- Hyperfine structure
In

atomic physics ,**hyperfine coupling**is the weak magnetic interaction betweenelectron s and nuclei. Hyperfine coupling causes the**hyperfine splitting**of atomic or molecular energy levels. The totality of energy levels spawned by hyperfine splitting is called the**hyperfine structure**of the atom's or molecule'sspectrum .**Terminology**The following terminology has evolved to describe atomic and/or molecular spectra:

* The "gross structure" is due to the energy difference of electronic orbitals with different principal

quantum number "n".* The "

fine structure " occurs only for "n">0; it is due to thespin-orbit coupling (the energy difference between the electron spin being parallel or antiparallel to the electron's orbital moment).* The "hyperfine structure" is due to an unpaired electron interacting with a nucleus having

nuclear spin quantum number I $e$ 0. The electron and nucleus (nuclei) are on the same atom or within the same molecule.* The "

superhyperfine structure " is due to an unpaired electron interacting with a nucleus having I $e$ 0. The electron and nucleus (nuclei) are on different atoms or different molecules.* The "

spin-spin structure " is due to interactions among nuclei having I $e$ 0. This phenomenon is especially important in NMR spectra**Theory**In first order, hyperfine coupling is a

magnetic dipole -dipole interaction, arising from the interaction of thenuclear magnetic moment with the magnetic field of the electron.According to classical thinking, the electron moving around the nucleus has a magnetic dipole moment, because it is charged. The interaction of this magnetic dipole moment with the magnetic moment of the nucleus (due to its spin) leads to hyperfine splitting.

However, due to the electron's spin, there is also hyperfine splitting for s-shell electrons, which have zero orbital angular momentum. In this case, the magnetic dipole interaction is even stronger, as the electron probability density does not vanish inside the nucleus ($~r=0~$).

The amount of correction to the Bohr

energy levels due to hyperfine splitting of the hydrogen atom is of the order:$frac\{m\}\{m\_\{\; m\; p\; alpha^4\; m\; c^2$

where :$~m~$ is the mass of an electron,:$~m\_\{\; m\; p\}~$ is the mass of a proton,:$~alpha~$ is the

fine structure constant $~(~alpha\; approx\; 1/137.036~)~$, and:$~c~$ is thespeed of light .For atoms other than hydrogen, the

nuclear spin $vec\{I\}$ and the total electron angular momentum $vec\{J\}\; =\; vec\{L\}\; +\; vec\{S\}$ get coupled, giving rise to the total angular momentum $vec\{F\}\; =\; vec\{J\}\; +\; vec\{I\}$. The hyperfine splitting is then:$Delta\; E\_\{\; m\; hfs\}\; =\; -\; (vec\{mu\}\_I\; cdot\; vec\{B\}\_J)\; =\; frac\{a\}\{2\}\; [\; F(F+1)\; -\; I(I+1)\; -\; J(J+1)]\; ,$where :$a\; =\; frac\{g\_I\; (vec\{mu\}\_\{\; m\; N\}\; cdot\; vec\{B\}\_J)\}\{sqrt\{J(J+1),$ clarifyme:$vec\{mu\}\_\{\; m\; N\}$ themagnetic dipole moment of the nucleus, and:$vec\{B\}\_J$ is the atomicmagnetic field .This interaction obeys the

Lande interval rule : The energy level is split into $~(J+I)\; -\; |J-I|+\; 1~$ energy levels, where $~J~$ denotes the total electron angular momentum and $~I~$ denotes the nuclear spin.Usually, $~Delta\; E\_\{\; m\; hfs\}/hbar~$ is of order of GHz; the hyperfine splitting is orders of magnitude smaller perturbation than the

fine structure .In a more advanced treatment, one also has to take the nuclear magnetic quadrupole moment into account. This is sometimes (?) referred to as "hyperfine structure anomaly".

**History**The optical hyperfine structure was already observed in 1881 by

Albert Abraham Michelson . It could, however, only be explained in terms of quantum mechanics in the 1920s.Wolfgang Pauli proposed the existence of a small nuclear magnetic moment in 1924.In 1935, M. Schiiler and T. Schmidt proposed the existence of a nuclear quadrupole moment in order to explain anomalies in the hyperfine structure.

**Measurements**Hyperfine interactions can be measured, among other ways, in atomic and molecular spectra and in

electron paramagnetic resonance spectra offree radical s and transition-metal ions.**Applications****Astrophysics**As the hyperfine splitting is very small, the transition frequencies usually are not optical, but in the range of radio- or microwave frequencies.

