I would like to estimate the $\ell=2$ ($d$-wave) contribution to elastic scattering cross section (or scattering length) for collisions such as $n$-$n$ and $n$-$p$ at low energy (a few MeV or less). I found the following resource
https://doi.org/10.1016/j.nds.2006.11.001
which gives the total cross section and also quotes scattering lengths $a_0$ and $a_1$ for n-p scattering, but it does not (as far as I can tell) pull out a value for $a_2$. I am hoping for either a known value, or a rough number or even an order-of-magnitude estimate. For example, the above paper says $a_0 \simeq -23.72\,$fm and $a_1 = 5.414\,$fm so $|a_1/a_0| \simeq 0.23$ for n-p scattering. Would it be reasonable to estimate $|a_2| \simeq 0.2 |a_1|$? Or is there a resource which would give the answer more precisely?
If $\sigma$ is the total cross section (20 barn) then one finds $$ \sigma - (\pi a_0^2 + \pi a_1^2) \simeq 1.4\,{\rm barn} $$ so this seems to suggest $|a_2| \simeq 6.7\,$fm, which is similar to (in fact a little larger than) $|a_1|$. So which is the better estimate, $$ |a_2| \simeq |a_1| \qquad or \qquad |a_2| \simeq 0.2 |a_1| ? $$