Definitions

# Spectral line

A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies.

Spectral lines are the result of interaction between a quantum system (usually atoms, but sometimes molecules or atomic nuclei) and single photons. When a photon has about the right amount of energy to allow a change in the energy state of the system (in the case of an atom this is usually an electron changing orbitals), the photon is absorbed. Then it will be slowly re-emitted, either in the same frequency as the original or in a cascade, where the sum of the energies of the photons emitted will be very different from the energy of the one absorbed. The direction of the new photons will be related to the direction of travel of the original photon.

Depending on the type of gas, the photon source and the observer, either an emission line or an absorption line will be produced. If the gas is between the photon source and the observer, a decrease in the intensity of light in the frequency of the incident photon will be seen, as the reemitted photons will mostly be in directions similar from the original one. This will be an absorption line. If the observer sees the gas, but not the original photon source, then the observer will not see the photons reemitted in a narrow frequency range. This will be an emission line.

Absorption and emission lines are highly atom-specific, and can be used to easily identify the chemical composition of any medium capable of letting light pass through it (typically gas is used). Several elements were discovered by spectroscopic means -- helium, thallium, cerium, etc. Spectral lines also depend on the physical conditions of the gas, so they are widely used to determine the chemical composition of stars and other celestial bodies that cannot be analyzed by other means, as well as their physical conditions.

Isomer shift is the displacement of an absorption line due to the absorbing nuclei having different s-electron densities from that of the emitting nuclei.

Mechanisms other than atom-photon interaction can produce spectral lines. Depending on the exact physical interaction (with molecules, single particles, etc.) the frequency of the involved photons will vary widely, and lines can be observed across all the electromagnetic spectrum, from radio waves to gamma rays.

## Spectral line broadening and shift

A spectral line extends over a range of frequencies, not a single frequency (i.e., it has a nonzero linewidth). In addition its center may be shifted from its nominal central wavelength. There are several reasons for this broadening and shift. These reasons may be divided into two broad categories - broadening due to local conditions and broadening due to extended conditions. Broadening due to local conditions is due to effects which hold in a small region around the emitting element, usually small enough to assure local thermodynamic equilibrium. Broadening due to extended conditions may result from changes to the spectral distribution of the radiation as it traverses its path to the observer. It also may result from the combining of radiation from a number of regions which are far from each other.

### Broadening due to local effects

• Natural broadening: The Energy-Time Uncertainty Principle relates the lifetime of an excited state with the precision of its energy, so the same excited level will have slightly different energies in different atoms. This broadening effect is described by a Lorentzian profile and there is no associated shift. Due to the uncertainty principle, natural broadening can be experimentally altered only to the extent that decay rates can be artificially suppressed or enhanced.
• Thermal Doppler broadening: The atoms in a gas which are emitting radiation will have a distribution of velocities. Each photon emitted will be red or blue shifted by the Doppler effect depending on the velocity of the atom relative to the observer. The higher the temperature of the gas, the wider the distribution of velocities in the gas. Since the spectral line is the combination of all of the emitted radiation, the higher the temperature of the gas, the broader will be the spectral line emitted from that gas. This broadening effect is described by a Doppler profile and there is no associated shift.
• Pressure broadening: the presence of nearby particles will affect the radiation emitted by an individual particle. There are two limiting cases by which this occurs:

*Impact pressure broadening: The collision of other particles with the emitting particle interrupts the emission process. The duration of the collision is much shorter than the lifetime of the emission process. This effect depends on both the density and the temperature of the gas. The broadening effect is described by a Lorentzian profile and there may be an associated shift.
*Quasistatic pressure broadening: The presence of other particles shifts the energy levels in the emitting particle, thereby altering the frequency of the emitted radiation. The duration of the influence is much longer than the lifetime of the emission process. This effect depends on the density of the gas, but is rather insensitive to temperature. The form of the line profile is determined by the functional form of the perturbing force with respect to distance from the perturbing particle. There may also be a shift in the line center. The Lévy skew alpha-stable distribution has been found to be a useful generalization describing a quasistatic line profile. (Peach, 1981 § 4.5).
Pressure broadening may also be classified by the nature of the perturbing force as follows:
*Linear Stark broadening occurs via the linear Stark effect which results from the interaction of an emitter with an electric field, which causes a shift in energy which is linear in the field strength. ($Delta E sim 1/r^2$)
*Resonance broadening occurs when the perturbing particle is of the same type as the emitting particle, which introduces the possibility of an energy exchange process. This broadening effect is described by a Lorentzian profile in both the impact and the quasistatic case. ($Delta E sim 1/r^3$)
*Quadratic Stark broadening occurs via the quadratic Stark effect which results from the interaction of an emitter with an electric field, which causes a shift in energy which is quadratic in the field strength. ($Delta E sim 1/r^4$)
*Van der Waals broadening occurs when the emitting particle is being perturbed by Van der Waals forces. For the quasistatic case, a Van der Waals profile is often useful in describing the profile. The energy shift as a function of distance is given in the wings by e.g. the Lennard-Jones potential ($Delta E sim 1/r^6$)

### Broadening due to non-local effects

Certain types of broadening are the result of conditions over a large region of space rather than simply upon conditions that are local to the emitting particle.

• Opacity broadening: Electromagnetic radiation emitted at a particular point in space can be absorbed as it travels through space. This absorption depends on wavelength. The line is broadened because photons at the line wings have a smaller reabsorption probability than photons at the line center. Indeed, the absorption near line center may be so great as to cause a self reversal in which the intensity at the center of the line is less than in the wings.
• Rotational broadening: Radiation emitted from a distant rotating body, such as a star, will be subject to a doppler shift due to the line-of-sight variations in velocity on opposite sides of the star. The greater the rate of rotation, the broader the line.

### Combined effects

Any of these mechanisms can act in isolation or in combination. Assuming each effect is independent of the other, the combined line profile will be the convolution of the line profiles of each mechanism. For example, a combination of thermal Doppler broadening and impact pressure broadening will yield a Voigt profile.