IR rule: Rmax ~ √(J·τ/NEI), with τ(R)=e-αR. In vacuum (τ=1) intensity enters as √J.
Radar's monostatic range scales only as σ1/4 (four-way spreading). Either way the exponent
is small — brute-force signature growth buys little range once the exponential atmosphere takes its cut.
Every doubling of J buys less range than the last — to hide you must attack J by orders of magnitude, component by component (L24).