### Spectral line profiles

In reality the spectral line under the influence of external conditions is broadened near its centre and can be represented in the form of a distribution curve shown in Fig.1.A distinction must be made berween the broadening of spectral lines under the influence of the Doppler effect (*Doppler broadening*) and the broadening due to collision of particles (

*Lorentz broadening*). The first type of broadening is dominant at low pressures, for example, in the upper terrestial atmosphere, the second one at a higher but not very high pressure. The half-width of the spectral lines

*is equal to the half of its width at half of maximum, as shown in Fig. 1.*

**α(ij)**Fig. 1. Definition of half-width ** α^{(ij)}** in the line shape

**.**

*Φ(ω*^{(ij)}- ω)

The *Doppler profile* on *Doppler broadening* is represented by a Gaussian

*, (1)*

**Φ**_{G}(WN^{j}, WN) = sqrt(ln2/π) exp(-ln2 · ((WN^{j}- WN)/D^{j})^{2})/D^{j }where * WN^{j }*is the position of

*(*

**j**th line*ω*on Fig. 1),

^{(ij)}*- the current point on wavenumber axis,*

**WN***-is a Doppler width for the*

**D**^{j}

*j**th*spectral line

*, (2)*

**D**^{J}= sqrt(2·ln2·N_{A}·k·T/m) · WN^{j}/ c

where** k** is the Boltzmann constant,

**is temperature (К),**

*T**- the speed of light,*

**c***is the molar mass of the isotopologue in grams and*

**m***is the Avogadro constant.*

**N**_{A}

The *Lorentz profile* can be represented as

** Φ_{L}(WN^{j}, WN) = π^{-1} · L^{j} / ((WN^{j} - WN)^{2} +( L^{j})^{2})** , (3)

where

*is the position of*

**WN**^{j }*(*

**j**th line*ω*on Fig. 1),

^{(ij)}*- the current point on wavenumber axis,*

**WN***-is a Lorentz width for the*

**L**^{j}

*j**th*spectral line. The values of the Lorentz half-width at

*and*

**T**_{ref}*of appropriate*

**P**_{ref}*data source*are represented in the database. In

*values of*

**TheoReTS***and*

**L**_{env}*should be typed by a user in the*

**L**_{self}*form.*

**Launch simulation**

When there is simultaneous statistically independed effects of Doppler and Lorentz types of broadening, the profile of spectral line is a convolution of Doppler and Lorentz profile - a *Voigt profile*.

*Φ _{V}(WN^{j}, WN) = ∫ *

**Φ**_{G}(WN^{j}, WN-x)

*·**. (4)*

**Φ**_{L}(WN^{j}, x) dxMore sophisticated line shape functions are now being applied for for building of line profiles but they are not used in the system for a while.