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A change between electronic energy eigenstates of a chemical atom or another system.

Determining the column density of a cloud of chemical atoms from the attenuation of a probe beam of light; the measured image integrates through the cloud along the viewing direction.

A quantum electrodynamics correction separates hydrogen atom levels such as $2s_{1/2}$ and $2p_{1/2}$ that coincide in the simplest model.

The Lamb shift measures an energy level displacement beyond a specified Dirac equation reference. In the point-proton, infinite-nuclear-mass Coulomb potential model, $2S_{1/2}$ and $2P_{1/2}$ share principal quantum number $n=2$ and total electronic angular momentum $j=1/2$, hence energy, despite differing orbital angular momentum values.^[ref]

The Lamb-Retherford experiment converts a small energy difference into a large detector change: prepare a long-lived quantum state, transfer population into a short-lived one, and read the surviving beam.

A restriction on transitions between quantum states for a specified interaction. An electric-dipole selection rule is one example.

A Rydberg atom has an electron excited to a large principal quantum number $n$. In a hydrogen-like model, the binding energy scales as $1/n^2$ and the orbital size as $n^2$. The outer electron is therefore weakly bound and its motion extends far beyond the compact core.

These properties make Rydberg atoms sensitive to applied electric fields and useful for studying controllable interactions such as Rydberg blockade. A field ramp can ionize different excited states at different thresholds, enabling state-selective field ionization. Real multi-electron atoms depart from the simple hydrogen-like spectrum, especially when the outer electron penetrates the core.

A cold atom has a small motional kinetic energy relative to a stated experimental scale. Usually an ensemble is prepared with a narrow velocity distribution through laser cooling or evaporative cooling of atoms; the quoted temperature characterizes motion rather than requiring the atom's internal electronic state to be thermally equilibrated.

Slower motion increases the time available for interrogation in atomic clocks or atom interferometry. In a release experiment, a cloud's growth after the trap is switched off constrains its velocity spread. Distinguishing initial cloud size from expansion avoids mistaking tight confinement for low motional temperature.

An ultracold gas is a dilute gas cooled until atomic motion becomes slow enough that quantum mechanics is essential to its preparation, collisions or collective state. There is no single temperature boundary independent of particle mass and number density: the overlap of thermal matter waves depends on the thermal de Broglie wavelength relative to interparticle spacing.

Laser cooling can prepare a cold trapped sample, and evaporative cooling of atoms can further increase its phase-space density of an atomic gas. Expansion after releasing a trap gives information about the velocity distribution. A small measured cloud alone is insufficient evidence for low temperature, because spatial confinement also depends on the trapping potential energy.

In LS coupling, an atomic term symbol specifies total electronic spin $S$, total orbital angular momentum $L$, and total angular momentum $J$. The superscript $2S+1$ is the spin multiplicity; the letters $S,P,D,F,\dots$ denote $L=0,1,2,3,\dots$. Coupling gives $J=|L-S|,\dots ,L+S$, and a fixed-$J$ level has $2J+1$ magnetic substates before an external field resolves them. For example, ${}^{3}P$ has $S=L=1$ and levels $J=0,1,2$, containing $1+3+5=9$ states altogether. A term symbol does not itself specify the radial electron configuration.

Electrons partially shield an atomic nucleus electric charge. At large distances a neutral chemical atom therefore does not generate the unscreened Coulomb potential of its bare atomic nucleus.

An atom is monovalent in a specified bonding or conduction model when its relevant valence is one. In the simple metallic free electron model, one monovalent atom per primitive unit cell supplies one conduction electron per cell. Counting the two spin states then fills half of a single energy band at zero temperature.

A muonic atom has a negative muon bound in the Coulomb potential of an atomic nucleus. Its much larger reduced mass than in an electronic chemical atom greatly reduces the orbital scale, increasing sensitivity of transition energies to the nuclear charge radius and nuclear charge distribution. Measuring muonic X-ray transitions therefore complements electron scattering. Strong relativistic and nuclear-size effects in heavy systems require a treatment beyond a point-nucleus nonrelativistic Coulomb spectrum.

