Pressure broadening, of spectral lines

Taking advantage of advances in computational atomic and plasma physics and of the availability of powerful supercomputers, a collaborative effort - the international Opacity Project - has been made to compute accurate atomic data required for opacity calculations. The work includes computation of energy levels, oscillator strengths, photoionization cross-sections and parameters for pressure broadening of spectral lines. Several... 

Such beams have many uses, including some important applications in spectroscopy. In particular, pressure broadening of spectral lines is removed in an effusive beam and, if observations are made perpendicular to the direction of the beam, Doppler broadening is considerably reduced because the velocity component in the direction of observation is very small. 

E. Lindholm Pressure broadening of spectral lines. Ark. Mat. Astron. Fys. 32A,... 

This article reviews the basic theory of the pressure broadening of spectral lines. 

Lamb dip spectroscopy provides a very sensitive tool for studying small frequency shifts and broadening of spectral lines which normally would be undetectable because they may be small compared to the doppler width. These investigations yield information about collisions at low pressures, where the effect of far distant collisions is not suppressed by the more effective close collisions. This allows the potential between the collision partners at large intermolecular distances to be examined. 

To consider gas molecules as isolated from interactions with their neighbors is often a useless approximation. When the gas has finite pressure, the molecules do in fact collide. When natural and collision broadening effects are combined, the line shape that results is also a lorentzian, but with a modified half-width at half maximum (HWHM). Twice the reciprocal of the mean time between collisions must be added to the sum of the natural lifetime reciprocals to obtain the new half-width. We may summarize by writing the probability per unit frequency of a transition at a frequency v for the combined natural and collision broadening of spectral lines for a gas under pressure ... 

Multiplying this expression by n yields the Voigt function that occurs in the description of spectral-line shapes resulting from combined Doppler and pressure broadening. We elaborate on these phenomena in Section I of Chapter 2. 

Spectroscopists have always known certain phenomena that are caused by collisions. A well-known example of such a process is the pressure broadening of allowed spectral lines. Pressure broadened lines are, however, not normally considered to be collision-induced, certainly not to that extent to which a specific line intensity may be understood in terms of an individual atomic or molecular dipole transition moment. The definition of collisional induction as we use it here implies a dipole component that arises from the interaction of two or more atoms or molecules, leading at high enough gas density to discernible spectral line intensities in excess of the sum of the absorption of the atoms/molecules of the complex. In other... 

In order to measure an absorption cross section, it is necessary to have a source of tunable radiation (or spectrometer) that has a spectral resolution narrower than the width of the molecular line (natural and/or Doppler) being measured. Inadequate spectral resolution will yield a too small (lower bound) value of ° i- An effective strategy is to pressure broaden the molecular line so that it becomes broader than the instrumental resolution (see Stark, et al., 1992 and Murray, et al., 1994). 

Figure 5-31. Vibrational temperature of CO2 molecules in plasma-ehemieal mierowave discharge as function of pressure. Measurements based on Doppler broadening of speetral lines of (1) lithium and (2) sodium stars indieate infra-red spectral measurement.

There is a second effect that causes a collisional narrowing of spectral lines. In the case of very long lifetimes of levels connected by an EM transition, the linewidth is determined by the diffusion time of the atoms out of the laser beam (Sect. 3.4). Inserting a noble gas into the sample cell decreases the diffusion rate and therefore increases the interaction time of the sample atoms with the laser field, which results in a decrease of the linewidth with pressure [3.36] until the pressure broadening overcompensates the narrowing effect. 

It is important to realize that the relaxation times might depend on some factors that are properties of the atom or molecule itself and on others that are related to its environment. Thus rotational spectra of gases have linewidths (related to the rotational relaxation times) that depend on the mean times between coUisions for the molecules, which in turn depend on the gas pressure. In liquids, the collision lifetimes are much shorter, and so rotational energy is effectively non-quantized. On the other hand, if the probability of collisions is reduced, as in a molecular beam, we can increase the relaxation time, reduce linewidths, and so improve resolution. Of course, the relaxation time only defines a minimum width of spectral lines, which may be broadened by other experimental factors. 

Whereas the resolution in linear Raman spectroscopy is limited in principle by the slit width of the spectrometer, a considerable improvement in the instrumental resolution was attained through the development of the techniques of nonlinear or coherent Raman spectroscopy, where the interaction of two laser beams with the third-order susceptibility of the sample creates the spectrum. In this case, the resolution is determined by the convoluted linewidth of the two lasers, the Doppler effect, and pressure broadening of the spectral lines. 

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