リンドハード理論
{\displaystyle {\begin{alignedat}{2}\epsilon (q,0)&=1+V_{q}\sum _{k,i}{\frac {q_{i}k_{i}{\frac {\hbar ^{2}}{m}}{\frac {\partial f_{k}}{\partial \mu }}}{\frac {\hbar ^{2}{\vec {k}}\cdot {\vec {q}}}{m}}}=1+V_{q}\sum _{k}{\frac {\partial f_{k}}{\partial \mu }}=1+{\frac {4\pi e^{2}}{\epsilon q^{2}}}{\frac {\partial }{\partial \mu }}{\frac {1}{L^{3}}}\sum _{k}{f_{k}}\\&=1+{\frac {4\pi e^{2}}{\epsilon q^{2}}}{\frac {\partial }{\partial \mu }}{\frac {N}{L^{3}}}=1+{\frac {4\pi e^{2}}{\epsilon q^{2}}}{\frac {\partial n}{\partial \mu }}\equiv 1+{\frac {\kappa ^{2}}{q^{2}}}.\end{alignedat}}}
ここで κ {\displaystyle \kappa } は κ = 4 π e 2 ε ∂ n ∂ μ {\displaystyle \kappa ={\sqrt {{\frac {4\pi e^{2}}{\epsilon }}{\frac {\partial n}{\partial \mu }}}}} で定義される3次元遮蔽波数(3次元遮蔽長の逆数)である。