Nuclear spin ( $I$ )

The total angular momentum of an atomic nucleus, including the orbital and intrinsic spin contributions of its constituent nucleons.

Table of contents
- Nuclear quadrupole moment Nuclear spin
- Nuclear magnetic dipole moment Nuclear spin

Nuclear quadrupole moment ( $Q = \int ρ (r) (3 z^{2} - r^{2}) d^{3} r$ )

The electric quadrupole moment of an atomic nucleus, conventionally specified in its stretched nuclear spin state. It measures a nonspherical nuclear charge distribution. Its interaction with the electronic electric-field gradient contributes to hyperfine structure and generally changes the magnetic-dipole Landé interval rule. A permanent rank-two moment vanishes for nuclear spin less than one.

Nuclear magnetic dipole moment ( $μ_{I} = g_{I} μ_{N} I$ )

The magnetic dipole moment associated with nuclear spin, using dimensionless angular momentum operators and the nuclear magneton

μ_{N}

. The quoted scalar moment is its expectation in the stretched quantum state,

μ_{I} = g_{I} μ_{N} I

. In the same electronic energy level, the leading magnetic-dipole hyperfine structure constant is proportional to

μ_{I} / I

, apart from isotope-dependent electronic and nuclear-size corrections.

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