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An ammonia maser uses an Ammonia molecular beam, maser state selection and a maser cavity to obtain amplification or sustained microwave oscillation. In the 1954 experiment by James Power Gordon, Herbert Jack Zeiger and Charles Hard Townes, a quadrupolar static electric field focused upper-state molecules toward the cavity and deflected lower-state molecules away. The reported $J=K=3$ ammonia inversion transition lies near $23.87\mathrm{GHz}$.^[ref]

Johannes Jacobus van Vaals coauthored research on molecular beam.^[ref]

A molecular beam also includes a stream of chemical atoms, then called an atomic beam. An oven supplies particles; aligned slits restrict their directions, and a vacuum limits subsequent collisions. Narrowing the directions does not by itself make every particle's speed equal. This gives a useful separation of tasks: prepare a path, select or measure speed, apply an interaction, and read the resulting particle counts or deflection.

An experimental atomic physicist who demonstrated a thermal atomic beam of sodium in 1911. Vapor escaped through narrow slits into an evacuated vessel and condensed on a wall cooled with liquid air. The deposit matched the geometry predicted for straight-line trajectories, giving a visible test of molecular motion between collisions and a foundation for later molecular beam experiments.^[ref]

The maser cavity stores a resonant electromagnetic wave so that an arriving molecule encounters a field left by earlier molecules. An output coupling lets part of that stored energy reach a detector. The same coupling also removes energy, so increasing extraction can prevent startup. The cavity provides feedback; the selected molecular beam supplies the useful internal energy.

Let $U$ be stored field energy, $\omega =2\pi {\nu }_0$, and $\kappa ={\kappa }_{\mathrm{int}}+{\kappa }_{\mathrm{out}}$ the total passive energy decay rate. Internal dissipation and output extraction contribute ${\kappa }_{\mathrm{int}}U$ and ${\kappa }_{\mathrm{out}}U$ to lost power. With this energy convention, the loaded quality factor isThe field amplitude decays at $\kappa /2$; confusing amplitude and energy decay introduces a factor of two into a maser oscillation threshold calculation.

A directed stream of molecules used to prepare samples for spectroscopy.

A molecular beam also includes a stream of chemical atoms, then called an atomic beam. An oven supplies particles; aligned slits restrict their directions, and a vacuum limits subsequent collisions. Narrowing the directions does not by itself make every particle's speed equal. This gives a useful separation of tasks: prepare a path, select or measure speed, apply an interaction, and read the resulting particle counts or deflection.

The advantage is unusually tangible. A magnetic field can separate spin components in the Stern-Gerlach experiment; even gravity can sort a beam by flight time. The effusive beam speed distribution explains which particles leave the source, while gravity deflection of an atomic beam explains how that distribution becomes a pattern on a detector.

The apparatus and dipole inference are described under dipole evidence for bond polarization. The rigid rotor supplies a general starting model for rotational quantum states; rotational spectroscopy measures their transition frequencies, while molecular beam electric resonance can select and analyze states through their Stark effects.

An actual implementation gives substance to the apparatus description above. In Johannes Jacobus van Vaals's experiments, heated samples expanded with argon through a nozzle, then molecular beam skimmers formed the molecular beam in vacuum. Nonuniform electric fields selected and analyzed quantum states; parallel plates housed the microwave interaction. A surface ionization detector supplied electric current to an electronic amplifier and a lock-in amplifier. Resonant transfer into a rejected quantum state reduced the detected flux. Phase locking stabilized the microwave frequencies; an absorber suppressed reflections that could distort spectral lines. The thesis reports preliminary electric dipole moment components for gaseous potassium cyanide from measurements in nonzero electric fields. Such inference uses the Stark effect, rather than measuring electronegativity. The source notes restrictions from electric-dipole selection rules and molecular beam transit time; its preliminary dipole report is not a full calibration record. These are documented features of this apparatus, not proposed controls for the earlier hydrogen chloride experiment.^[ref]

A molecular beam skimmer is a small aperture, commonly at the tip of a cone, that transmits the central part of an expanding molecular beam into a downstream chamber. It separates source and measurement regions so that differential pumping can maintain a lower background pressure after the source. Its geometry selects directions; that selection alone does not give all transmitted molecules the same speed.

