Question

In scattering theory, the differential cross-section determines:

• A. The probability of a particle being deflected by a specific angle
• B. The total energy of the scattering particles
• C. The phase shift of the wave function
• D. The conservation of angular momentum

Hint:

Differential cross-section \( \frac{d\sigma}{d\Omega} \) measures the angular probability distribution of scattered particles. Higher values at a given angle mean more particles scatter in that direction.

Answer 1

The Correct Option is A

Step 1: In scattering theory, the differential cross-section \( \frac{d\sigma}{d\Omega} \) represents how likely a particle is to scatter into a particular solid angle \( d\Omega \). It provides a measure of the angular distribution of scattered particles.
Step 2: The quantity \( \frac{d\sigma}{d\Omega} \) tells us the probability per unit solid angle that a particle will scatter in a particular direction, i.e., by a specific angle.
Step 3: This concept is fundamental in nuclear and particle physics, as well as in classical scattering experiments, and helps experimentalists determine how interactions vary with direction.
Why the other options are incorrect:

• (B) The total energy of scattering particles is a separate conserved quantity and is not determined by the differential cross-section.
• (C) The phase shift affects the cross-section but is not what the cross-section directly measures.
• (D) Conservation of angular momentum is a general principle but is not what the differential cross-section quantifies.