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Muon spin spectroscopy, also known as μSR, is an experimental technique based on the implantation of spin-polarized
muon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of  ''ħ'', but with a much greater mass. It is classified as a ...
s in matter and on the detection of the influence of the atomic, molecular or crystalline surroundings on their spin motion. The motion of the muon
spin Spin or spinning most often refers to: * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin quantum number, a number which defines the value of a particle's spin * Spinning (textiles), the creation of yarn or thr ...
is due to the magnetic field experienced by the particle and may provide information on its local environment in a very similar way to other magnetic resonance techniques, such as
electron spin resonance Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spin ...
(ESR or EPR) and, more closely,
nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
(NMR).


Introduction

Muon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of  ''ħ'', but with a much greater mass. It is classified as a ...
spin spectroscopy is an atomic, molecular and condensed matter experimental technique that exploits nuclear detection methods. In analogy with the acronyms for the previously established spectroscopies
NMR Nuclear magnetic resonance (NMR) is a physical phenomenon in which atomic nucleus, nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near and far field, near field) and respond by producing ...
and ESR, muon spin spectroscopy is also known as μSR. The acronym stands for muon spin rotation, relaxation, or resonance, depending respectively on whether the muon spin motion is predominantly a rotation (more precisely a
precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In o ...
around a still
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
), a relaxation towards an equilibrium direction, or a more complex dynamic dictated by the addition of short
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the u ...
pulses. μSR does not require any
radio-frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the ...
technique to align the probing spin. More generally speaking, muon spin spectroscopy includes any study of the interactions of the muon's magnetic moment with its surroundings when implanted into any kind of matter. Its two most notable features are its ability to study local environments, due to the short effective range of muon interactions with matter, and the characteristic time-window (10−13 – 10−5 s) of the dynamical processes in atomic, molecular and condensed media. The closest parallel to μSR is "pulsed NMR", in which one observes time-dependent transverse nuclear polarization or the so-called " free induction decay" of the nuclear polarization. However, a key difference is that in μSR one uses a specifically implanted spin (the muon's) and does not rely on internal nuclear spins. Although particles are used as a probe, μSR is not a diffraction technique. A clear distinction between the μSR technique and those involving neutrons or
X-rays An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
is that scattering is not involved.
Neutron diffraction Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of Neutron temperature, thermal or ...
techniques, for example, use the change in energy and/or momentum of a scattered
neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
to deduce the sample properties. In contrast, the implanted muons are not diffracted but remain in a sample until they decay. Only a careful analysis of the decay product (i.e. a
positron The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatt ...
) provides information about the interaction between the implanted muon and its environment in the sample. As with many of the other nuclear methods, μSR relies on discoveries and developments made in the field of particle physics. Following the discovery of the muon by Seth Neddermeyer and Carl D. Anderson in 1936, pioneer experiments on its properties were performed with
cosmic rays Cosmic rays or astroparticles are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar ...
. Indeed, with one muon hitting each square centimeter of the earth's surface every minute, the muons constitute the foremost constituent of cosmic rays arriving at ground level. However, μSR experiments require muon fluxes of the order of 10^4-10^7 muons per second per square centimeter. Such fluxes can only be obtained in high-energy
particle accelerators A particle accelerator is a machine that uses electromagnetic fields to propel electric charge, charged particles to very high speeds and energies to contain them in well-defined particle beam, beams. Small accelerators are used for fundamental ...
which have been developed during the last 50 years.


Muon production

The collision of an accelerated proton beam (typical energy 600 MeV) with the nuclei of a production target produces positive pions (\pi^+) via the possible reactions: : \begin p + p & \rightarrow & p + n + \pi^+\\ p + n & \rightarrow & n + n + \pi^+\\ \end From the subsequent weak decay of the
pions In particle physics, a pion (, ) or pi meson, denoted with the Greek letter pi (), is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, mo ...
(MEAN lifetime \tau_ = 26.03 ns) positive muons (\mu^+) are formed via the two body decay: : \pi^+ \rightarrow \mu^+ + \nu_ .
Parity violation In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point ref ...
in the weak interactions implies that only left-handed neutrinos exist, with their
spin Spin or spinning most often refers to: * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin quantum number, a number which defines the value of a particle's spin * Spinning (textiles), the creation of yarn or thr ...
antiparallel to their linear momentum (likewise only right-handed anti-neutrino are found in nature). Since the pion is spinless both the neutrino and the \mu^+ are ejected with spin antiparallel to their momentum in the pion rest frame. This is the key to provide spin-polarised muon beams. According to the value of the pion momentum different types of \mu^+-beams are available for μSR measurements.


