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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 ?

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  • $\begingroup$ This seems a very broad question. You're essentially asking for a review article on scattering. There must be something along these lines out there in Googlespace. $\endgroup$ Jan 22 '14 at 12:10
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    $\begingroup$ A good rule of thumb is to remember these quantum numbers correspond to angular momentum. S wave is the zero angular momentum quantum number , l=0, and will correspond to a classical head on collision. P is l=1 and d l=2 which means higher angular momentum between scatterer and incoming. The atomic orbitals would give some intuition about functional shapes of the Y_l_m functions en.wikipedia.org/wiki/Atomic_orbitals $\endgroup$
    – anna v
    Jan 22 '14 at 12:44
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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.

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