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Encyclopedia > Hyperfine structure

In atomic physics, hyperfine structure is a small perturbation in the energy levels (or spectra) of atoms or molecules due to the magnetic dipole-dipole interaction, arising from the interaction of the nuclear magnetic dipole with the magnetic field of the electron. Atomic physics (or atom physics) is the field of physics that studies atoms as isolated systems comprised of electrons and an atomic nucleus. ... Perturbation is a term used in astronomy to describe alterations to an objects orbit caused by gravitational interactions with other bodies. ... Properties In chemistry and physics, an atom (Greek Î¬Ï„Î¿Î¼Î¿Î½ meaning indivisible) is the smallest possible particle of a chemical element that retains its chemical properties. ... In chemistry, a molecule is an aggregate of at least two atoms in a definite arrangement held together by special forces. ... This article is about the electromagnetic phenomenon. ... The nuclear magnetic moment is the magnetic moment of an atomic nucleus and arrises from the spin of the protons and neutrons. ...

## Contents

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. In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is generated by the motion of its center of mass about an external point. ...

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 on the order of: Niels Bohr Niels Henrik David Bohr (October 7, 1885 – November 18, Danish physicist who made essential contributions to understanding atomic structure and quantum mechanics. ...

$frac{m}{m_p} alpha^4 m c^2$

where

m is the mass of an electron
mp is the mass of a proton
α is the fine structure constant (1/137.036)
c is the speed 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 The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... The speed of light in a vacuum is denoted by the letter c. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is generated by the motion of its center of mass about an external point. ... In atomic physics, the total angular quantum momentum numbers parameterize the total angular momentum of a given electron, by combining its orbital angular momentum and its intrinsic angular momentum (i. ...

$Delta E_{hfs} = - vec{mu}_I vec{B}_J = frac{a}{2} [ F(F+1) - I(I+1) - J(J+1)],$

where

$a = frac{g_I vec{mu}_N vec{B}_J}{sqrt{J(J+1)}},$

with $vec{mu}_N$ the magnetic dipole moment of the nucleus.

This interaction obeys the Lande interval rule: The energy level is split into (J + I) − | JI | + 1 energy levels, where J denotes the total electron angular momentum and I denotes the nuclear spin.

With $Delta E_{hfs} approx hbar$, the hyperfine splitting is a much smaller perturbation than the fine structure. 1. ...

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. Albert Abraham Michelson. ... This article is about Austrian-Swiss physicist Wolfgang Pauli. ...

In 1935, M. Schiiler and T. Schmidt proposed the existence of a nuclear quadrupole moment in order to explain anomalies in the hyperfine structure.

## 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 in interstellar medium. In physics and astronomy, the 21 cm line is the name for a highly forbidden emission line of hydrogen. ... The distribution of ionized hydrogen (known by astronomers as H II (aitch two) from old spectroscopic terminology) in the parts of the Galactic interstellar medium visible from the Earths northern hemisphere (from the Wisconsin H-Alpha Mapper Survey) In astronomy, the interstellar medium (or ISM) is the matter (interstellar...

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. It has been suggested that Minimum deterrence be merged into this article or section. ... Professor Frank Drake Frank Drake (born May 28, 1930, Chicago, Illinois) is an American astronomer and astrophysicist. ... On board the unmanned spacecraft Pioneer 10 and Pioneer 11 is a plaque with a pictorial message from mankind. ... The Voyager Golden Record. ...

### Nuclear technology

The AVLIS and MLIS processes use hyperfine splitting caused by differences between the mass of atomic nucleus for 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 tuned dye lasers are used as the sources of the necessary exact wavelength radiation. AVLIS Is an acronym which stands for atomic vapor laser isotope separation and is a method by which specially tuned lasers are used to separate isotopes of uranium using selective ionization of hyperfine transitions. ... Molecular laser isotope separation (MLIS) is a method of isotope separation, where specially tuned lasers are used to separate isotopes of uranium using selective ionization of hyperfine transitions of uranium hexafluoride molecules. ... A dye laser used at the Starfire Optical Range for LIDAR and laser guide star experiments is tuned to the sodium D line and used to excite sodium atoms in the upper atmosphere. ...

### 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 and Q factor, which can thus be used as a basis for very precise atomic clocks. Typically, the hyperfine structure transition frequency of a particular isotope of caesium or rubidium atoms is used as a basis for these clocks. Microwave image of 3C353 galaxy at 8. ... The Q factor or quality factor is a measure of the rate at which a vibrating system dissipates its energy into heat. ... Atomic clock Chip-Scale Atomic Clock Unveiled by NIST An atomic clock is a type of clock that uses an atomic resonance frequency standard as its counter. ... General Name, Symbol, Number caesium, Cs, 55 Chemical series alkali metals Group, Period, Block 1, 6, s Appearance silvery gold Atomic mass 132. ... General Name, Symbol, Number rubidium, Rb, 37 Chemical series alkali metals Group, Period, Block 1, 5, s Appearance grey white Atomic mass 85. ...

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. Look up second in Wiktionary, the free dictionary. ...

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: 1983 (MCMLXXXIII) was a common year starting on Saturday of the Gregorian calendar. ... metre or meter, see meter (disambiguation) The metre (in the U.S., chiefly meter) is a measure of length, approximately equal to 3. ...

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.

### Qubit in ion-trap quantum computing

The hyperfine states of a trapped ion are commonly used for storing qubits in ion-trap quantum computing. They have the advantage of having a very long lifetimes, experimentally exceeding ~10 min (compared to ~1 s for metastable electronic levels). // An ion is an atom or a group of atoms (a chemical substance), or subatomic particle, with a net electric charge. ... To meet Wikipedias quality standards and make it more accessible, this article needs a better explanation of technical details or more context regarding applications or importance to make it more accessible to a general audience, or at least to technical readers outside this specialty. ... Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. ...

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 of laser 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 stimulated Raman transition. Microwave image of 3C353 galaxy at 8. ... Lasers range in size from microscopic diode lasers (top) with numerous applications, to football field sized neodymium glass lasers (bottom) used for inertial confinement fusion, nuclear weapons research and other high energy density physics experiments. ... Raman spectroscopy is a spectroscopic technique used in condensed matter physics and chemistry to study vibrational, rotational, and other low-frequency modes in a system. ...

Results from FactBites:

 Spartanburg SC | GoUpstate.com | Spartanburg Herald-Journal (809 words) In atomic physics, hyperfine structure is a small perturbation in the energy levels (or spectra) of atoms or molecules due to the magnetic dipole-dipole interaction, arising from the interaction of the nuclear magnetic moment with the magnetic field of the electron. 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 hyperfine structure transition frequency of a particular isotope of caesium or rubidium atoms is used as a basis for these clocks.
 Science Fair Projects - Hyperfine structure (622 words) Hyperfine structure is a small perturbation in the energy levels (or spectrum) of atoms or molecules due to the magnetic dipole-dipole interaction, arrising from the interaction of the nuclear magnetic dipole with the magnetic field of the electron. 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 hyperfine structure transition frequency of a particular isotope of caesium or rubidium atoms is used as a basis for these clocks.
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