In pion nucleon scattering, the pion and nucleon can combine to form a short lived
bound state called the Δ particle (𝜋 + N → Δ). The masses of the pion,
nucleon and the Δ particle are 140 MeV/c2, 938 MeV/c2 and 1230 MeV/c2,
respectively. In the lab frame, where the nucleon is at rest, what is the minimum
energy (in MeV/c2, rounded off to one decimal place) of the pion to produce the
Δ particle?
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.60)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Nuclear & Particle Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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