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A subatomic particle is a constituent or excitation studied at the level below ordinary atomic structure. The category includes elementary particles, such as the electron, and composite hadrons, such as the proton and neutron.

Calling something a particle does not require a tiny classical solid sphere. Quantum mechanics describes localized detections and wave-like propagation, while high-energy scattering probes whether internal structure is resolved. A particle detector usually infers a particle from transferred energy, emitted light or a trajectory reconstructed from many interactions. The measured track width and the particle's intrinsic spatial structure are therefore different quantities.

Succinate is the dianion of succinic acid, a four-carbon dicarboxylic acid with structure ${}^{-}\mathrm{OOC}-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_2-\mathrm{CO}{\mathrm{O}}^{-}$. It is an intermediate of the citric acid cycle.

Succinate dehydrogenase oxidizes succinate to fumarate, creating a carbon-carbon double bond while passing reducing equivalents into the respiratory machinery. This connects carbon-skeleton chemistry with electron transfer.

The SNO Collaboration used $1000$ tonnes of heavy water in a $12\mathrm{m}$ acrylic sphere, surrounded by ordinary water shielding and $9456$ photomultipliers. Weak charged current (CC) breakup of a deuteron selects electron neutrinos; weak neutral current (NC) breakup measures all active neutrino flavors; electron elastic scattering (ES) has reduced non-electron sensitivity.^[ref]

Hot electrons in galaxy clusters scatter photons of the cosmic microwave background, producing a characteristic spectral distortion. The thermal contribution measures a line-of-sight integral of electron pressure, whereas X-ray emission depends approximately on the integral of electron density squared times a temperature-dependent emissivity. Combining the two with a geometrical model can constrain a cluster's physical size and hence its angular diameter distance. Temperature structure and departures from the assumed geometry introduce systematic uncertainty.

In a local London equation description, the measured London penetration depth satisfies ${\lambda }_L^2=m/({\mu }_0{n}_s{e}^2)$ when $n_s$ counts superconducting electrons and $m$ is their effective mass. Thus screening measures $n_s/m$. If instead one counts Cooper pairs, use pair mass $2m$ and pair electric charge $-2e$, giving pair density $n_s/2$ for the same screening length. Identifying this superconducting carrier density with the total conduction-electron density requires the additional assumption that the relevant carriers all participate in screening at the measurement temperature.

Superconductivity is a phase of matter that supports steady electric current with zero bulk electrical resistivity and exhibits the Meissner effect: equilibrium screening of a sufficiently weak, static magnetic field from the interior. It occurs below a material-dependent superconducting transition temperature, provided the electric current and applied magnetic field are also sufficiently small. ^[ref] Bulk expulsion means that a sample much thicker than its London penetration depth has an almost field-free interior; the magnetic field need not vanish at its surface. Conventional BCS theory explains superconductivity through correlated electrons forming Cooper pairs. ^[ref]

The two observations answer different questions. A resistance-versus-temperature experiment for superconductivity asks whether a steady electric current requires a measurable electric potential difference. A Field-cooled Meissner experiment asks whether a magnetic field already present in the material is expelled when it enters superconductivity. An ideal perfect conductor with zero electrical resistivity can preserve that pre-existing magnetic field; zero electrical resistance alone therefore does not establish the Meissner effect.

The usefulness follows directly from Joule heating, $P=I^{2}R$: maintaining a steady electric current through a segment with zero electrical resistance produces no resistive heating in that segment. This makes persistent electric currents attractive for producing steady magnetic fields. The beauty is that one phase has both a transport property and an equilibrium magnetic response, and the second cannot be inferred just by making an ordinary electrical resistance very small. The London equations encode this extra magnetic response. ^[ref]

Super-Kamiokande is an underground water Cherenkov detector in Japan. Its roughly 50,000-ton water target is viewed by photomultipliers around the tank. A neutrino is observed indirectly when an interaction produces charged secondaries that emit Cherenkov radiation.^[ref]

Photon arrival times and detected charges constrain interaction position and outgoing directions. Ring appearance helps distinguish showering electrons from more track-like muons, enabling the Super-Kamiokande atmospheric-neutrino experiment. The water mass is both target and optical medium: transparency, sensor timing and background rejection affect reconstruction. The useful fiducial volume is smaller than the full water volume.

