Bethe-Bloch: z²-scaling ratio z=2/z=1 = 4; Legendre ⟨P2,P2⟩=2/5; ⟨P1,P2⟩=0

Sympy-exact symbolic witness of the Bethe-Bloch z²-scaling and Legendre-polynomial orthogonality relations supporting multiple-scattering angular expansion. Setup: K, z, Z, A, β, γ, m_e, c, I_ion, T_max sp-symbols positive. Full…