Understanding the Binding Energy Per Nucleon: Why Intermediate Nuclei Excel

The concept of binding energy per nucleon (BE/N) is fundamental in nuclear physics. It measures the energy required to remove a nucleon (proton or neutron) from a nucleus. This energy varies across different sizes of nuclei, with intermediate-sized nuclei exhibiting the highest binding energy per nucleon. In this article, we will delve into why this phenomenon occurs and explore the underlying factors.

Nuclear Forces

The binding of nucleons in a nucleus is primarily governed by the strong nuclear force. This force is short-range and attractive, making it crucial for the stability of nuclei. In smaller nuclei, the number of nucleons is limited, resulting in fewer interactions between nucleons. Consequently, the binding energy per nucleon is relatively lower due to the lack of extensive interactions.

In larger nuclei, the presence of repulsive forces between protons exacerbates the situation. Protons, being positively charged, experience repulsion from each other, which can reduce the overall binding energy efficiency. As a result, the binding energy per nucleon in very large nuclei tends to decrease.

Optimal Balance and Stability

Intermediate-sized nuclei, approximately those with mass numbers around 56 (such as iron), strike an optimal balance between attractive and repulsive forces. These nuclei benefit from the efficient binding provided by the strong nuclear force, which effectively holds a sufficient number of nucleons together. The repulsive forces from protons are not strong enough to overcome the binding energy, leading to higher binding energy per nucleon.

This optimal balance is achieved because in these nuclei, the strong nuclear force is strong enough to overcome the repulsive effects between protons, resulting in a more stable configuration and higher binding energy.

Shell Effects and Energy Levels

Nucleons, similar to electrons in atoms, occupy energy levels. Shell effects play a crucial role in the stability of certain nuclear configurations. Intermediate nuclei often have filled or nearly filled shells, leading to more stable arrangements and higher binding energies. These filled shells provide an extra layer of stability, enhancing the binding energy per nucleon.

Nuclear Stability and Beyond 56 Protons

As nuclei grow larger, they become increasingly unstable due to the growing ratio of repulsive electromagnetic forces from protons to the attractive strong nuclear forces. This instability leads to a decrease in binding energy per nucleon for very heavy nuclei. For example, beyond 56 protons, the 4-hedral symmetry that was efficient for smaller nuclei becomes less favorable.

For nuclei with more than 56 protons, the 12-hedral symmetry with an angle of 108 degrees becomes necessary. However, achieving this symmetrical arrangement requires inputting additional energy to squeeze the angle from 109.5 degrees (4-hedral symmetry) to 108 degrees. This additional energy input reduces the overall binding energy per nucleon.

In summary, intermediate nuclei excel in terms of binding energy per nucleon because they maximize the attractive interactions of the strong nuclear force while minimizing the effects of repulsion among protons, leading to greater overall stability.

My Theory of Everything

I propose a unique perspective on nuclear structure in my theory of everything. According to my view, nuclei can be envisioned as symmetric crystal-like lattices composed of ring-shaped protons. For up to 56 protons, the fusion is spontaneous in a 4-hedral symmetry, with an angle of 109.5 degrees, leading to an increase in binding energy per nucleon. For more than 56 protons, this symmetry becomes unfeasible, and a different 12-hedral symmetry with an angle of 108 degrees is needed, which requires an input of energy to achieve.