Super-Kamiokande used $535$ days ($33.0$ kiloton-years) and $22.5$ fiducial kilotons of water. Inner photomultiplier times and charges reconstructed interactions; the outer anticoincidence detector vetoed entering particles and marked exits. Contained single-ring events used likelihood classification: electron particle showers blur rings; muons give sharper edges. The $1.33\mathrm{GeV}$ visible-energy sample division is not a universal detection threshold. Simulation estimated classification efficiency above about $98\%$, distinct from total detection efficiency; stopping muons and decay electrons checked classification.^[ref]

Downward neutrinos travel about $15\mathrm{km}$; upward ones about $13000\mathrm{km}$. The multi-GeV muon-like up/down asymmetry was $-0.296\pm 0.048\pm 0.010$; electron-like events lacked a comparable effect. Calibration constrained directional bias. This was disappearance evidence; tau neutrino appearance was untagged and sterile conversion remained possible.^[ref]

Writing $U$ and $D$ for the selected upward and downward populations, the asymmetry is $A=(U-D)/(U+D)$: a negative value means fewer upward events. An absolute source-normalization error alone rescales both populations and leaves this ratio unchanged. A direction-dependent response error need not cancel.

A supernova remnant is the expanding stellar debris and shocked surrounding gas left by a supernova. The debris drives an outward shock wave into the ambient interstellar medium; a reverse shock wave heats the ejecta as the expansion is decelerated. Hot plasma emits X-rays, while accelerated electrons produce synchrotron radiation in the magnetic field. Comparing successive images measures expansion, and X-ray spectroscopy maps the expelled chemical elements. In Cassiopeia A, the Chandra X-ray Observatory resolves the outer shock and heated debris. Such observations connect an explosion's kinetic energy and newly produced elements to the subsequent heating and enrichment of the interstellar medium.^[ref]

An rf field restricted to a metal's skin layer can transfer energy coherently to electrons whose orbits return to that layer. With magnetic field parallel to the surface, resonance can occur at $\omega =n{\omega }_c$, producing harmonics at $B_n=m_c\omega /(ne)$. Surface loss or cavity impedance replaces simple bulk transmission as the measured signal.

Surface ionization forms ions when atoms interact with a surface and leave after exchanging electrons. For positive ion production at a hot surface, the equilibrium Saha-Langmuir ratio has the form $n_{+}/n_0=(g_{+}/g_0)\exp [(W-I)/(k_{B}T)]$, where $W$ is the surface work function, $I$ the atomic ionization energy, and $g_{+}/g_0$ a statistical-weight ratio.

A high work function favors leaving an electron behind. Alkali atoms, with relatively low ionization energies, can therefore be detected efficiently by converting neutral arrivals into countable ionic signals. Surface condition and temperature matter, so the equilibrium expression is a model to check rather than a universal detector calibration.^[ref]

A surface ionization detector detects a neutral atomic beam by converting incident chemical atoms into ions on a hot surface. For suitable alkali metals, a heated tungsten surface can favor loss of an electron: the competing surface work function and atomic ionization energy make the efficiency strongly dependent on species, surface condition and temperature. An electric field then collects the resulting ions, producing an electric current or a count after amplification. A response therefore requires an efficiency measurement calibration; it is not automatically equal to the incident particle flux.

A 2002 imaging experiment used a tungsten-coated heated ribbon followed by a microchannel plate detector and a phosphor screen. It recorded where the arriving neutral chemical atoms struck, rather than just their total rate. The reported approximately $20\mu \mathrm{m}$ spatial resolution and roughly $50\%$ detection efficiency belong to that apparatus and its conditions, rather than to every surface ionization detector.^[ref]

An electron with kinetic energy $\alpha m_e{c}^2$ annihilating with a stationary positron into two equal-angle photons has $\tan \varphi =\sqrt{2/\alpha }$ for $\alpha >0$. Equal photon energies follow from the specified symmetric laboratory geometry.

At fixed magnetic field, ultrarelativistic electrons lose energy through synchrotron radiation at a rate proportional to $E^2$. For steady injection $Q(E)\propto E^{-s}$, negligible escape and $s>1$, integrating the energy-space continuity equation gives $N(E)=|\dot{E}{|}^{-1}{\int }_E^{\infty }Q(E^{\prime })d{E}^{\prime }\propto E^{-(s+1)}$. Above the cooling break, the optically thin radiation spectral index therefore steepens from $(s-1)/2$ to $s/2$.