Energy classes of muon beams

Muon beams are classified into three types based on the
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
of the muons being produced: high-energy, surface or "Arizona", and ultra-slow muon beams. ''High-energy muon beams'' are formed by the pions escaping the production target at high energies. They are collected over a certain solid angle by quadrupole magnets and directed onto a decay section consisting of a long
superconducting Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases g ...
solenoid upright=1.20, An illustration of a solenoid upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whos ...
with a field of several tesla. If the pion momentum is not too high, a large fraction of the pions will have decayed before they reach the end of the solenoid. In the laboratory frame the polarization of a high-energy muon beam is limited to about 80% and its energy is of the order of ~40-50MeV. Although such a high energy beam requires the use of suitable moderators and samples with sufficient thickness, it guarantees a homogeneous implantation of the muons in the sample volume. Such beams are also used to study specimens inside of recipients, e.g. samples inside pressure cells. Such muon beams are available at
PSI Psi, PSI or Ψ may refer to: Alphabetic letters * Psi (Greek) (Ψ or ψ), the twenty-third letter of the Greek alphabet * Psi (Cyrillic), letter of the early Cyrillic alphabet, adopted from Greek Arts and entertainment * "Psi" as an abbreviat ...
,
TRIUMF Triumf may refer to: * TRIUMF, Canada's national particle accelerator centre * 14959 TRIUMF, a minor planet * S-400 Triumf, a Russian anti-aircraft weapon system developed in the 1990s * Triumf Riza (1979–2007), Kosovo police officer and member o ...
,
J-PARC J-PARC (Japan Proton Accelerator Research Complex) is a high intensity proton accelerator facility. It is a joint project between KEK and JAEA and is located at the Tokai campus of JAEA. J-PARC aims for the frontier in materials and life scien ...
an
RIKEN-RAL
The second type of muon beam is often called the ''surface'' or ''Arizona'' beam (recalling the pioneering work of Pifer ''et al.'' from the
University of Arizona The University of Arizona (Arizona, U of A, UArizona, or UA) is a Public university, public Land-grant university, land-grant research university in Tucson, Arizona, United States. Founded in 1885 by the 13th Arizona Territorial Legislature, it ...
). In these beams, muons arise from pions decaying at rest inside but near the surface of the production target. Such muons are 100% polarized, ideally monochromatic, and have a very low momentum of 29.8 MeV/c (corresponding to a kinetic energy of 4.1 MeV). They have a range width in matter of the order of 180 mg/cm2. The paramount advantage of this type of beam is the ability to use relatively thin samples. Beams of this type are available at PSI (Swiss Muon Source SμS), TRIUMF, J-PARC,
ISIS Neutron and Muon Source The ISIS Neutron and Muon Source is a pulsed neutron and muon source, established 1984 at the Rutherford Appleton Laboratory of the Science and Technology Facilities Council, on the Harwell Science and Innovation Campus in Oxfordshire, United ...
and RIKEN-RAL. Positive muon beams of even lower energy (''ultra-slow muons'' with energy down to the eV-keV range) can be obtained by further reducing the energy of an Arizona beam by utilizing the energy-loss characteristics of large
band gap In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to t ...
solid moderators. This technique was pioneered by researchers at the TRIUMF cyclotron facility in
Vancouver, B.C. Vancouver is a major city in Western Canada, located in the Lower Mainland region of British Columbia. As the most populous city in the province, the 2021 Canadian census recorded 662,248 people in the city, up from 631,486 in 2016. The Met ...
,
Canada Canada is a country in North America. Its Provinces and territories of Canada, ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, making it the world's List of coun ...
. It was christened with the acronym μSOL (muon separator on-line) and initially employed LiF as the moderating solid. The same 1986 paper also reported the observation of negative
muonium Muonium () is an exotic atom made up of an antimuon and an electron, which was discovered in 1960 by Vernon W. Hughes and is given the chemical symbol Mu. During the muon's lifetime, muonium can undergo chemical reactions. Description Beca ...
ions (i.e., Mu− or μ+ e− e−) in vacuum. In 1987, the slow μ+ production rate was increased 100-fold using thin-film rare-gas solid moderators, producing a usable flux of low-energy positive muons. This production technique was subsequently adopted by PSI for their low-energy positive muon beam facility. The tunable energy range of such muon beams corresponds to implantation depths in solids of less than a nanometer up to several hundred nanometers. Therefore, the study of magnetic properties as a function of the distance from the surface of the sample is possible. At the present time, PSI is the only facility where such a low-energy muon beam is available on a regular basis. Technical developments have been also conducted at RIKEN-RAL, but with a strongly reduced low-energy muon rate.
J-PARC J-PARC (Japan Proton Accelerator Research Complex) is a high intensity proton accelerator facility. It is a joint project between KEK and JAEA and is located at the Tokai campus of JAEA. J-PARC aims for the frontier in materials and life scien ...
is projecting the development of a high-intensity low-energy muon beam.


