# Lande - g factor for two electron system for j j coupling

The Lande g factor, often denoted as g, describes the splitting of energy levels in atoms due to the interaction of the magnetic moment associated with angular momentum (either orbital or spin) with an external magnetic field. For a two-electron system with j−j coupling (where j is the total angular momentum quantum number), the Lande g factor depends on whether we are considering the total angular momentum J vector or the total spin vector S.

In j-j coupling, the spin vector S_1* and orbital vector J_1* of one electron combine together to form their resultant J_1*. Similarly l*_2 and S_2* of another electron combine together to form total angular momentum J*.

The magnetic moment associated with l_1* and S_1* are given by

Then resultant total magnetic moment is given by ( for one electron)

g_1 is Lande g factor for one electron. Similarly the resultant total magnetic moment for second electron is given by

g_2 is Lande g factor for second electron. Finally J_1* and J_2* combine together to from their resultant J*

The resultant total magnetic moment is given by

is called Lande g factor for two valence electron system in J-J coupling.

These factors are crucial in determining the Zeeman effect (the splitting of spectral lines in a magnetic field) and are derived from quantum mechanical considerations of angular momentum and its interaction with magnetic fields. They provide important information about the structure and behaviour of atomic energy levels in the presence of external magnetic fields.

This note is a part of the Physics Repository.