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Lab ↔ COM collisions, two-body decay, and Lorentz boosts. Copy LaTeX for free. Pro: worksheet PDF, batch CSV, course pack, saved notebook.
2-body collision
Beam particle 1 on fixed target 2. Algebraic θ* from tan θ_lab; illegal angles throw. Masses & KE in MeV (natural).
- √s (MeV)
- 1925.90
- Available KE in CM (MeV)
- 49.3511
- β (v/c) of CM
- 0.224930
- γ_CM
- 1.02630
- E₁* (MeV)
- 962.948
- E₂* (MeV)
- 962.948
- θ_lab max (kinematic)
- 90.00°
- ρ = β_CM / β₁*
- 1.00000
- Kinematic cone
- ρ=1 · θ_lab ≤ 90°
- θ* (unique)
- 61.30°
- E₁ lab (MeV)
- 1012.29
- E₂ lab (MeV)
- 964.258
Gold check: equal mass ⇒ θ_lab^max = 90° (independent of beam KE).
Lorentz factors
- γ
- 1.25000
- γβ
- 0.750000
- β (v/c)
- 0.600000
- Time dilation γ
- 1.25000
- Length contraction 1/γ
- 0.800000
- Rest energy (MeV)
- 0.511000
- Total energy (MeV)
- 0.638750
- Kinetic energy (MeV)
- 0.127750
Two-body decay
Parent → daughter 1 + daughter 2. θ* is the rest-frame emission angle of daughter 1 relative to the boost axis.
- Q-value (MeV)
- 33.4010
- E₁* (MeV)
- 109.777
- E₂* (MeV)
- 29.7931
- p* (MeV/c)
- 29.7887
- β (v/c) parent
- 0.676714
- γ parent
- 1.35824
- E₁ lab (MeV)
- 170.079
- E₂ lab (MeV)
- 19.4919
- θ₁ lab
- 8.260°
- θ₂ lab
- -100.7°
Saved history
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Ten homework-shaped initial conditions with gold checks. Titles are free; JSON + answer keys are Pro.
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- γ at β = 0.6
- Compton at 90°
- Fresnel air → glass, normal incidence
- Product error σ(xy)
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