Line Shapes and Radiation Transfer

Abstract

The shapes of collisionally broadened atomic lines is a topic almost as old as Fraunhofer's discovery of the existence of discrete lines. Lorentz provided the first quantitative theory in 1906 1, and Weisskopf advanced this to the impact theory by 1933 2. Holtsmark 3, Kuhn 4 and Margenau 5 meanwhile developed the quasistatic or statistical theory which describes the line wing, and Jablonski put this on a quantum mechanical footing in the context of free–free molecular radiation 6 ; 7. By the 1940s, satellite bands in the line wings, and a variety of high and low pressure line shapes and broadening rates had been measured. Initial confusion regarding the validity of the contrasting impact versus static approaches was largely resolved by unified treatments of the Fourier integral theory 8 ; 9 ; 10 ; 11 ; 12 ; 13. Baranger then provided a quantum basis for the impact theory, including level degeneracies 14. Descriptions can be found in a variety of reviews and references therein, including 2 ; 5 ; 15 ; 16 ; 17 ; 18 ; 19 ; 20. The broadening of molecular lines involves the additional complication of rotationally nonadiabatic collisions; this was initially addressed by Anderson 12 ; 13 and later with great thoroughness by van Kranendonk 21. This chapter and most of the above theories are concerned with neutral atomic gases, which is sometimes called pressure broadening. In plasmas, electron, ion, and neutral collisions all contribute to the line shapes and strengths; thus the emitted lines provide a powerful diagnostic of plasma conditions. Neither molecular nor plasma broadening will be covered here; the latter is reviewed in 17 ; 18 ; 19 ; 20 ; 22, and in Chaps. 51 and 63.line broadeningpressure broadeningline broadeningpressure