Hyperfine interaction

An interaction between a nucleus's magnetic or electric multipole moments and its electronic surroundings. Magnetic contact and dipolar terms can couple nuclear spin to electron spin or orbital magnetic moments. The resulting small energy shifts contribute to hyperfine structure; the contact term can also mediate conduction-electron-mediated exchange between nuclear moments in a metal.

For electronic

J = 1/2

, nuclear spin

I

and conserved angular momentum component

m

, define

Δ_{hf} = A (I + 1/2)

and the dimensionless field

x

shown in the title. The hyperfine-plus-magnetic energies are

E_{\pm} (m) = - \frac{Δ _{hf}}{2 ( 2 I + 1 )} + g_{I} μ_{B} m B \pm \frac{Δ _{hf}}{2} 1 + \frac{4 m x}{2 I + 1} + x^{2} .

(1)

The factors

g_{I}, g_{J}

use the same Hamiltonian convention and Bohr-magneton units. The two stretched states require the branch consistent with their unique spin configuration. The formula follows by diagonalizing each two-dimensional fixed-

m

block; it connects weak-field coupled-spin levels to decoupled high-field states. The name refers to Gregory Breit and Isidor Isaac Rabi.^[ref]

Stretched hyperfine Zeeman state ( $m_{F} = \pm (I + 1/2)$ )

 0  0

For electronic

J = 1/2

, an extremal total projection has only one product state rather than a two-dimensional spin block. With dimensionless angular-momentum operators and nuclear Zeeman coefficient