear attraction between a neutron and a proton is somewhat larger than the attraction between two neutrons or two protons. In nuclear physics this difference is called the symmetry energy. Because of this symmetry interaction the most tightly bound nuclei result from a balanced competition between the attractive symmetry energy and the coulomb repulsion between protons. As you deviate from this balance by having too many or too few neutrons, the resulting nuclei are less stable.

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