# Literature canon — primary sources for the OpenCretin scaling-law engine
**2026-06-05.** Pulled from primary sources (Dicke, Gross-Haroche, Ketterle/Cornell-Wieman Nobel,
de Groot, Molisch-Oehry, Babb-Kirby) so the engine is built on what these people DERIVED, not on
from-weights priors. This replaces "I reason about superradiance from my prior."

## ★★ 0. THE FRAME CORRECTION (operator, 2026-06-05) — "superradiance conserves energy" is a CLOSED-system theorem, FALSE in this open driven quasi-equilibrium

I (Opus) asserted: "superradiance conserves total radiated energy — peak ∝ N², width ∝ 1/N, so
∫ ∝ N = the stored excitation. It redistributes in time, not magnitude." **That is the
ISOLATED-ENSEMBLE result** (N atoms pre-excited, no pump, no bath, decaying once — Dicke 1954,
Gross-Haroche). It is the same class of error as S=B, single-T, Holstein-linear: a clean
closed-form theorem imported past its boundary of validity into the DRIVEN OPEN regime that is the
entire point of the device.

**Operator's correction (the right ordering principle):** this is a driven open quasi-equilibrium
with a CONTINUOUS CHEMICAL RESERVOIR held at the bond-energy scale (H–O ≈ 4.8 eV ≈ 55,000 K). The
right question is NOT "how much excitation is stored" but: **WHICH interaction is being
entropically driven, through WHICH channel, between WHICH temperature scales.** Energy/entropy
cascades DOWN from the ~55,000 K bond reservoir to the cold radiation sink; the RATE of the cascade
is set by the fastest available channel.

**The load-bearing consequence (operator, verbatim sense):** *"if a radiative atom is added and it
COOLS a region, it INCREASES total radiated energy, because it drives a pulsed DE-population of
states."* Adding a fast radiator (or a cooperative/superradiant channel) lowers the local effective
temperature of the radiating mode → STEEPENS the gradient from the reservoir → INCREASES the heat
flux out of the chemical reservoir into radiation. The radiator is a BETTER PIPE between the
55,000 K source and the cold sink.
- CLOSED system: a better pipe drains a fixed tank faster (∫ conserved — my wrong default).
- OPEN system, reservoir refilled at fixed T: a better pipe RAISES the steady throughput → MORE
  total radiated energy, because you pull harder on the reservoir.

The conserved quantity is NOT the radiated energy — it is the FREE-ENERGY THROUGHPUT of the
reservoir, and a lower-impedance radiative channel raises it. The N² is a **channel-impedance
effect on an open pipe** (Le Chatelier / coupled-reservoir), NOT a temporal redistribution of a
closed budget. The Dicke "∝N" theorem ASSUMES the excitation reservoir is finite and closed; the
moment it is a chemical bath at fixed high T with finite-rate coupling, that assumption is void.

**Build implication (corrects §1 below):** the superradiance gate must NOT use closed-system
Arecchi-Courtens / "does coherence survive in the bulk" as the ONLY path. It must also ask the
THERMODYNAMIC-DRIVE question: is there a reservoir-driven entropic cascade (the reaction cline at
the bond-energy scale) that the cooperative channel can ACCELERATE? That is a free-energy-flux
condition, not just a coherence-survival condition. The default-N / N²-gated-off framing in §1 is
BACKWARDS for the driven cline — there, opening the cooperative channel increases throughput.

## 1. Superradiance — the N vs N² gate (the CLOSED-system coherence conditions — necessary but NOT the whole story; see §0)

**τ_R = 8π·τ_sp / (3·n·L·λ²)** — cooperative emission time. τ_sp(Na D) = 16 ns.
(Gross & Haroche 1982, Phys Rep 93:301; 1/τ_R = N·μ/τ_sp, μ = 3λ²/(8πA).)

**N² (cooperative) survives ONLY if BOTH:**
1. **τ_R < min(T₂_collision, T₂*_Doppler)** — coherence outlives the cooperative time.
   (also the stricter t_D < T₂, t_D ≈ τ_R·ln N — build-up delay must beat dephasing.)
2. **Arecchi-Courtens: τ_E = L/c < τ_R** — atoms phase-lock before the photon escapes.

**At device conditions (n~1e21/m³, L~0.1m, λ=589nm):** τ_R ≈ 4 ps (fast), BUT τ_E = L/c =
0.3 ns ≫ τ_R → **propagation kills cooperativity along the long axis.** Rajabi-Houde (ApJ 826:216,
2016): "it is not expected that superradiance could arise in a thermally relaxed gas." Doppler
(Δν_D≈2.6 GHz @2000K → T₂*≈60ps) + collisional dephasing dominate.

**DEFAULT = N (incoherent). N² is GATED, not assumed.** SR sneaks back in 3 corners, each checked
PER-PIXEL (τ_R vs T₂):
(a) inversion-pumped subset where chemiluminescent feed beats collisional thermalization (the
    device's hot reaction cline — where SR is EARNED),
(b) sub-wavelength dense pockets (n_Na ≳ 3e20 → λ/4 ≈ 147 nm spacing),
(c) long pencils where Nμ ≫ 1 even at small per-pixel inversion.

**This is the operator's "N branch AND N² branch":** both real, the engine computes τ_R/T₂ per cell
and lets the cell PICK its exponent. SR lights up where earned, absent in the thermalized bulk.
Higher scalings (operator): pooling n3p² (super-linear), 3-body recomb n³, stimulated/ASE
exponential e^(gL) in path. The local log-log slope of I vs n_Na = the regime number.

