Workbench
Lab ↔ COM collisions, two-body decay, and Lorentz boosts. Copy LaTeX for free. Pro: named workspace, sweeps, dataset export, PDF, course-pack JSON, local history.
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
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°
Named workspace
Save up to 20 named input sets and restore them later — included with Pro.
Unlock Pro →Parameter sweep
Build a grid over one or two inputs (cap 200 rows) and download CSV — included with Pro.
Unlock Pro →Saved history
Pro unlocks a local notebook of your last 50 calculations.
Unlock Pro →Batch CSV sweeps
Parameter grids for collisions, decays, Compton, and Bosch–Hale ⟨σv⟩ — included with Pro.
Unlock Pro →Dataset bench
Full pagePaste x, y[, σ] CSV. Choose a fit model below. Fit and plots are free; PDF and residual CSV are Pro.
Ordinary least squares in y.
- model
- Linear y = ax + b
- N
- 5
- slope a
- 2.02600
- σ(a)
- 0.0460145
- intercept b
- -0.0460000
- σ(b)
- 0.152613
- residual σ
- 0.145511
- R²
- 0.998455
- χ²
- 4.03668
- ν
- 3
- χ²/ν
- 1.34556
Course pack
Ten homework-shaped initial conditions with gold checks. Titles are free; JSON + answer keys are Pro.
- pp elastic at 100 MeV, 30°
- Equal-mass gold check at 90°
- Kinematic cone (m1 > m2)
- π⁰ → γγ at rest vs in flight
- γ at β = 0.6
- Compton at 90°
- Fresnel air → glass, normal incidence
- Product error σ(xy)
- DT reactivity at 10 keV
- Kepler lab: eccentricity overlay