What is an effective scattering length?

[fiedl]

While the source code uses the (geometric) scattering length, which is the mean free path between scatterings, other literature and several plots use the effective scattering length instead. But what is it?

[fiedl]

Wiki: https://wiki.icecube.wisc.edu/index.php/Effective_scattering_length

[fiedl]

% latex
\lambda_\mathrm{e} = \frac{\lambda_\mathrm{sca}}{1-\langle\cos\theta\rangle}, \ \ \
\mathrm{south\ polar\ ice:} \ 
\langle\cos\theta\rangle = 0.94
\\
\text{effective scattering length:}\ \lambda_\mathrm{e} \\
\text{geometric scattering length:}\ \lambda_\mathrm{sca} \\
\text{mean scattering angle:}\ \langle\theta\rangle \\

[fiedl]

Good explanations are in:

Lundberg et al., Light tracking through ice and water -- Scattering and absorption in heterogeneous media with Photonics, https://arxiv.org/pdf/astro-ph/0702108.pdf, 2007

Ackermann et al., Optical properties of deep glacial ice at the South Pole, https://doi.org/10.1029/2005jd006687, 2006

[fiedl]

I've summarized from these papers: