# saturation property of nuclear forces ? and its relation binding energy per nucleon constantcy?

Please explain why binding energy per nucleon is constant(pratically) for atomic number, A, larger than 30 and less than 170, and explain the saturation property of nuclear forces with analogy that is easy to understand?

• There was some problem with formatting that I corrected by the < symbols used. It is a valid question so I do not see why the down vote – anna v Mar 8 '14 at 6:18

You have to realized that the combined forces that bind the protons and neutrons together are a complex interplay between two forces:

a)The electromagnetic one, where the charge of a proton repels the charge of another proton and no binding could occur

b) the strong force , the force that binds the quarks into the protons and neutrons, and spills over around each proton and neutron and is an attractive one.

From this you can understand that the number of particles that can be "bound" depends on the interplay of the repulsive and attractive forces and is a many body problem not solvable analytically, but with various nuclear models. These models are fairly successful in describing the behavior of the nuclei and the way the energy is distributed ( binding energy).

A third process that enters the problem is that neutrons are not stable, if they are not bound within a collective nuclear potential they decay ( beta decays of isotopes).

Qualitatively you can think that after a certain mass number (A) , the assumption of average density will be fairly good Too many protons would spoil the broth by repulsion, so the mass number is limited at the high end, too many neutrons would have outer energy level neutrons decay and this is also a limit. On the lower end of mass number, the number of nucleons in the nucleus is too small and the statistical arguments of density can no longer be a good approximation.

• How is this related to maximum number of nucleons that can be around another one? I still don't find it clear as to why would nuclei of atoms having A more than 170 will have less binding energy per nucleon. Please help – Quark Jan 7 '16 at 0:48
• @Quark If you are familiar with the hydrogen atom energy levels , you see that quantum mechanically the higher the energy quantum number n the smaller the distance to the zero which defines the binding of the electron. An electron caught by a proton at a high n has very small bininding energy. hyperphysics.phy-astr.gsu.edu/hbase/hyde.html . A very successful nuclear model is the shell model of the nucleus hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html , which assumes a collective potential from the spill over strong force – anna v Jan 7 '16 at 5:26
• with energy levels that are occupied by nucleons which obey quantum numbers and Pauli exclusion . Close to the 0 of the effective potential, the high n quantum number, the binding will be small for the extra nucleon added after a certain n. The depth of the potential depends on fits to the table of nuclei . – anna v Jan 7 '16 at 5:29