Spectroscopy

The distribution of emitted radiation with wavelength or frequency. Resolved atomic spectral lines correspond to transitions between energy levels; a source's excitation and optical depth affect the observed intensities.

Identification of constituents from characteristic emission lines or absorption lines in a resolved spectrum. Historical prism instruments used a narrow slit, collimator, prism and observing telescope.

The wavelength- or frequency-dependent absorption of a specified specimen. Composition, optical path length, concentration, linewidths and illumination determine its transmitted colour; a single band gap does not specify that colour.

Dark absorption features in the solar spectrum, mapped and labelled by Joseph von Fraunhofer. They give reproducible wavelength landmarks for spectroscopy and optical measurements. Solar and terrestrial absorbers contribute different features to a ground-observed solar spectrum.

A coherent second-order optical method generating light at the sum of two incident frequencies. Its electric-dipole response is sensitive to broken inversion symmetry and molecular orientation at interfaces.

electron paramagnetic resonance measures resonant transitions involving unpaired electron magnetic moments. A spin label attached to a protein or lipid can report local motion or distances under appropriately designed pulse experiments.

For $H=D{S}_z^2+g{\mu }_{B}B{S}_z$ with $D>0$ and a transverse oscillating field, the allowed gaps are $g{\mu }_{B}B$, $|g{\mu }_{B}B-2D|$ and $g{\mu }_{B}B+2D$. Below $h\nu =2D$, the positive-field solutions are $h\nu$, $2D-h\nu$ and $2D+h\nu$ in units of $g{\mu }_{B}B$. At $h\nu =D$ two transitions coincide, leaving two distinct resonance fields. At $h\nu =2D$ a zero-field resonance must be counted separately.

Inverse photoemission spectroscopy injects an electron of known kinetic energy into a sample and detects the photon emitted as it enters an unoccupied electronic state. Conservation of energy, together with incident-angle information and an appropriate surface model, probes the unoccupied electronic band structure. Ordinary angle-resolved photoemission spectroscopy instead removes electrons from occupied states.

Energy resolution specifies the characteristic energy separation or broadening that an instrument can distinguish, with a stated width convention and measurement geometry. Resolving a phonon in inelastic scattering requires measuring a small energy transfer as well as momentum transfer. It is distinct from the incident beam's central energy.

Comparison of an observed spectrum with a shifted template or line mask as a function of trial Doppler velocity. The fitted correlation centre combines the position information from many spectral lines; its sign convention can produce a peak or a dip.

Assigning wavelengths to detector positions using reference features, so a change in a spectral-line position can be interpreted as a physical wavelength shift.

The wavelength-dependent distribution of sunlight, including absorption lines used to investigate the solar atmosphere.

An isotope shift is a difference between corresponding atomic transition frequencies in different isotopes. One contribution comes from nuclear mass, through recoil and electron correlations; another comes from the changing nuclear charge distribution. For a specified transition, the leading finite-size contribution is often written $\delta {\nu }_{\mathrm{field}}=F\delta ⟨r^2⟩$, with an electronic factor $F$. Extracting changes of nuclear charge radius therefore requires separating mass and finite-size contributions rather than identifying the entire shift with radius.

Spectroscopy based on the energy distribution of electrons, including photoemission spectroscopy.

Elemental analysis using Characteristic X-rays, commonly excited by an electron beam.

Measurement of the energy lost by transmitted electrons to electronic, vibrational or other excitations.

Fine structure near a core-loss edge that reflects unoccupied electronic states and local bonding.

Spectroscopy using X-rays, including X-ray emission spectroscopy.

Oscillatory absorption above a core-ionization edge caused by interference between outgoing and neighbor-scattered photoelectron waves. It probes local coordination, distances and disorder. The high-energy shell expansion is distinct from the more complicated near-edge regime; phase corrections are required before interpreting Fourier-transform peaks as bond lengths.

The bond-direction variance of relative atomic displacement. A Gaussian distance distribution damps the coherent round-trip phase by $e^{-2k^2{\sigma }^2}$. Correlated atomic motion and static bond disorder contribute, so this is not generally a single atom's mean-square displacement about its lattice site.

An absorption spectrum close to a core-level ionization threshold. Polarization-dependent core-to-unoccupied-state transitions probe orbital orientation and adsorbate geometry.

Variation of absorption with incident electric-field direction. For a localized $1s\to {\pi }^{\ast }$ transition the dipole matrix element is proportional to the component of the field along the pi-orbital normal.

For a diatomic molecular axis $\mathbf{n}$ and unit electric-field polarization $\mathbf{e}$, the axial and summed two transverse dipole transition directions have the displayed geometrical factors. Radial matrix elements differ between resonances. If axes have polar tilt $\beta$ and random azimuth, with electric-field angle $\alpha$ to the surface normal, the mean axial factor is ${\cos }^2\beta {\cos }^2\alpha +\frac{1}{2}{\sin }^2\beta {\sin }^2\alpha$. Polarization-dependent near-edge absorption therefore constrains an orientation distribution, subject to substrate hybridization and instrumental normalization.