Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

==== I computed δ=σeffN0\delta=\sigma_{\rm eff}N_0δ=σeffN0 for three sample cross sections and five sample column densities. (These are representative / order-of-magnitude inputs so you can see scaling — I show later which are realistic.) ====

Cross-sections used
* Thomson: σT=6.65×10−29 m2\sigma_T = 6.65\times10^{-29}\,\mathrm{m}^2σT=6.65×10−29m2  (conservative floor for scattering off free electrons)
* Small resonance: σ=10−22 m2\sigma = 10^{-22}\,\mathrm{m}^2σ=10−22m2 (typical of modest atomic/molecular resonant cross sections)
* Large line: σ=10−18 m2\sigma = 10^{-18}\,\mathrm{m}^2σ=10−18m2 (strong resonant / line cross section; upper bound for a single narrow line at peak)

Columns N0N_0N0 used
* Interplanetary: 5×1015 m−25\times10^{15}\,\mathrm m^{-2}5×1015m−2  (very low)
* Diffuse ISM: 1×1020 m−21\times10^{20}\,\mathrm m^{-2}1×1020m−2
* Atmosphere-effective: 1×1023 m−21\times10^{23}\,\mathrm m^{-2}1×1023m−2 (order of magnitude guess for an effective interacting column — see below)
* Dense material surface: 1×1025 m−21\times10^{25}\,\mathrm m^{-2}1×1025m−2 (surface/solid interacting layer)
* Photosphere-like: 1×1028 m−21\times10^{28}\,\mathrm m^{-2}1×1028m−2 (very large column that illustrates dense stellar layers)

Numeric results (delta = σ·N₀)

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(I printed the full table numerically in the run so you can check exact entries.)