Threshold Energy For Nuclear Reaction

Threshold Energy in Nuclear Reactions

In nuclear physics, the threshold energy is the minimum kinetic energy that a projectile particle must possess in order to make a particular nuclear reaction occur.

Definition

The threshold energy for a nuclear reaction is defined as the minimum energy of the incoming particle required to overcome the energy difference between the reactants and the products, ensuring the reaction can proceed while conserving both energy and momentum.

Explanation

If a reaction absorbs energy (i.e., it is endothermic), the projectile must supply not only this reaction energy but also additional energy to satisfy momentum conservation. Thus, the actual threshold energy is slightly higher than the reaction’s Q-value (when Q is negative).

Threshold Energy (E_th) = −Q × (1 + m_a / M_A)

where Q is the reaction energy, m_a is the mass of the projectile, and M_A is the mass of the target nucleus.

Example

In the reaction p + ³H → ³He + n, if the reaction Q-value is negative, the proton must have at least the threshold energy computed from the above relation for the reaction to take place.

Summary

The concept of threshold energy helps determine the minimum energy requirement for initiating endothermic nuclear reactions and plays a vital role in nuclear reactor design and particle accelerator physics.