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Nuclear Force

Nuclear Force (Properties)

The nucleus contains positively charged protons and neutral neutrons packed together in a very small volume. If only the electrostatic force were present, the strong repulsive forces between the protons would cause the nucleus to fly apart immediately. Since stable nuclei exist, there must be a very strong attractive force acting within the nucleus that overcomes the electrostatic repulsion and holds the nucleons together. This force is called the nuclear force or the strong nuclear force. It is one of the four fundamental forces in nature (along with gravitational, electromagnetic, and weak nuclear forces).

Properties of the Nuclear Force

Based on experimental observations of nuclear structure and nuclear reactions, the strong nuclear force exhibits several distinct properties:

  1. Strongest Fundamental Force: The nuclear force is the strongest of all the fundamental forces. It is about 100 times stronger than the electromagnetic force at typical nuclear distances ($10^{-15}$ m) and vastly stronger than the gravitational force. This immense strength is necessary to bind protons together against their mutual electrostatic repulsion.
  2. Short-Ranged Force: The nuclear force is a very short-ranged force. Its strength is significant only over distances comparable to the size of a nucleus (a few femtometers, $10^{-15}$ m). At distances larger than about 1 femtometer, the force is strongly attractive. At distances much larger than a few femtometers (say, beyond $4 \times 10^{-15}$ m), its strength decreases rapidly and becomes negligible compared to the Coulomb force. This explains why the nuclear force primarily acts within the nucleus and does not affect electrons orbiting the nucleus.
  3. Attractive over Short Distances (but Repulsive at Very Short Distances): The nuclear force is primarily attractive at distances between nucleons typically found in a nucleus (around 0.8 fm to 4 fm). This attraction holds the nucleus together. However, experimental evidence suggests that the force becomes strongly repulsive at very short distances (less than about 0.8 fm). This repulsion prevents the nucleus from collapsing into a point and gives it a finite size.

    Graph showing the potential energy between two nucleons versus distance, illustrating the short-range attractive and repulsive nature of nuclear force

    Potential energy between two nucleons as a function of distance. Negative potential energy indicates attraction.

  4. Charge-Independent: The nuclear force is approximately charge-independent. It acts equally strongly between a proton and a proton (p-p), a neutron and a neutron (n-n), and a proton and a neutron (p-n). While there are small differences, the primary strong interaction does not depend on whether the particles are charged or neutral. This property helps explain why the binding energy per nucleon is roughly constant for most nuclei (saturation).
  5. Spin-Dependent: The nuclear force depends on the relative orientation of the spins of the interacting nucleons. The force is stronger when the spins of the two nucleons are parallel than when they are anti-parallel. This is important for understanding the magnetic moments and spins of nuclei.
  6. Saturated Force: The nuclear force exhibits saturation. A nucleon interacts strongly only with a limited number of its nearest neighbours within the nucleus. This is unlike the Coulomb force or gravitational force, which are long-ranged and every particle interacts with every other particle in the system. The saturation property explains why the binding energy per nucleon is relatively constant for nuclei with $A > 20$ and why heavy nuclei become unstable. Adding more nucleons to an already large nucleus doesn't significantly increase the binding per nucleon because the new nucleons only interact with their immediate neighbours and don't feel the force from nucleons far away in the nucleus.
  7. Non-Central Force Component: The nuclear force is not entirely a central force (a force directed solely along the line joining the centers of the two interacting particles). It has a small tensor component which depends on the orientation of the nucleons' relative to the line joining them and also on their spins. This non-central component is important for understanding the quadrupole moments of nuclei.

The exact nature of the strong nuclear force is described in terms of the exchange of particles called mesons between nucleons, or more fundamentally, in terms of the interactions between quarks (constituents of protons and neutrons) mediated by gluons (described by Quantum Chromodynamics, QCD). However, the properties listed above provide a macroscopic description of how the force behaves between nucleons within the nucleus.

Understanding the nuclear force is crucial for explaining nuclear stability, the properties of different isotopes, nuclear reactions (fission and fusion), and the behaviour of nuclear matter in extreme conditions (e.g., in neutron stars).

Example 1. Explain why the gravitational force and electrostatic force alone cannot hold the nucleus together.

Answer:

The nucleus contains protons (positively charged) and neutrons (neutral). The particles within the nucleus are nucleons.

1. Electrostatic Force: Protons are positively charged. Like charges repel each other. Therefore, there is a strong electrostatic repulsive force between every pair of protons within the nucleus. This repulsive force tends to push the protons apart and disrupt the nucleus. Neutrons are electrically neutral, so they do not experience electrostatic forces.

2. Gravitational Force: All particles with mass attract each other through the gravitational force. Both protons and neutrons have mass, so there are attractive gravitational forces between all nucleons. However, the gravitational force is extremely weak compared to the electrostatic force. The electrostatic repulsion between two protons at nuclear distances is vastly stronger (by a factor of around $10^{36}$) than the gravitational attraction between them.

Therefore, the attractive gravitational force is completely negligible compared to the repulsive electrostatic force between protons in the nucleus.

To hold the positively charged protons together and prevent them from being pushed apart by electrostatic repulsion, a much stronger attractive force is required. This is the role of the strong nuclear force, which is attractive between all nucleons (p-p, n-n, p-n) at short range and is strong enough to overcome the electrostatic repulsion between protons and bind the nucleus into a stable entity.