Forbidden mechanism
Encyclopedia
In physics
, a forbidden mechanism or forbidden line is a spectral line
emitted by atom
s undergoing nominally "forbidden" energy transitions not normally allowed by the selection rules of quantum mechanics
. In formal physics, this means that the process cannot proceed via the most efficient (electric dipole) route. Although the transitions are nominally "forbidden", there is a small probability of their spontaneous occurrence, should an atom
or molecule
be raised to an excited state. More precisely, there is a certain probability that such an excited atom will make a forbidden transition to a lower energy state per unit time; by definition this probability is much lower than that for
any transition permitted by the selection rules. Therefore, if a state can de-excite via a permitted transition (or otherwise, e.g. via collisions) it will almost certainly do so rather than choosing the forbidden route. Nevertheless, "forbidden" transitions are only relatively unlikely: states that can only decay in this way (so-called meta-stable
states) usually have lifetimes of order milliseconds to seconds, compared to less than a microsecond for decay via permitted transitions.
and neodymium
make them useful as dopants for solid-state lasing media. In such media the atoms are held in a matrix which keeps them from de-exciting by collision, and the long half life of their excited states makes them easy to "optically pump" to create a large population of excited atoms. Neodymium doped glass derives its unusual coloration from "forbidden" f-f transitions within the neodymium atom, and is used in extremely high power solid state lasers.
gases and plasmas, either in outer space
or in the extreme upper atmosphere of the Earth
. Even the hardest laboratory vacuum
on Earth is still too dense for forbidden line emission to occur before atoms are collision
ally de-excited. However, in space environments, densities may be only a few atoms per cubic centimetre
, making atomic collisions unlikely. Under such conditions, once an atom or molecule has been excited for any reason into a meta-stable state, then it is almost certain to decay by emitting a forbidden-line photon. Since meta-stable states are rather common, forbidden transitions account for a significant percentage of the photons emitted by the ultra-low density gas in space.
Forbidden lines of nitrogen
([N II] at 654.8 and 658.4 nm), sulfur
([S II] at 671.6 and 673.1 nm), and oxygen
([O II] at 372.7 nm, and [O III] at 495.9 and 500.7 nm) are commonly observed in astrophysical plasmas. These lines are extremely important to the energy balance
of such things as planetary nebula
e and H II region
s. Also, the forbidden 21-cm hydrogen line
is of the utmost importance for radio astronomy as it allows very cold neutral hydrogen gas to be seen.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, a forbidden mechanism or forbidden line is a spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...
emitted by atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s undergoing nominally "forbidden" energy transitions not normally allowed by the selection rules of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. In formal physics, this means that the process cannot proceed via the most efficient (electric dipole) route. Although the transitions are nominally "forbidden", there is a small probability of their spontaneous occurrence, should an atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
or molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
be raised to an excited state. More precisely, there is a certain probability that such an excited atom will make a forbidden transition to a lower energy state per unit time; by definition this probability is much lower than that for
any transition permitted by the selection rules. Therefore, if a state can de-excite via a permitted transition (or otherwise, e.g. via collisions) it will almost certainly do so rather than choosing the forbidden route. Nevertheless, "forbidden" transitions are only relatively unlikely: states that can only decay in this way (so-called meta-stable
Metastability
Metastability describes the extended duration of certain equilibria acquired by complex systems when leaving their most stable state after an external action....
states) usually have lifetimes of order milliseconds to seconds, compared to less than a microsecond for decay via permitted transitions.
In solid-state physics
Forbidden transitions in rare earth atoms such as erbiumErbium
Erbium is a chemical element in the lanthanide series, with the symbol Er and atomic number 68. A silvery-white solid metal when artificially isolated, natural erbium is always found in chemical combination with other elements on Earth...
and neodymium
Neodymium
Neodymium is a chemical element with the symbol Nd and atomic number 60. It is a soft silvery metal that tarnishes in air. Neodymium was discovered in 1885 by the Austrian chemist Carl Auer von Welsbach. It is present in significant quantities in the ore minerals monazite and bastnäsite...
make them useful as dopants for solid-state lasing media. In such media the atoms are held in a matrix which keeps them from de-exciting by collision, and the long half life of their excited states makes them easy to "optically pump" to create a large population of excited atoms. Neodymium doped glass derives its unusual coloration from "forbidden" f-f transitions within the neodymium atom, and is used in extremely high power solid state lasers.
In astrophysics
Forbidden emission lines have only been observed in extremely low-densityDensity
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
gases and plasmas, either in outer space
Outer space
Outer space is the void that exists between celestial bodies, including the Earth. It is not completely empty, but consists of a hard vacuum containing a low density of particles: predominantly a plasma of hydrogen and helium, as well as electromagnetic radiation, magnetic fields, and neutrinos....
or in the extreme upper atmosphere of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
. Even the hardest laboratory vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
on Earth is still too dense for forbidden line emission to occur before atoms are collision
Collision
A collision is an isolated event which two or more moving bodies exert forces on each other for a relatively short time.Although the most common colloquial use of the word "collision" refers to accidents in which two or more objects collide, the scientific use of the word "collision" implies...
ally de-excited. However, in space environments, densities may be only a few atoms per cubic centimetre
Cubic centimetre
A cubic centimetre is a commonly used unit of volume extending the derived SI-unit cubic metre, and corresponds to the volume of a cube measuring 1 cm × 1 cm × 1 cm...
, making atomic collisions unlikely. Under such conditions, once an atom or molecule has been excited for any reason into a meta-stable state, then it is almost certain to decay by emitting a forbidden-line photon. Since meta-stable states are rather common, forbidden transitions account for a significant percentage of the photons emitted by the ultra-low density gas in space.
Notation
Forbidden line transitions are noted by placing square brackets around the atomic or molecular species in question, e.g. [O III] or [S II].Forbidden lines of nitrogen
Nitrogen
Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...
([N II] at 654.8 and 658.4 nm), sulfur
Sulfur
Sulfur or sulphur is the chemical element with atomic number 16. In the periodic table it is represented by the symbol S. It is an abundant, multivalent non-metal. Under normal conditions, sulfur atoms form cyclic octatomic molecules with chemical formula S8. Elemental sulfur is a bright yellow...
([S II] at 671.6 and 673.1 nm), and oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
([O II] at 372.7 nm, and [O III] at 495.9 and 500.7 nm) are commonly observed in astrophysical plasmas. These lines are extremely important to the energy balance
Energy balance
Energy balance may refer to:* First law of thermodynamics, according to which energy cannot be created or destroyed, only modified in form* Energy balance , a measurement of the biological homeostasis of energy in living systems...
of such things as planetary nebula
Planetary nebula
A planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas ejected during the asymptotic giant branch phase of certain types of stars late in their life...
e and H II region
H II region
An H II region is a large, low-density cloud of partially ionized gas in which star formation has recently taken place. The short-lived, blue stars forged in these regions emit copious amounts of ultraviolet light, ionizing the surrounding gas...
s. Also, the forbidden 21-cm hydrogen line
Hydrogen line
The hydrogen line, 21 centimeter line or HI line refers to the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation is at the precise frequency of 1420.40575177 MHz, which is equivalent to the vacuum...
is of the utmost importance for radio astronomy as it allows very cold neutral hydrogen gas to be seen.