Editing Spectral line (section)

== Line broadening and shift ==
There are a number of effects which control [[spectral line shape]]. A spectral line extends over a tiny [[spectral band]] with a nonzero range of frequencies, not a single frequency (i.e., a nonzero [[spectral width]]). 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 general 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 lifetime of excited states results in natural broadening, also known as lifetime broadening. The [[uncertainty principle]] relates the lifetime of an excited state (due to [[Spontaneous emission|spontaneous radiative decay]] or the [[Auger effect|Auger process]]) with the uncertainty of its energy. 
Some authors use the term "radiative broadening" to refer specifically to the part of natural broadening caused by the spontaneous radiative decay.<ref>{{Cite book| publisher = Wiley| isbn = 978-0-471-12533-4| last1 = Krainov| first1 = Vladimir| last2 = Reiss| first2 = Howard| last3 = Smirnov| first3 = Boris| title = Radiative Processes in Atomic Physics| date = 1997| doi = 10.1002/3527605606}}</ref>
A short lifetime will have a large energy uncertainty and a broad emission. This broadening effect results in an unshifted [[Lorentzian function|Lorentzian profile]]. The natural broadening can be experimentally altered only to the extent that decay rates can be artificially suppressed or enhanced.<ref>For example, in the following article, decay was suppressed via a microwave cavity, thus reducing the natural broadening: {{cite journal|last=Gabrielse|first=Gerald|author2=H. Dehmelt |title=Observation of Inhibited Spontaneous Emission|journal=Physical Review Letters|volume=55|pages=67–70|year=1985|doi=10.1103/PhysRevLett.55.67|pmid=10031682|issue=1|bibcode=1985PhRvL..55...67G}}</ref>

==== Thermal Doppler broadening ====
{{Main|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 a combination of all of the emitted radiation, the higher the temperature of the gas, the broader the spectral line emitted from that gas. This broadening effect is described by a [[Gaussian function|Gaussian 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'' or ''collisional broadening'': The collision of other particles with the light emitting particle interrupts the emission process, and by shortening the characteristic time for the process, increases the uncertainty in the energy emitted (as occurs in natural broadening).<ref>{{cite web|url=http://www.fas.harvard.edu/~scdiroff/lds/QuantumRelativity/CollisionalBroadening/CollisionalBroadening.html |title=Collisional Broadening |publisher=Fas.harvard.edu |archive-url=https://web.archive.org/web/20150924042746/http://www.fas.harvard.edu/~scdiroff/lds/QuantumRelativity/CollisionalBroadening/CollisionalBroadening.html |access-date=2015-09-24|archive-date=2015-09-24 }}</ref><!--<ref>{{cite web|url=http://www.fas.harvard.edu/~scdiroff/lds/QuantumRelativity/CollisionalBroadening/CollisionalBroadening.html |title=Collisional Broadening |publisher=Fas.harvard.edu |access-date=2015-05-02}}</ref>--> 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 function|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 (see [[spectral band]]), 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 general expression for the lineshape resulting from quasistatic pressure broadening is a 4-parameter generalization of the Gaussian distribution known as a [[stable distribution]].<ref>{{cite journal | first = G. | last = Peach | year = 1981 | title = Theory of the pressure broadening and shift of spectral lines | journal = Advances in Physics | volume = 30 | issue = 3 | pages = 367–474 | url = http://journalsonline.tandf.co.uk/openurl.asp?genre=article&eissn=1460-6976&volume=30&issue=3&spage=367 | archive-url = https://archive.today/20130114060003/http://journalsonline.tandf.co.uk/openurl.asp?genre=article&eissn=1460-6976&volume=30&issue=3&spage=367 | url-status = dead | archive-date = 2013-01-14 | doi = 10.1080/00018738100101467 | bibcode = 1981AdPhy..30..367P | access-date = 2005-12-09 | url-access = subscription }}</ref>

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 of a charged particle at a distance <math>r</math>, causing a shift in energy that is linear in the field strength. <math>(\Delta E \sim 1/r^2)</math>
* ''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. <math>(\Delta E \sim 1/r^3)</math>
* ''Quadratic Stark broadening'' occurs via the [[quadratic Stark effect]], which results from the interaction of an emitter with an electric field, causing a shift in energy that is quadratic in the field strength. <math>(\Delta E \sim 1/r^4)</math>
* ''Van der Waals broadening'' occurs when the emitting particle is being perturbed by [[Van der Waals force]]s. For the quasistatic case, a [[Lévy distribution|Van der Waals profile]]<ref group="note">"Van der Waals profile" appears as lowercase in almost all sources, such as: [https://books.google.com/books?id=Wve2AAAAIAAJ&q=%22Van+der+Waals+profile%22&dq=%22Van+der+Waals+profile%22&hl=en Statistical mechanics of the liquid surface] by Clive Anthony Croxton, 1980, A Wiley-Interscience publication, {{ISBN|0-471-27663-4}}, {{ISBN|978-0-471-27663-0}}; and in [https://books.google.com/books?id=2XpVAAAAMAAJ&q=%22Van+der+Waals+profile%22&dq=%22Van+der+Waals+profile%22&hl=en Journal of technical physics], Volume 36, by Instytut Podstawowych Problemów Techniki (Polska Akademia Nauk), publisher: Państwowe Wydawn. Naukowe., 1995,<!-- and many more --></ref> is often useful in describing the profile. The energy shift as a function of distance between the interacting particles is given in the wings by e.g. the [[Lennard-Jones potential]]. <math>(\Delta E \sim 1/r^6)</math>

==== Inhomogeneous broadening ====
''[[Inhomogeneous broadening]]'' is a general term for broadening because some emitting particles are in a different local environment from others, and therefore emit at a different frequency. This term is used especially for solids, where surfaces, grain boundaries, and stoichiometry variations can create a variety of local environments for a given atom to occupy. In liquids, the effects of inhomogeneous broadening is sometimes reduced by a process called ''[[motional narrowing]]''.

=== 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 ====
Opacity broadening is an example of a non-local broadening mechanism. Electromagnetic radiation emitted at a particular point in space can be reabsorbed as it travels through space. This absorption depends on wavelength. The line is broadened because the photons at the line center have a greater reabsorption probability than the photons at the line wings. Indeed, the reabsorption near the 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. This process is also sometimes called '''self-absorption'''.

==== Macroscopic Doppler broadening ====
Radiation emitted by a moving source is subject to [[Doppler shift]] due to a finite line-of-sight velocity projection. If different parts of the emitting body have different velocities (along the line of sight), the resulting line will be broadened, with the line width proportional to the width of the velocity distribution. For example, radiation emitted from a distant rotating body, such as a [[star]], will be broadened due to the line-of-sight variations in velocity on opposite sides of the star (this effect usually referred to as rotational broadening). The greater the rate of rotation, the broader the line. Another example is an imploding [[Plasma (physics)|plasma]] shell in a [[Z-pinch]].

=== Combined effects ===
Each of these mechanisms can act in isolation or in combination with others. Assuming each effect is independent, the observed line profile is a convolution of the line profiles of each mechanism. For example, a combination of the thermal Doppler broadening and the impact pressure broadening yields a [[Voigt profile]].

However, the different line broadening mechanisms are not always independent. For example, the collisional effects and the motional Doppler shifts can act in a coherent manner, resulting under some conditions even in a collisional ''narrowing'', known as the [[Dicke effect]].