Hyperfine structure
In atoms, hyperfine structure arises from the energy of the nuclear magnetic dipole moment interacting with the magnetic field generated by the electrons and the energy of the nuclear electric quadrupole moment in the electric field gradient due to the distribution of charge within the atom.
Hyperfine structure, with energy shifts typically orders of magnitudes smaller than those of a fine-structure shift, results from the interactions of the nucleus (or nuclei, in molecules) with internally generated electric and magnetic fields.
In 1935, H. Schüler and Theodor Schmidt proposed the existence of a nuclear quadrupole moment in order to explain anomalies in the hyperfine structure of Europium, Cassiopium (older name for Lutetium), Indium, Antimony, and Mercury.
[2] The theory of hyperfine structure comes directly from electromagnetism, consisting of the interaction of the nuclear multipole moments (excluding the electric monopole) with internally generated fields.
For a many-electron atom this expression is generally written in terms of the total orbital angular momentum,
For states with a well defined projection of the orbital angular momentum, Lz, we can write
The first term gives the energy of the nuclear dipole in the field due to the electronic orbital angular momentum.
The second term gives the energy of the "finite distance" interaction of the nuclear dipole with the field due to the electron spin magnetic moments.
The final term, often known as the Fermi contact term relates to the direct interaction of the nuclear dipole with the spin dipoles and is only non-zero for states with a finite electron spin density at the position of the nucleus (those with unpaired electrons in s-subshells).
It has been argued that one may get a different expression when taking into account the detailed nuclear magnetic moment distribution.
In this case (generally true for light elements), we can project N onto J (where J = L + S is the total electronic angular momentum) and we have:[7]
where i and j are the tensor indices running from 1 to 3, xi and xj are the spatial variables x, y and z depending on the values of i and j respectively, δij is the Kronecker delta and ρ(r) is the charge density.
From the definition of the components it is clear that the quadrupole tensor is a symmetric matrix (Qij = Qji) that is also traceless (
A typical simple example of the hyperfine structure due to the interactions discussed above is in the rotational transitions of hydrogen cyanide (1H12C14N) in its ground vibrational state.
These contributing interactions to the hyperfine structure in the molecule are listed here in descending order of influence.
For consecutively higher-J transitions, there are small but significant changes in the relative intensities and positions of each individual hyperfine component.
Hyperfine structure gives the 21 cm line observed in H I regions in interstellar medium.
Carl Sagan and Frank Drake considered the hyperfine transition of hydrogen to be a sufficiently universal phenomenon so as to be used as a base unit of time and length on the Pioneer plaque and later Voyager Golden Record.
The separations among neighboring components in a hyperfine spectrum of an observed rotational transition are usually small enough to fit within the receiver's IF band.
Since the optical depth varies with frequency, strength ratios among the hyperfine components differ from that of their intrinsic (or optically thin) intensities (these are so-called hyperfine anomalies, often observed in the rotational transitions of HCN[14]).
Important methods are nuclear magnetic resonance, Mössbauer spectroscopy, and perturbed angular correlation.
The hyperfine structure transition can be used to make a microwave notch filter with very high stability, repeatability and Q factor, which can thus be used as a basis for very precise atomic clocks.
Typically, the transition frequency of a particular isotope of caesium or rubidium atoms is used as a basis for these clocks.
Due to the accuracy of hyperfine structure transition-based atomic clocks, they are now used as the basis for the definition of the second.
On October 21, 1983, the 17th CGPM defined the meter as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second.
[16][17] The hyperfine splitting in hydrogen and in muonium have been used to measure the value of the fine-structure constant α.
Comparison with measurements of α in other physical systems provides a stringent test of QED.
The hyperfine states of a trapped ion are commonly used for storing qubits in ion-trap quantum computing.
They have the advantage of having very long lifetimes, experimentally exceeding ~10 minutes (compared to ~1 s for metastable electronic levels).
In addition, near-field gradients have been exploited to individually address two ions separated by approximately 4.3 micrometers directly with microwave radiation.
