# Arrangement of Nucleons due to Strong Force

I was reading up on the fundamental forces of nature and I was wondering about the arrangements of nucleons due to the strong force. Considering electromagnetic repulsion, having 2 protons "bonding" together in the following arrangement:

p-p


would be impossible due to repulsion. However, according to strong force, once the protons are close enough, strong force should take over and bind them together rather stably.

Similarly, in a system with 2 neutrons and 2 protons, a bonding like below should be attainable:

n-n
| |
p-p


However, in most textbooks and sites I have checked, they usually describe an alternating pattern instead. Hence, I would like to know why these arrangements are not possible.

• You shouldn't take the pictures of colored balls as indicative of anything. These systems don't behave like bonding atoms and don't have a well defined inter-object geometry because the objects don't have well defined positions. – dmckee Apr 27 '16 at 2:20
• To add to @dmckee, unlike in the case of atoms, where the single-electron wave function can be somewhat visualized, these multi-particle systems don't leave us with many options to do a "show and tell", either. There are reasonable semiclassical shell models of nuclei, but how much faith you want to put in them to visualize the arrangement of individual protons and neutrons probably depends on your familiarity with the details of nuclear physics. Personally I would stay away from imagining that geometric pictures suitable for humans are of much value at this scale. – CuriousOne Apr 27 '16 at 2:37
• The following paper might give a bit of a taste for how complex this problem is: "Quantum Monte Carlo methods for nuclear physics" J. Carlson, which you can download at arxiv.org/pdf/1412.3081 . The same author has a 1988 paper about the alpha particle structure, but I can't find an accessible version. – CuriousOne Apr 27 '16 at 5:52
• The following question may be of interest to you physics.stackexchange.com/questions/147499/… – jim Apr 27 '16 at 8:43

Nuclei belong to the quantum mechanical framework, the underlying network of all natural forces.

They are composed out of protons and neutrons . Protons and neutrons are composed out of 3 quarks each , between quarks , the strong force described by quantum chromodynamics generates the "bag" where the quarks are tightly bound and exist in a sea of gluons ( the exchange particle of the force) and quark antiquark pairs. Here is a proton:

The image is a good approximation of the large number of gluon exchanges between the valence quarks that hold the nucleus bound in its mass envelope.

The nuclear strong force is a spill over force called residual, out of the nucleon bags , similar to the van der Waals forces in the atomic electromagnetic scale, and they are the forces that hold a proton and a neutron together in a deuteron.

Unlike the strong force itself, the nuclear force, or residual strong force, does diminish in strength, and in fact diminishes rapidly with distance. The decrease is approximately as a negative exponential power of distance, though there is no simple expression known for this; see Yukawa potential. This fact, together with the less-rapid decrease of the disruptive electromagnetic force between protons with distance, causes the instability of larger atomic nuclei, such as all those with atomic numbers larger than 82 (the element lead).

Due to the self interactive nature of the gluon exchanges, which are at the kernel of all nuclear forces, the nucleons cannot arrange themselves in a crystal structure as in solids where the photon does not self interact so an image of a nucleus as a crystal like structure is wrong from the basic level. There are regularities which the repulsive electromagnetic versus attractive strong force the nucleons into, but these are not spatial, they are regularities in quantum numbers, like baryon number and charge, as seen in an isotope table. For certain combinations nuclei are stable, for others extremely unstable.

The nuclear shell model is quite successful in classifying nuclei in energy levels. The alpha particles are particularly stable and appear often in decays of unstable nuclei due to their stronger binding, and have been used in modeling the shell levels. All these models are in energy levels and quantum numbers, there is no spatial symmetry at the nuclear level.

• Amplifying @annav comment on the success of the nuclear shell model at describing nucleon distributions inside heavy nuclei, see arxiv.org/ftp/arxiv/papers/1504/1504.05507.pdf where experimental charge density differences between Pb and Tl nuclei are compared with $3s\frac{1}{2}$ wave functions (the last occupied proton shell model state in Pb). Nuclei are true quantum objects. – Lewis Miller Apr 28 '16 at 0:07