''Continuous'' vs. ''pulsed'' muon beams

In addition to the above-mentioned classification based on energy, muon beams are also divided according to the time structure of the particle accelerator, i.e. continuous or pulsed. For ''continuous'' muon sources no dominating time structure is present. By selecting an appropriate incoming muon rate, muons are implanted into the sample one-by-one. The main advantage is that the time resolution is solely determined by the detector construction and the read-out electronics. There are two main limitations for this type of source, however: (i) unrejected charged particles accidentally hitting the detectors produce non-negligible random background counts; this compromises measurements after a few muon lifetimes, when the random background exceeds the true decay events; and (ii) the requirement to detect muons one at a time sets a maximum event rate. The background problem can be reduced by the use of electrostatic deflectors to ensure that no muons enter the sample before the decay of the previous muon. PSI and TRIUMF host the two continuous muon sources available for μSR experiments. At ''pulsed'' muon sources
protons A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' ( elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an electron (the pro ...
hitting the production target are bunched into short, intense, and widely separated pulses that provide a similar time structure in the secondary muon beam. An advantage of pulsed muon sources is that the event rate is only limited by detector construction. Furthermore, detectors are active only after the incoming muon pulse, strongly reducing the accidental background counts. The virtual absence of background allows the extension of the time window for measurements up to about ten times the muon mean lifetime. The principal downside is that the width of the muon pulse limits the time resolution. ISIS Neutron and Muon Source and J-PARC are the two ''pulsed'' muon sources available for μSR experiments.


Spectroscopic technique


Muon implantation

The muons are implanted into the sample of interest where they lose energy very quickly. Fortunately, this deceleration process occurs in such a way that it does not jeopardize a μSR measurement. On one side it is very fast (much faster than 100 ps), which is much shorter than a typical μSR time window (up to 20 μs), and on the other side, all the processes involved during the deceleration are Coulombic (
ionization Ionization or ionisation is the process by which an atom or a molecule acquires a negative or positive Electric charge, charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged at ...
of atoms,
electron scattering Electron scattering occurs when electrons are displaced from their original trajectory. This is due to the electrostatic forces within matter interaction or, if an external magnetic field is present, the electron may be deflected by the Lorentz ...
,
electron capture Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. Th ...
) in origin and do not interact with the muon spin, so that the muon is thermalized without any significant loss of polarization. The positive muons usually adopt interstitial sites of the crystallographic lattice, markedly distinguished by their electronic (charge) state. The spectroscopy of a muon chemically bound to an unpaired electron is remarkably different from that of all other muon states, which motivates the historical distinction in ''paramagnetic'' and ''diamagnetic'' states. Note that many ''diamagnetic'' muon states really behave like paramagnetic centers, according to the standard definition of a
paramagnet Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
. For example, in most metallic samples, which are Pauli paramagnets, the muon's positive charge is collectively screened by a cloud of
conduction Conductor or conduction may refer to: Biology and medicine * Bone conduction, the conduction of sound to the inner ear * Conduction aphasia, a language disorder Mathematics * Conductor (ring theory) * Conductor of an abelian variety * Condu ...
electrons. Thus, in metals, the muon is not bound to a single electron, hence it is in the so-called ''diamagnetic'' state and behaves like a free muon. In insulators or
semiconductors A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping levels ...
a collective screening cannot take place and the muon will usually pick up one electron and form a so-called
muonium Muonium () is an exotic atom made up of an antimuon and an electron, which was discovered in 1960 by Vernon W. Hughes and is given the chemical symbol Mu. During the muon's lifetime, muonium can undergo chemical reactions. Description Beca ...
(Mu=μ++e−), which has similar size (
Bohr radius The Bohr radius () is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an at ...
),
reduced mass In physics, reduced mass is a measure of the effective inertial mass of a system with two or more particles when the particles are interacting with each other. Reduced mass allows the two-body problem to be solved as if it were a one-body probl ...
, and
ionization energy In physics and chemistry, ionization energy (IE) is the minimum energy required to remove the most loosely bound electron of an isolated gaseous atom, Ion, positive ion, or molecule. The first ionization energy is quantitatively expressed as : ...
to the
hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
atom. This is the prototype of the so-called ''paramagnetic'' state.


