Hyperfine Structure and Nuclear Effects

Hyperfine structure is the very small splitting of atomic levels caused by the interaction of the electrons with the magnetic and electric moments of the nucleus and by the finite size and mass of the nucleus.

Definition

Hyperfine structure is the splitting of fine-structure levels caused by the interaction of the atomic electrons with the multipole moments of the nucleus, principally the nuclear magnetic dipole and electric quadrupole, producing sublevels labelled by the total angular momentum F = I + J.

Scope

This topic covers the coupling of nuclear spin to the electronic angular momentum to give the total atomic angular momentum F, the magnetic-dipole and electric-quadrupole hyperfine interactions, the Landé interval rule for hyperfine multiplets, and the related nuclear effects of isotope shift arising from finite nuclear mass and size. It connects atomic spectroscopy to the measurement of nuclear moments.

Core questions

• How does nuclear spin couple to the electronic angular momentum?
• What nuclear moments produce the magnetic-dipole and electric-quadrupole hyperfine interactions?
• How can atomic spectroscopy be used to measure nuclear moments?
• What causes the isotope shift between spectral lines of different isotopes?

Key concepts

• Nuclear spin I and total angular momentum F
• Magnetic-dipole hyperfine constant
• Electric-quadrupole interaction
• Hyperfine Landé interval rule
• Mass and volume isotope shifts
• 21-centimetre hydrogen line

Key theories

Magnetic-dipole hyperfine interaction

The nuclear magnetic moment interacts with the magnetic field produced by the electrons at the nucleus, splitting each fine-structure level into hyperfine components whose spacings follow an interval rule proportional to F.

Electric-quadrupole and isotope effects

A non-spherical nucleus has an electric quadrupole moment that perturbs the levels, while differences in nuclear mass and charge radius between isotopes shift the lines, allowing nuclear properties to be inferred from optical spectra.

Clinical relevance

The caesium hyperfine transition defines the SI second and thus underlies global timekeeping and satellite navigation, the neutral-hydrogen 21-centimetre hyperfine line is a primary tool of radio astronomy, and hyperfine and isotope-shift spectroscopy provides a sensitive route to measuring nuclear spins, moments, and charge radii.

History

Pauli proposed in 1924 that nuclear spin causes the closely spaced hyperfine lines seen in spectra. Rabi's molecular-beam magnetic-resonance method in the 1930s measured hyperfine intervals and nuclear moments precisely, and the caesium hyperfine transition was adopted in 1967 as the definition of the second.

Key figures

• Wolfgang Pauli
• Hans Kopfermann
• Isidor Rabi

Seminal works

• foot2005
• kopfermann1958

Frequently asked questions

What is the total angular momentum F?

F is the vector sum of the nuclear spin I and the total electronic angular momentum J. Hyperfine sublevels are labelled by the allowed values of F, ranging from |I − J| to I + J, much as fine-structure levels are labelled by J.

Why does the caesium clock use a hyperfine transition?

The ground-state hyperfine transition in caesium-133 is at a microwave frequency that is sharp, reproducible, and insensitive to many perturbations, making it an excellent, stable reference; the SI second is defined as a fixed number of its oscillations.