Level 5 · Graduate study · advanced assessment
Nuclear-channel closure examination
Demand simultaneous closure across reaction rate, products, radiation, heat, and complete facility energy accounting.
Complete all three challenges. Show assumptions, units, uncertainty, and the boundary between calculation, model-dependent inference, observation, and unresolved claim.
Challenge 1 · derivation
Close the reaction-network ledger
For a specified two-channel reaction network, derive production rates, detector count rates, nuclear power, and complete facility gain from cross sections, densities, efficiencies, branching fractions, and Q-values.
Required deliverables
- • Reaction and detector equations with units
- • Channel-by-channel energy ledger
- • Conservation and limiting-case checks
Scoring criteria · 20 points
- • Rate and branching derivation: 8 points
- • Detection and power accounting: 7 points
- • Closure checks: 5 points
Challenge 2 · analysis
Fit products and heat jointly
Given synthetic product, radiation, calorimetry, and electrical-input records, fit a shared reaction-rate model. Test whether any single rate can explain all channels within uncertainty and diagnose structured residuals.
Required deliverables
- • Joint likelihood or weighted objective
- • Residual and posterior/prediction plots
- • Model-adequacy decision with uncertainty
Scoring criteria · 20 points
- • Shared-rate model is correctly constructed: 7 points
- • Uncertainties and correlations considered: 7 points
- • Adequacy conclusion is evidence bounded: 6 points
Challenge 3 · design
Build a multi-channel replication
Design a cross-laboratory nuclear-claim test requiring synchronized calorimetry, isotopic products, radiation channels, blanks, and known-source calibration. Define how anomalous heat without products will be reported.
Required deliverables
- • Shared protocol and specimen chain of custody
- • Calibration, blank, and contamination-control matrix
- • Sequential release gates for heat, products, and replication
Scoring criteria · 20 points
- • Channels and controls are co-registered: 7 points
- • Contamination and calibration addressed: 7 points
- • Release gates prevent selective reporting: 6 points
Instructor solution outlines
Look for reasoning that survives inspection
1. Close the reaction-network ledger
- • Separate physical production from detector acceptance and efficiency.
- • Weight each channel by its own Q-value and branching fraction.
- • Include all facility inputs; detector counts cannot substitute for calorimetric closure.
2. Fit products and heat jointly
- • Link every predicted channel to one latent physical reaction rate.
- • Include background and efficiency nuisance parameters rather than subtracting them invisibly.
- • Reject closure when heat and products require incompatible rates, even if one channel appears significant.
3. Build a multi-channel replication
- • Lock sample IDs and analysis plans before unblinding.
- • Use independent laboratories for at least one product assay and one calorimetric check.
- • Classify heat-only outcomes as unresolved or non-nuclear under the declared network, not as confirmed nuclear evidence.