Synchrotron radiation is electromagnetic radiation emitted by relativistic charged particles undergoing transverse acceleration, typically when a magnetic field bends their paths. For ultrarelativistic particles, emission is concentrated near the instantaneous direction of motion rather than distributed isotropically.

A circulating electron beam therefore loses energy even when the bending magnet itself does no work. Radiofrequency accelerating fields replenish that loss in a storage ring. The extracted radiation is useful as an intense source for spectroscopy and imaging; its angular distribution, polarization and optical spectrum depend on particle energy and magnetic geometry. In synchrotron cooling, those same radiation losses reshape a particle population.

The change in overpotential per decade of current density in the activation-controlled regime of a Tafel equation. In a single-step Butler-Volmer equation with constant transfer coefficient, the anodic slope is $b_a=RT\ln 10/({\alpha }_{a}nF)$, where $T$ is temperature, $R$ is the molar gas constant, $n$ is the number of transferred electrons and $F$ is the Faraday constant. The magnitude of the cathodic slope is $b_c=RT\ln 10/({\alpha }_{c}nF)$. Inferring one from the other requires the model's relation between the two coefficients; the equality ${\alpha }_a+{\alpha }_c=1$ applies to this effective single-step model and need not describe a multistep reaction.

For a nearly massless incident tau neutrino and stationary target of mass $M_T$, the initial Mandelstam variables give $s=M_T^2+2M_T{E}_{\nu }$. At threshold the final tau lepton and the lightest allowed recoil system have no relative momentum, so $s=(m_{\tau }+M_X{)}^2$. This proves the formula. A free neutron recoil channel gives approximately $3.45\mathrm{GeV}$; an electron target has a different recoil and a threshold near $3.09\mathrm{TeV}$.

Choose $m_{\tau }=2\mathrm{GeV}$ and $\sqrt{s}=6\mathrm{GeV}$ purely for illustration. Then each parent has $E_{\tau }=3\mathrm{GeV}$, $|{\mathbf{p}}_{\tau }|=\sqrt{5}\mathrm{GeV}$ and $\beta =\sqrt{5}/3$. Treat all six daughters as massless, including the charged electron and antimuon, and generate each three-body particle decay with constant squared decay amplitude. Choose the parent direction isotropically and the two decays independently; this omits the physical production angular law and spin correlations.

The Lorentz-invariant phase space factorizes through $t=q^2$ into a two-body decay to $\ell +q$, followed by a two-body decay of $q$:After angular integration the first factor contributes $1-t/m_{\tau }^2=x$, while the massless second factor is constant. Since $|dt|=m_{\tau }^{2}dx$, the normalized chosen density is $f(x)=2x$. Drawing $x=\sqrt{U}$ with $U$ uniform on $[0,1]$ implements this density. Isotropic directions, followed by a Lorentz boost for the invisible pair and another for the parent, conserve the complete four-momentum of each generated event.

Define transverse acoplanarity by $\alpha =\pi -\Delta \varphi$, where $\Delta \varphi \in [0,\pi ]$ is the angle between the two visible momentum projections perpendicular to the beam. A fully visible two-body event with zero initial transverse momentum has $\alpha =0$ and $M_{\mathrm{miss}}^2=0$. The toy tau lepton events spread away from that point. These observables are complementary: an angular imbalance asks about directions, while the missing invariant mass also uses the visible energies and longitudinal momenta.

A Lorentz-invariant phase space density supplies allowed configurations and their geometric measure. A physical weak interaction decay amplitude reweights them and correlates spins. Consequently the plotted density is a lesson about conservation and available configurations, not a predicted experimental rate or a fit to the discovery sample. The massless charged-daughter approximation is also unsuitable near the muon rest-energy threshold.

The tau is the charged lepton of the third fermion generation. In the massless approximation its charged-current W boson partial decay width equals those of the electron and muon, reflecting lepton universality.

The tau lepton has electric charge $-1$ in units of the positive elementary electric charge; ${\tau }^{+}$ is its antiparticle. Its weak charged current decays make the tau lepton useful for testing lepton universality. They also illustrate how particle detection can establish a short-lived parent through visible daughters and a consistent invisible recoil.

For a linearly split orbital doublet occupied by one electron or one hole, the lower adiabatic branch has a cusp $-g|Q|$. A harmonic elastic cost produces equal minima at $Q=\pm g/K$. Orbital degeneracy therefore establishes instability of the regular geometry, but cannot alone distinguish opposite tetragonal distortions. A symmetry-allowed cubic elastic invariant in the two-component distortion can select one sign.