In scattering theory, what is a good intuitive picture to think of s-wave, p-wave or d-wave collisions ? What is their importance and what are the examples where a particular one is assumed to be the only important one and rest are taken as negligible ?
I found the very last paragraph of the following answer quite explanatory: https://physics.stackexchange.com/a/8324/46100
Interpretation of the Partial Wave Expansion: In the literature, you will often come across terms such as $s$-wave scattering. The partial wave expansion decomposes the scattering process into the scattering of incoming waves with definite angular momentum quantum number. It explains in which way $s$-, $p$-, $d$-waves etc. are affected by the potential. For low energy scattering, only the first few $l$-quantum numbers are affected. If all but the first term are discarded, only the $s$-waves take part in the scattering process. This is an approximation that is, for example, made in the scattering of the atoms in a Bose-Einstein condensate.