mcmillan_exponent
plain-language theorem explainer
The McMillan exponent definition supplies the factor 1.04(1 + λ_k)/(λ_k - μ*) evaluated at the rung-dependent electron-phonon coupling. Hydride superconductor researchers cite it when collapsing the Tc optimization to a single integer rung parameter k. The definition is a direct algebraic substitution of the rung-specific coupling into the classic McMillan expression.
Claim. The McMillan exponent is defined as $1.04(1 + λ_k)/(λ_k - μ^*)$, where $λ_k$ is the electron-phonon coupling at phi-rung $k$ and $μ^*$ is the Coulomb pseudopotential.
background
The hydride superconductor module models hydrogen-dominant materials with bare phonon frequency ω_0 = √(K/m_H) and coupling λ_k = λ_0 φ^k on the phi-ladder. The McMillan Tc formula then becomes Tc(k) = (ω_p(k)/1.2) exp(-exponent), with the exponent supplied by this definition. Upstream results include the dimensionless bridge ratio K = φ^{1/2} and rung indexing conventions from anchor policies and mass ladders.
proof idea
One-line wrapper that substitutes the rung-dependent coupling lambda_at_rung into the numerator and denominator of the standard McMillan factor.
why it matters
This definition is invoked directly by T_c_phi_rung to compute the critical temperature at each phi-rung. It supplies the structural piece for RS_PAT_010 by reducing the optimization landscape to a discrete search over integer k, consistent with the module headline that the landscape collapses from continuous multi-parameter search to single-parameter rung selection.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.