The Line Source Function

Abstract

In this chapter we shall have need of the following quantities and relationships in addition to those defined in Chapter I:

$$j > i$$

$${A_{ji}} = {\text{spontaneous transition probability}}$$

$${B_{ji}} = {\text{Induced transition coefficient}}$$

$${B_{ij}} = \frac{{{{\tilde \omega }_j}}}{{{{\tilde \omega }_i}}}{B_{ji}}$$

((II-1))

$${A_{ji}} = \frac{{2h{v^3}}}{{{c^2}}}{B_{ji}}$$

((II-2))

$${B_{ij}} = {\text{absorption coefficient}}$$

$${C_{ij}} = {\text{collisional transition probability from }}i{\text{ to }}j$$

$${R_{ij}} = {\text{combined transition probability from }}i{\text{ to }}j$$

$$\begin{array}{*{20}{c}} {{P_{{\text{ij}}}}}& = &{{{\tilde \omega }_i}{e^{ - {x_i}/kT}}{R_{ij}}} \\ {}& = &{{W_{\text{i}}}{R_{{\text{ij}}}}} \\ {{P_{{\text{ii}}}}}& = &{\sum\limits_{\text{j}} {{P_{{\text{ij}}}}} } \end{array}$$

((II-3))

$${\chi _{\text{i}}} = {\text{excitation energy}}$$

$${C_{{\text{ij}}}}{W_{\text{i}}} = {C_{{\text{ji}}}}{W_{\text{j}}}$$

ψ _ν = profile of A _ji normalized to unit area.