Spin orbit interaction

Amith2006

1. The problem statement, all variables and given/known data
The general expression for potential energy of a magnetic dipole placed in magnetic field B is given by,
E = -m.B
Where m=magnetic dipole moment
It is given in a book that due to spin orbit interaction, the potential energy possessed by an electron can be written as,
E(s) = K(L.S)

They argue that m is proportional to S(spin quantum number) and B is proportional to L(orbital quantum number).Hence the expression.What is K in the above expression? They have calculated the value of K in one of the problems and I found that it has different values for different atoms.



2. Relevant equations



3. The attempt at a solution