The magnetic moment

associated with the total electronic angular momentum

of an atom and its nuclear magnetic moment

associated with its nuclear spin

(

** **is the Bohr magneton and

,

are the electronic and nuclear

-factors, respectively) are coupled by the hyperfine Hamiltonian

. If

the system has

groups of degenerate energy eigenstates, labeled by the total atomic angular momentum

, which takes values

. Each group consists of

degenerate sublevels, yielding a total of

substates, labeled

and

.

When placed in an external magnetic field

the combined hyperfine-Zeeman Hamiltonian reads

,

and its energy eigenvalues are found by diagonalization. If one of the spins, say

, is 1/2, the diagonalization yields an algebraic expression

for the energies of the states

, known as the Breit-Rabi formula.

is the hyperfine splitting for

, that is, the energy difference between the states belonging to the manifolds

.

By introducing the dimensionless parameter

the energies can be written in the dimensionless form

which have an explicit dependence (given by

and

) on the specific atom considered.

Considering that

is in general on the order of a few times

of

, one can neglect the second term to obtain a universal expression

with

that is valid for all Zeeman-hyperfine problems in which one of the spins is 1/2. It is the latter equation that is displayed in the present Demonstration.