Sources: Dicke PR 93:99 (1954); Gross-Haroche PhysRep 93:301 (1982); Rajabi-Houde ApJ 826:216 (2016,
explicit τ_R/t_D/Arecchi-Courtens/dephasing); Skribanowitz PRL 30:309 (1973); Gross PRL 36:1035 (1976).

## 2. Alkali coherent matter (Ketterle / Cornell-Wieman Nobel 2001)
- BEC onset: **n·λ_dB³ ≥ ζ(3/2) ≈ 2.612**, λ_dB = h/√(2πmk_BT).
- Why alkalis: single valence e⁻ → strong cycling D-line (Na 589, τ=16ns), magnetic trap, +a_s.
- Ketterle superradiant Rayleigh scattering from BEC (Inouye Science 285:571, 1999): coherence
  enforced by macroscopic condensate phase; decay ∝ N_condensate. THE CLEAN coherent limit.
- **LightCell sits ~9 OOM away in T and phase-space density** — use the Nobel regime as a sanity
  CEILING for what coherent collective Na looks like, NOT as a model.
Sources: Cornell-Wieman RMP 74:875 (2002); Ketterle Nobel lecture; Inouye Science 285:571.

## 3. de Groot — HPS Na₂ continuum + self-reversal + 589→819 migration
- HPS regime: p_Na 5-40 kPa, T_axis ~4000 K. (de Groot & van Vliet, *The High-Pressure Sodium
  Lamp*, 1986; J Phys D 8:651, 1975.)
- **Self-reversal & migration:** as p_Na rises, the D-core saturates + self-reverses (M-shaped),
  emission moves to the pressure-broadened WINGS, to 819 (cascade), and to the **Na₂ continuum**.
  The "migration" is **wing-pumping + dimer continuum**, NOT a shift of the D-line itself.
- Na₂ cross-section paper: de Groot & van Rooijen, Proc 12th ICPIG (1975) p.135 (paywalled;
  substitute Chung-Kirby-Babb arXiv physics/0008060 theoretical σ(λ)).

## 4. Na₂ DIMER — the ~670 nm shoulder carrier (operator was right it's missing)
- **D₀(Na₂, X¹Σg⁺) = 6022 cm⁻¹ = 0.747 eV** (NIST direct, Jones et al.). R_e = 3.079 Å.
- **The Row-108 ~670 nm "weak shoulder" = Na₂ A¹Σu⁺→X¹Σg⁺ BOUND-FREE** (red wing, 610nm→IR,
  Babb-Kirby). For a pure-Na flame this is THE carrier (NaHg/NaHe only with buffer gas).
- Also a³Σu⁺→b³Σg⁺ triplet bound-free 600-900nm; B¹Πu←X obscures D-wings λ<540nm.
- **Equilibrium 2Na⇌Na₂:** K_p(T) = p(Na₂)/p(Na)² = (k_BT)⁻¹·q(Na₂)/q(Na)², q(Na₂) has
  exp(D₀/k_BT). Dimer fraction ≈ 1e-4 @2000K, ≈1e-2 @1200K (wall) — STEEPLY T-dependent →
  dimer absorption strongest in the COOL boundary layer, where it self-reverses the D-line.
- **DUAL ROLE:** population SINK (depletes free radiating Na, ∝ n_Na²) AND continuum RADIATOR.
  Must be in the chemistry (gibbs already has Na2... check) AND the spectrum (new continuum term).
- Na₂ data: A-X T_e≈14,680 cm⁻¹ (~681nm); fluorescence series 655/756 nm. B-X 488 nm.
Sources: NIST D₀ (Jones et al., pubmed 9913658); Chung-Kirby-Babb arXiv physics/0008060.

## 5. Molisch-Oehry trapping — where Holstein breaks (confirms B4)
- Doppler g_D(k₀R) ≈ 1.60/[k₀R·√(π ln k₀R)]; Lorentz g_L ≈ 1.115/√(π k₀R). Γ_eff = g·Γ_nat.
- **Holstein linear theory BREAKS at n*/n > 1e-2** (bleaching: κ reduced by (1−2n*/n);
  kernel becomes density-dependent). Plus PFR when collision rate < Doppler width; polarization;
  inhomogeneous excitation. The chemiluminescent inversion zone is EXACTLY this regime → need
  bleaching correction or full coupled CR-RT, NOT the linear g.
Source: Molisch-Oehry, *Radiation Trapping in Atomic Vapours* (OUP 1998); Holstein PR 72:1212 (1947).

## What's paywalled (flagged, use substitutes)
de Groot-van Rooijen 1975 σ_Na2(λ) curves → use Chung-Kirby-Babb. Gross-Haroche full prefactors →
the Nμ/τ_sp form is established in derivative lit. Ketterle lecture body / Molisch-Oehry eq pages
→ standard forms confirmed from secondary sources.

## Build implications (→ #73, #75)
1. Superradiance = per-pixel τ_R/T₂ GATE, not a global multiplier. Default N, N² where earned.
2. Na₂ dimer: add bound-free A-X continuum (Babb-Kirby σ) weighted by K_p(T)·n_Na², AND as a
   free-Na sink in the chemistry. Reproduces the ~670 shoulder + the cool-skin self-reversal.
3. Holstein g only valid n*/n<1e-2; else coupled CR-RT (the 2-D occupied-level grid, #75).
4. The local log-log slope I(n_Na) = the live regime readout (#73 scaling-law explorable).