The surface also perturbs the beam. At high source number density, particles reflected from the skimmer walls can collide with the incoming flow and create shock waves, reducing and heating the transmitted beam. A 2017 experiment cooled the skimmer and measured a beam-flux increase of about eightfold under its tested conditions. A pulsed plasma glow made the disturbed flow visible; cooling reduced reflected momentum and, at lower temperatures, promoted adsorption. This tests why a narrower geometric opening is not a complete model of a real skimmer.^[ref]

The NIST validation report used $1\%$ carbonyl sulfide in argon to illustrate the readout. A pulsed nozzle injected a molecular beam along a two-mirror cavity. Approximately $1\mu \mathrm{s}$ excitation prepared quantum coherence; a receiver digitized the decaying electric field, then a Fourier transform produced spectral lines. Counterpropagating cavity waves produced a Doppler shift doublet; its midpoint represents one rest-frame transition.^[ref]

The portable electronics used a common microwave source and a $30\mathrm{MHz}$ offset derived from a $10\mathrm{MHz}$ reference. Cavity tuning selects the accessible band; it does not independently calibrate the line's frequency. Absolute accuracy also requires a characterized reference and receiver offset.^[ref]

Reported controls included nozzle off/on, carrier-gas changes, and a blind nitrogen mixture. Assigned components were correctly identified. Single-component standards supplied preliminary concentration calibration; one standard per quantified component left response validation incomplete. Condensation and departure from thermal equilibrium in the nozzle were acknowledged limitations.^[ref]

The lesson is that rotational spectral line assignment and concentration inference answer different questions. Reproducible frequencies support molecular identity; converting signal size into concentration requires calibrated response under the same transfer and excitation conditions. The thermal absorption example above does not model a nozzle's nonequilibrium populations or the cavity's pulsed response.

Awarded to Otto Stern for the molecular beam method and discovery of the proton magnetic moment. The molecular beam article develops direct measurements of particle speeds.^[ref]

Nuclear magnetic resonance detects the response of atomic nuclei with a magnetic moment to a radio frequency magnetic field in a steady magnetic field. Its striking possibility is to measure a nuclear property through an ordinary electrical signal from a bulk sample: an enormous number of tiny magnetic moments can produce a measurable change in a receiving circuit.

For a nucleus with spin angular momentum $\mathbf{J}$, define its gyromagnetic ratio by $\mathbf{\mu }=\gamma \mathbf{J}$. Throughout this article $\gamma$ is angular, measured in radians per second per tesla; $\gamma /(2\pi )$ is the corresponding value in cycles per second per tesla. With ${\mathbf{B}}_0=B_0\hat{\mathbf{z}}$, the Hamiltonian is $H=-\gamma B_0{J}_z$. Adjacent energy levels differ byThus a measured resonance frequency and a calibrated magnetic field determine $|\gamma |$. Converting that into a nuclear magnetic moment also requires the spin quantum number: the maximum projection has magnitude $|\gamma |\hslash I$. This simple experiment does not by itself determine the sign of $\gamma$.

The Rabi molecular beam magnetic resonance experiment detects transitions through changes in a selected molecular beam. The bulk experiments below instead detect electrical consequences of nuclear magnetization in matter at ordinary density. A small Boltzmann distribution population imbalance is multiplied by a very large number of nuclei. For noninteracting spin one-half nuclei of number density $n$ and positive $\gamma$, their equilibrium magnetization isThis follows by weighting the two projections $\pm \gamma \hslash /2$ with their Boltzmann distribution probabilities. It explains both the smallness of the bulk polarization at ordinary temperature and the value of many nuclei contributing to one receiving circuit.

NMR spectroscopy measures resonant responses of atomic nuclei to applied electromagnetic radiation in a magnetic field. In residual-group monitoring of polyurethane formation, distinguishable signal integrals supply a relative residual-group readout; overlap or very weak signals can limit that inference.

A particle beam is a directed stream of particles prepared for transport, interaction or detection. A molecular beam can contain neutral chemical atoms or molecules; an accelerator beam can contain charged electrons, protons or ions. Its direction, energy spread, spatial distribution and particle flux describe different aspects of the preparation.

A source, direction-selecting apertures or focusing elements, a transport region and a detector perform separate tasks. For a charged beam, electric fields can change its energy and magnetic fields can bend its trajectory through the Lorentz force. A neutral atomic beam requires interactions appropriate to its neutral constituents. A vacuum reduces unwanted collisions along either transport path, but it does not itself make every particle's speed equal.

A laboratory vacuum is a region with substantially reduced gas pressure, rather than an experimentally perfect absence of matter. Lowering the number density increases the mean free path, allowing a molecular beam to travel with fewer collisions. In molecular flow, the mean free path exceeds the apparatus dimensions, so wall encounters dominate.

A vacuum pump competes with leaks and outgassing. For an isothermal vessel of volume $V$, constant gas load $Q$ in pressure-volume per unit time, and effective pumping speed $S$, gas balance givesThis ideal model predicts a pump-down time constant $V/S$ and a limiting pressure $Q/S$. A restricted connecting pipe reduces the effective pumping speed; a larger pump alone need not fix it. Measuring the pressure transient tests the model, while deviations can reveal changing outgassing or pumping speed.^[ref]