Orbital parallax infers a system's Euclidean distance by comparing the angular size of an orbit with its physical size. If an orbital fit gives a deprojected angular semimajor axis $\alpha$ in radians and spectroscopy gives the corresponding physical semimajor axis $a$, the small-angle approximation gives $d=a/\alpha$.

The scales must describe the same orbit. In a binary star, radial-velocity amplitudes, orbital period and eccentricity give physical projected orbital sizes; the astrometric geometry can supply the orbital inclination needed to remove that projection. The mass-distance degeneracy of an angular stellar orbit gives a worked example of why adding a physical velocity measurement changes what can be inferred.^[ref]

Machine learning develops algorithms that use data or experience to improve performance on a specified task. The task, the experience available to the algorithm and the performance criterion must all be stated. A statistical classification system might learn from labelled training data; an unsupervised learning method instead looks for structure without those labels.^[ref]

For example, a linear regression model can learn coefficients predicting a numerical outcome from measured inputs. Minimizing its error on the training data determines a fitted model, but does not establish how well it predicts new observations. A separate test set estimates performance on data withheld from fitting. Overfitting occurs when fitting peculiarities of the training data impairs this generalization; data leakage can make the evaluation misleading.^[ref]

Statistical learning supplies tools for reasoning about these prediction and uncertainty questions. A useful learned model is therefore assessed through an explicit task and evaluation, alongside the running time and other resources needed to train and use it.

An antibiotic that interferes with bacterial protein synthesis. Its resistance markers have been used in molecular genetics, including the 1973 plasmid construction experiment, linking an experimentally selectable growth trait with carriage of a genetic construct.

An aminoglycoside antibiotic that interferes with bacterial protein synthesis. Resistance can provide a selectable marker in molecular genetics, as in the 1973 plasmid construction experiment; survival under selection identifies a phenotype rather than every detail of the inserted DNA.

The ability of a microorganism to grow under antibiotic exposure that inhibits a susceptible comparison, often reflected in an increased minimum inhibitory concentration. Survival alone does not establish resistance: antibiotic tolerance and bacterial persistence concern killing and survival without necessarily changing that growth threshold.

A dipole antenna uses two conducting arms carrying an oscillating current, commonly fed across a central gap. Its changing charge and current distributions produce electromagnetic radiation. A short straight dipole has far-zone power proportional to ${\sin }^2\theta$ relative to its axis: it radiates most strongly sideways and has axial nulls. A practical half-wave dipole has a nonuniform current distribution and a different exact pattern and input impedance. Geometric wire length, electrical length and the surrounding dielectric or conducting structures all affect resonance and matching.

An antenna beam pattern gives an antenna's directional response as a function of observation angle. A normalized power pattern divides radiation intensity by its peak; a field-amplitude pattern is its square root under a consistent impedance convention. The beam solid angle integrates the normalized power pattern over direction, so ideal directivity is $4\pi /{\Omega }_A$. A short dipole antenna has a power pattern proportional to ${\sin }^2\theta$, zero along its axis and maximum broadside. A narrow main lobe can coexist with sidelobes, so beamwidth alone does not specify the complete response.

The antenna temperature expresses the noise power delivered by a receiving antenna as an equivalent input noise temperature. It depends on the sky and surroundings weighted by the antenna beam pattern, as well as losses in the antenna; it need not be the physical temperature of either the antenna or a single astronomical source.

Antenna gain compares the far-field energy flux in a specified direction with the flux that an isotropic radiator would produce using the same input power. Thus $S_r=G{P}_{\mathrm{in}}/(4\pi r^2)$. Gain includes radiation efficiency; it must be distinguished from a voltage or current amplifier gain and from directivity when losses matter.