Detection of muon polarization

The decay of the positive muon into a positron and two neutrinos occurs via the weak interaction process after a
mean lifetime A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and ( lambda) is a positive ra ...
of τμ = 2.197034(21) μs: : \mu^+ \rightarrow e^+ + \nu_e + \bar_~. Parity violation in the weak interaction leads in this more complicated case ( three body decay) to an anisotropic distribution of the positron emission with respect to the spin direction of the μ+ at the decay time. The positron emission probability is given by : W(\theta)d\theta \propto (1 + a\cos\theta)d\theta~, where \theta is the angle between the positron trajectory and the μ+-spin, and a is an intrinsic asymmetry parameter determined by the weak decay mechanism. This anisotropic emission constitutes in fact the basics for the μSR technique. The average asymmetry A is measured over a statistical ensemble of implanted muons and it depends on further experimental parameters, such as the beam spin polarization P_, close to one, as already mentioned. Theoretically A =1/3 is obtained if all emitted positrons are detected with the same efficiency, irrespective of their energy. Practically, values of A ≈ 0.25 are routinely obtained. The muon spin motion may be measured over a time scale dictated by the muon decay, ''i.e.'' a few times τμ, roughly 10 μs. The asymmetry in the muon decay correlates the positron emission and the muon spin directions. The simplest example is when the spin direction of all muons remains constant in time after implantation (no motion). In this case the asymmetry shows up as an imbalance between the positron counts in two equivalent detectors placed in front and behind the sample, along the beam axis. Each of them records an exponentially decaying rate as a function of the time ''t'' elapsed from implantation, according to :N_\alpha(t)=N_0 \exp(-t/\tau_\mu) (1+\alpha A) with \alpha=\pm 1 for the detector looking towards and away from the spin arrow, respectively. Considering that the huge muon spin polarization is completely outside thermal equilibrium, a dynamical relaxation towards the equilibrium unpolarized state typically shows up in the count rate, as an additional decay factor in front of the experimental asymmetry parameter, ''A''. A magnetic field parallel to the initial muon spin direction probes the dynamical relaxation rate as a function of the additional muon Zeeman energy, without introducing additional coherent spin dynamics. This experimental arrangement is called Longitudinal Field (LF) μSR. A special case of LF μSR is Zero Field (ZF) μSR, when the external magnetic field is zero. This experimental condition is particularly important since it allows to probe any internal quasi-static (i.e. static on the muon time-scale) magnetic field of field distribution at the muon site. Internal quasi-static fields may appear spontaneously, not induced by the magnetic response of the sample to an external field They are produced by disordered nuclear magnetic moments or, more importantly, by ordered electron magnetic moments and orbital currents. Another simple type of μSR experiment is when implanted all muon spins
precess Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In ot ...
coherently around the external magnetic field of modulus B, perpendicular to the beam axis, causing the count unbalance to oscillate at the corresponding Larmor frequency \omega between the same two detectors, according to :N_\alpha(t)=N_0 \exp(-t/\tau_\mu) (1+\alpha A\cos\omega t) Since the Larmor frequency is \omega=\gamma_\mu B, with a
gyromagnetic ratio In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol , gamma. Its SI u ...
\gamma_\mu=851.616 Mrad(sT)−1, the frequency spectrum obtained by means of this experimental arrangement provides a direct measure of the internal magnetic field intensity distribution. The distribution produces an additional decay factor of the experimental asymmetry ''A''. This method is usually referred to as Transverse Field (TF) μSR. A more general case is when the initial muon spin direction (coinciding with the detector axis) forms an angle \theta with the field direction. In this case the muon spin precession describes a cone which results in both a longitudinal component, A\cos^2\theta, and a transverse precessing component, A\sin^2\theta\cos\omega t, of the total asymmetry. ZF μSR experiments in the presence of a spontaneous internal field fall into this category as well.


