Editing Angular momentum coupling (section)

===LS coupling===
[[File:LS coupling (corrected).png|thumb|250x250px|Illustration of L–S coupling. Total angular momentum '''J''' is green, orbital '''L''' is blue, and spin '''S''' is red.]]
In light atoms (generally ''Z''&nbsp;≤&nbsp;30<ref>[http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Electronic_Spectroscopy/The_atomic_spectrum/Atomic_Term_Symbols/The_Russell_Saunders_Coupling_Scheme The Russell Saunders Coupling Scheme] R. J. Lancashire, UCDavis ChemWiki (accessed 26 Dec.2015)</ref>), electron spins '''s'''<sub>''i''</sub> interact among themselves so they combine to form a total spin angular momentum '''S'''. The same happens with orbital angular momenta '''ℓ'''<sub>''i''</sub>, forming a total orbital angular momentum '''L'''. The interaction between the quantum numbers '''L''' and '''S''' is called '''Russell&ndash;Saunders coupling''' (after [[Henry Norris Russell]] and [[Frederick Albert Saunders|Frederick Saunders]]<!-- (1875-1963) -->) or '''LS coupling'''. Then '''S''' and '''L''' couple together and form a total angular momentum '''J''':<ref>{{cite book|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles|edition=2nd|author=R. Resnick, R. Eisberg|publisher=John Wiley & Sons|year=1985|page=[https://archive.org/details/quantumphysicsof00eisb/page/281 281]|isbn=978-0-471-87373-0|url=https://archive.org/details/quantumphysicsof00eisb/page/281}}</ref><ref>{{cite book|title = Physics of Atoms and Molecules|url = https://archive.org/details/physicsatomsmole00bran_159|url-access = limited|author=B.H. Bransden, C.J.Joachain|publisher=Longman|year=1983|pages=[https://archive.org/details/physicsatomsmole00bran_159/page/n346 339]–341|isbn=0-582-44401-2}}</ref>

:<math>\mathbf J = \mathbf L + \mathbf S, \, </math>

where '''L''' and '''S''' are the totals:

: <math>\mathbf L = \sum_i \boldsymbol{\ell}_i, \ \mathbf S = \sum_i \mathbf{s}_i. \, </math>

This is an approximation which is good as long as any external magnetic fields are weak.  In larger magnetic fields, these two momenta decouple, giving rise to a different splitting pattern in the energy levels (the [[Paschen–Back effect]]), and the size of LS coupling term becomes small.<ref>{{cite book|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles|edition=2nd|author=R. Resnick, R. Eisberg|publisher=John Wiley & Sons|year=1985|isbn=978-0-471-87373-0|url=https://archive.org/details/quantumphysicsof00eisb}}</ref>

For an extensive example on how LS-coupling is practically applied, see the article on [[term symbol]]s.