The L-S coupling is also known as ‘Russel-Saunders’ coupling after the two astronomers who first used it in studying atomic spectra emitted by stars. In atoms which obey this coupling we introduce the various perturbations in the order :

**a) Spin-Spin Correlation :**

**s**of magnitude

**which is constant of motion.**

*√s(s+1).h/2π***s**takes values from

*s = (s1- s2) , (s1 -s2)+1 ,………*

*s’ = ( 0, 1 )*

*If we couple s3 = 1/2 with s’ = 0 ,we get*

*=> s’ = 0 ,s3 = 1/2*

*Therefore, S = s3 = 1/2*

*If we couple s’ = 1 and s3 = 1/2*

*Hence, S = 1/2 ,1/2 , 3/2*

*Hence, For a three electron system there are two doublets.*

*Multiplicity for ( s = 1/2 ) = 2s + 1*

*= 2(1/2) + 1*

*= 2 (Doublets)*

*For s = 3/2*

*Multiplicity = 2s + 1*

*= 2(3/2) + 1*

*= 4*

**b) Orbital-Orbital Interaction :-**

*√l(l+1).h/2π*

**L**has following values :

**c) Spin-Orbital Interaction :-**

**L**and the resultant spin angular momentum vector

**S**are coupled each other to form total angular momentum vector

**J**

**J**=

**L**+

**S**

**J**is quantised having value

*√ j (j+1).h/2π*

*where,**j*is inner quantum number.