The Inglis–Teller equation represents an approximate relationship between the

plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...

density and the principal quantum number of the highest bound state of an atom. The equation was derived by

David R. Inglis David Robert Inglis is a contemporary sociologist and academic. Education and career Inglis earned a bachelor's degree in sociology from the University of Cambridge and then went on to complete his Master's and PhD in sociology at the University ...

and Edward Teller in 1939. In a plasma, atomic levels are broadened and shifted due to the

Stark effect The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several compon ...

, caused by electric microfields formed by the charged plasma particles ( ions and electrons). The Stark broadening increases with the principal quantum number

n

, while the energy separation between the nearby levels

n

and

(n + 1)

decreases. Therefore, above a certain

n

all levels become merged. Assuming a neutral atomic radiator in a plasma consisting of singly charged ions (and neglecting the electrons), the equation reads :

N n^ = 0.027 a_0^\,,

where

N

is the ion particle density and

a_0

is the Bohr radius. The equation readily generalizes to cases of multiply charged plasma ions and/or charged radiator. Allowance for the effect of electrons is also possible, as was discussed already in the original study. Spectroscopically, this phenomenon appears as discrete spectral lines merging into

continuous spectrum In physics, a continuous spectrum usually means a set of attainable values for some physical quantity (such as energy or wavelength) that is best described as an interval of real numbers, as opposed to a discrete spectrum, a set of attainable ...

. Therefore, by using the (appropriately generalized) Inglis–Teller equation it is possible to infer the density of laboratory and astrophysical plasmas.

References

{{DEFAULTSORT:Inglis-Teller equation Spectroscopy Edward Teller 1939 in science