Strong nuclear force and Iron nucleus

[jvicens]

While reading the book " Cosmic Catastrophes. Supernovae, Gamma-Ray Bursts and Adventures in Hyperspace" by J.Craig Wheeler I came across this line:
"By the happenstance of the nature of the strong nuclear force among protons and neutrons, the fifty-six particles of an iron nucleus are more tightly bound together than in any other element (with the possible exception of a couple of exotic elements like rare isotopes of nickel, which cannot easily be formed in bature)."

The question I have is what makes iron nucleus the most tightly bounded nucleus? Is the answer related to the semi-empirical analysis done by Weizsacker in 1935 on binding energy?

 

[Astronuc]

Most tightly bound nuclei -
http://hyperphysics.phy-astr.gsu.edu/Hbase/nucene/nucbin2.html#c1

Shell model of nucleus - magic numbers
http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/shell.html#c2

58 nucleons also appears to be a magic number.

Nuclear structure concepts -
http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/nucstructcon.html#c1

The stability has to do with the nucleon pairing, and above Fe, it appears the coulomb repulsion is a factor. See departure from N = P in this figure.
http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/neutexc.html#c1 Actually Ca⁴⁰ is the heaviest nuclide with P = N = 20. After that, N > P.

₂₆Fe⁵⁴ is stable, and of course ₂₆Fe⁵⁶ is stable and is the third most tightly bound. Fe⁵⁶ is the most abundant heavy isotope in supernova cores.
http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/shell2.html

 

[jtbell]

In the "big picture" of things, the two most important competing factors in nuclear stability are the attraction caused by the strong nuclear force, and the electrostatic repulsion of the protons. Below iron, the attractive forces generally increase at a greater rate than the repulsive forces, as atomic number increases. Above iron, the opposite is true. This can be described using a simple "liquid drop" model of nuclei which leads to the "semi-empirical binding energy formula" (Google!).

There are local exceptions between pairs of adjacent nuclei because of other factors (pairing, etc.).

 

[jvicens]

Astronuc, jtbell,

Thanks for your replies and the links.
I got it now!