Hyperfine structure gives the

21 cm line observed in HI region ininterstellar medium .Carl Sagan andFrank 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 thePioneer plaque and laterVoyager Golden Record .In

radio astronomy , heterodyne receivers are widely used in detection of the electromagnetic signals from celestial objects. The separations among various components of a hyperfine structure are usually small enough to fit into the receiver's IF band. Becauseoptical depth varies with frequency, strength ratios among the hyperfine components differ from that of their intrinsic intensities. From this we can derive the object's physical parameters. [*cite journal | author=Tatematsu, K., Umemoto, T., Kandori, R. et al. | title= N*]_{2}H^{+}Observations of Molecular Cloud Cores in Taurus | journal=Astrophysical Journal | year=2004| volume=606 | pages= 333–340 | doi= 10.1086/382862**Nuclear technology**The

AVLIS process uses the hyperfine splitting of between optical transitions in uranium-235 and uranium-238 to selectively photoionize only the uranium-235 atoms and then separate the ionized particles from the non-ionized ones. Precisely tuneddye laser s are used as the sources of the necessary exact wavelength radiation.**Use in defining the SI second and meter**The hyperfine structure transition can be used to make a

microwave notch filter with very high stability, repeatability andQ factor , which can thus be used as a basis for very preciseatomic clock s. Typically, the hyperfine structure transition frequency of a particular isotope ofcaesium orrubidium 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. One

second is now "defined" to be "exactly" 9,192,631,770 cycles of the hyperfine structure transition frequency of caesium-133 atoms.Since 1983, the meter is defined by declaring the speed of light in a vacuum to be exactly 299,792,458 metres per second. Thus:

"The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second."

**Precision tests of quantum electrodynamics**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.**Qubit in ion-trap quantum computing**The hyperfine states of a trapped

ion are commonly used for storingqubit s inion-trap quantum computing . They have the advantage of having very long lifetimes, experimentally exceeding ~10 min (compared to ~1 s for metastable electronic levels).The frequency associated with the states' energy separation is in the

microwave region, making it possible to drive hyperfine transitions using microwave radiation. However, at present no emitter is available that can be focused to address a particular ion from a sequence. Instead, a pair oflaser pulses can be used to drive the transition, by having their frequency difference ("detuning") equal to the required transition's frequency. This is essentially a stimulatedRaman transition .**See also*** Spin-spin structure (J-J splitting) in NMR spectroscopy

*Energy level s

*Quantum numbers **References****Further reading*** G. Herzberg, "Atomic Spectra and Atomic Structure". Dover, New York, 1944. See especially chapter 5.

* M. Symons, "Chemical and Biochemical Aspects of Electron-Spin Resonance Spectroscopy". Wiley, New York, 1978

* J. A. Weil, J. R. Bolton, and J. E. Wertz, "Electron Paramagnetic Resonance: Elementary Theory and Practical Applications". Wiley-Interscience, New York, 2001

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### Look at other dictionaries:

**hyperfine structure**— /huy peuhr fuyn , huy /, Physics. the splitting of the lines of an atomic spectrum, produced by the angular momentum of the nucleus of the atom. Cf. fine structure. [1925 30; HYPER + FINE1] * * * ▪ physics in spectroscopy, the splitting of… … Universalium**hyperfine structure**— hipersmulkioji sandara statusas T sritis fizika atitikmenys: angl. hyperfine structure vok. Hyperfeinstruktur, f rus. сверхтонкая структура, f; сверхтонкое строение, n pranc. structure hyperfine, f … Fizikos terminų žodynas**hyperfine structure**— hipersmulkioji sandara statusas T sritis chemija apibrėžtis Smulkiosios sandaros linijų ar smailių papildoma skaida. atitikmenys: angl. hyperfine structure rus. сверхтонкая структура; сверхтонкое строение ryšiai: sinonimas – hipersmulkioji… … Chemijos terminų aiškinamasis žodynas**hyperfine structure**— noun a closely spaced structure of lines in the spectrum of an atom or molecule due to nuclear isotopic effects and/or to nuclear spin … Wiktionary**hyperfine structure**— /ˌhaɪpəfaɪn ˈstrʌktʃə/ (say .huypuhfuyn strukchuh) noun 1. the occurrence of very closely spaced energy levels in an atom, due to coupling between the momentum of the orbital electrons and the spin of the nucleus. 2. the splitting of certain… … Australian English dictionary**hyperfine structure**— … Useful english dictionary**hyperfine structure transition**— hipersmulkusis šuolis statusas T sritis radioelektronika atitikmenys: angl. hyperfine structure transition; hyperfine transition vok. hyperfeiner Übergang, m; Hyperfeinstrukturübergang, m rus. переход между подуровнями сверхтонкой структуры, m;… … Radioelektronikos terminų žodynas**hyperfine structure splitting**— hipersmulkusis suskilimas statusas T sritis fizika atitikmenys: angl. hyperfine splitting; hyperfine structure splitting vok. Hyperfeinaufspaltung, f; Hyperfeinstrukturaufspaltung, f rus. сверхтонкое расщепление, n pranc. dédoublement de la… … Fizikos terminų žodynas**hyperfine-structure spectrum**— hipersmulkiosios sandaros spektras statusas T sritis fizika atitikmenys: angl. hyperfine spectrum; hyperfine structure spectrum vok. Hyperfeinspektrum, n; Hyperfeinstrukturspektrum, n rus. спектр сверхтонкой структуры, m pranc. spectre à… … Fizikos terminų žodynas**hyperfine structure level**— hipersmulkiosios sandaros lygmuo statusas T sritis fizika atitikmenys: angl. hyperfine structure level vok. Hyperfeinstruktur Niveau, n rus. уровень сверхтонкой структуры, m pranc. niveau de structure hyperfine, m … Fizikos terminų žodynas