Hyperfine structure

The hyperfine structure is an energy splitting in the spectral lines of atomic spectra. It is about 2,000 times smaller than that of the fine- splitting. The hyperfine structure is partly due to the interaction of the electrons with the magnetic ( dipole ) and electric ( quadrupole ) moments of the core and on the other on the isotope of the elements.

• 2.1 core mass effect
• 2.2 core volume effect

Nuclear spin effect

In a narrow sense is understood to mean the hyperfine splitting of the energy levels of an atom - with respect to the level of the fine structure - because of the coupling of the magnetic moment of the nucleus with the magnetic field which generate the electron in its place:

The indices mean:

• : MRI
• : Envelope angular momentum.

The largest hyperfine splitting point s electrons, because only they have a greater probability at the nucleus.

In a weak external magnetic field, the energy levels split according to a similar formula to continue to the magnetic quantum number mF of the hyperfine structure ( Zeeman effect). In a strong external magnetic decoupling of the core and the sheath of angular momentum, so that after splitting of the magnetic quantum number Mi of the core was observed ( the Paschen-Back effect).

Mathematical formulation

The coupling means that the total angular momentum of the atom, which is the sum of the envelope of the nuclear spin angular momentum, and is quantized:

Is the interaction energy

It is

• The Landé factor of the core
• The nuclear magneton   the elementary electric charge
• The reduced Planck constant
• The proton mass

The magnetic moment and the angular momentum of the core are related as follows:

For the determination of VHFs you need the sizes gI and BJ. gI can be determined by nuclear magnetic resonance measurements, BJ from the wave function of the electrons is, however, only be calculated numerically for atoms with atomic numbers greater than 1.

Applications

Transitions between hyperfine states are used in atomic clocks, because their frequency ( like that of all atomic transitions ) is constant. Moreover, it is very well with relatively simple means to produce and measure, as it is in the radio frequency or microwave range.

The frequency for the transition of the ground state of the hydrogen atom between the F = 1 and F = 0 (spin- flip ) is 1.420 GHz, which corresponds to a wavelength of 21 cm. These so-called HI- line is of great importance for radio astronomy. By Doppler shift of this line, the motion of interstellar gas clouds can be determined relative to the earth.

Isotope effects

There is also the isotope effects. Unlike MRI, they provide no splitting within a single atom, but a shift of the spectral lines for different isotopes of the same element. This is obtained with a mixture of isotopes, a splitting of the lines.

Core mass effect

The core mass effect is based on the co-movement of the atomic nucleus. This manifests itself in a lower effective mass of the electron. Since the nuclei of different isotopes have different mass, the effective mass of their electrons is also slightly different, which results in a corresponding shift of all states in the direction of higher energy. Since the Kernmitbewegung decreases with increasing mass of the nucleus, plays this effect especially for light nuclei play a role.

Core volume effect

The core volume effect due to the finite size of the atomic nucleus. S- electron states ( that is, with orbital angular momentum 0) have a non-negligible probability in the core, where the potential has not the pure Coulomb form. This difference is an increase of the energies of the states, which depends on the volume of the core. In absolute terms, this effect is greatest in heavy atoms, since these have the largest atomic nuclei. However, the splitting is in turn greater in the smaller nuclei, since the ratios of the core volumes of different isotopes are larger here.