Part 1 : Nanoparticles Module 6 : Mie theory for Scattering and absorption by                    a sphere and ellipsoids
Lecture 5 : Electrostatic approximation
 
where $L_1$ , $L_2$ , $L_3$ are called geometrical factors given by
\begin{displaymath}L_1 =\frac{abc}{2}\,\int_0^\infty \,\frac{dq}{(a^2+q)f(q)}\,,\end{displaymath}
\begin{displaymath}L_2 =\frac{abc}{2}\,\int_0^\infty \,\frac{dq}{(b^2+q)f(q)}\,,\end{displaymath}
\begin{displaymath}L_3 =\frac{abc}{2}\,\int_0^\infty \,\frac{dq}{(c^2+q)f(q)}\,,\end{displaymath}
with $f(q)=\sqrt{(a^2+q)(b^2+q)(c^2+q)}$. One can show that $L_1+L_2+L_3=1$ (left as a problem) and $L_1\le L_2\le L_3$.