Applications

Muon spin rotation and relaxation are mostly performed with positive muons. They are well suited to the study of
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
s at the atomic scale inside matter, such as those produced by various kinds of
magnetism Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, ...
and/or
superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
encountered in compounds occurring in nature or artificially produced by modern
material science A material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geol ...
. The London penetration depth is one of the most important parameters characterizing a superconductor because its inverse square provides a measure of the density ''ns'' of
Cooper pairs In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
. The dependence of ''ns'' on temperature and magnetic field directly indicates the symmetry of the superconducting gap. Muon spin spectroscopy provides a way to measure the penetration depth, and so has been used to study high-temperature cuprate superconductors since their discovery in 1986. Other important fields of application of μSR exploit the fact that positive muons capture electrons to form
muonium Muonium () is an exotic atom made up of an antimuon and an electron, which was discovered in 1960 by Vernon W. Hughes and is given the chemical symbol Mu. During the muon's lifetime, muonium can undergo chemical reactions. Description Beca ...
atoms which behave chemically as light
isotope Isotopes are distinct nuclear species (or ''nuclides'') of the same chemical element. They have the same atomic number (number of protons in their Atomic nucleus, nuclei) and position in the periodic table (and hence belong to the same chemica ...
s of the
hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
atom. This allows investigation of the largest known
kinetic isotope effect In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for t ...
in some of the simplest types of chemical reactions, as well as the early stages of formation of
radical Radical (from Latin: ', root) may refer to: Politics and ideology Politics *Classical radicalism, the Radical Movement that began in late 18th century Britain and spread to continental Europe and Latin America in the 19th century *Radical politics ...
s in organic chemicals. Muonium is also studied as an analogue of hydrogen in
semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...
s, where hydrogen is one of the most ubiquitous impurities.


Facilities

μSR requires a
particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel electric charge, charged particles to very high speeds and energies to contain them in well-defined particle beam, beams. Small accelerators are used for fundamental ...
for the production of a muon beam. This is presently achieved at few large scale facilities in the world: the CMMS continuous source at
TRIUMF Triumf may refer to: * TRIUMF, Canada's national particle accelerator centre * 14959 TRIUMF, a minor planet * S-400 Triumf, a Russian anti-aircraft weapon system developed in the 1990s * Triumf Riza (1979–2007), Kosovo police officer and member o ...
in Vancouver, Canada; the SμS continuous source at the
Paul Scherrer Institut The Paul Scherrer Institute (PSI) is a multi-disciplinary research institute for natural and engineering sciences in Switzerland. It is located in the Canton of Aargau in the municipalities Villigen and Würenlingen on either side of the Riv ...
(PSI) in Villigen, Switzerland; the
ISIS Neutron and Muon Source The ISIS Neutron and Muon Source is a pulsed neutron and muon source, established 1984 at the Rutherford Appleton Laboratory of the Science and Technology Facilities Council, on the Harwell Science and Innovation Campus in Oxfordshire, United ...
and RIKEN-RAL pulsed sources at the
Rutherford Appleton Laboratory The Rutherford Appleton Laboratory (RAL) is one of the national scientific research laboratories in the UK operated by the Science and Technology Facilities Council (STFC). It began as the Rutherford High Energy Laboratory, merged with the At ...
in Chilton, United Kingdom; and the
J-PARC J-PARC (Japan Proton Accelerator Research Complex) is a high intensity proton accelerator facility. It is a joint project between KEK and JAEA and is located at the Tokai campus of JAEA. J-PARC aims for the frontier in materials and life scien ...
facility in Tokai, Japan, where a new pulsed source is being built to replace that at
KEK , known as KEK, is a Japanese organization whose purpose is to operate the largest particle physics laboratory in Japan, situated in Tsukuba, Ibaraki prefecture. It was established in 1997. The term "KEK" is also used to refer to the laboratory ...
in Tsukuba, Japan. Muon beams are also available at the Laboratory of Nuclear Problems,
Joint Institute for Nuclear Research The Joint Institute for Nuclear Research (JINR, ), in Dubna, Moscow Oblast (110 km north of Moscow), Russia, is an international research center for nuclear sciences, with 5,500 staff members including 1,200 researchers holding over 1,000 ...
(JINR) in Dubna, Russia. The International Society for μSR Spectroscopy (ISMS) exists to promote the worldwide advancement of μSR. Membership in the society is open free of charge to all individuals in academia, government laboratories and industry who have an interest in the society's goals.


See also

*
Muon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of  ''ħ'', but with a much greater mass. It is classified as a ...
*
Muonium Muonium () is an exotic atom made up of an antimuon and an electron, which was discovered in 1960 by Vernon W. Hughes and is given the chemical symbol Mu. During the muon's lifetime, muonium can undergo chemical reactions. Description Beca ...
*
Nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
*
Perturbed angular correlation The perturbed γ-γ angular correlation, PAC for short or PAC-Spectroscopy, is a method of nuclear solid-state physics with which magnetic field, magnetic and electric fields in crystal structures can be measured. In doing so, electrical field gra ...


Notes


References

{{Reflist


External links


μSR basic literature

Integrated Infrastructure Initiative for Neutron Scattering and Muon Spectroscopy (NMI3)



Video - What are muons and how are they produced?
Spectroscopy Scientific techniques