Widths Doppler effect

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

In order to dissipate the recoil energy Mossbauer was the first to use atoms in solid crystal lattices as emitters and also to cool both emitter and absorber. In this way it could be shown that the 7-ray emission from radioactive cobalt metal was absorbed by metallic iron. However, it was also found that if the iron sample were in any other chemical state, the different chemical surroundings of the iron nucleus produce a sufficient effect on the nuclear energy levels for absorption no longer to occur. To enable a search for the precisely required absorption frequency, a scan based on the Doppler effect was developed. It was noted that a velocity of 102 ms-1 produced an enormous Doppler shift and using the same equation (7) it follows that a readily attainable displacement of the source at a velocity of 1 cms-1 produces a shift of 108 Hz. This shift corresponds to about 100 line-widths and provides a reasonable scan width. 

The second factor involves the theory that defines the natural width of the lines. Radiations emitted by atoms are not totally monochromatic. With plasmas in particular, where the collision frequency is high (this greatly reduces the lifetime of the excited states), Heisenberg s uncertainty principle is fully operational (see Fig. 15.4). Moreover, elevated temperatures increase the speed of the atoms, enlarging line widths by the Doppler effect. The natural width of spectral lines at 6000 K is in the order of several picometres. 

Besides the uncertainty broadening just discussed, there are other causes of line broadening which make line widths generally considerably greater than the natural width (3.88). The Doppler effect causes an apparent change in radiation frequency for molecules with a component of velocity cobs in the direction of observation of the radiation. Different molecules have different values of cobs and we get a Doppler broadened line. 

In most optical excitations the resolution is determined by the Doppler effect or the finite linewidth of the light source. The Doppler effect gives a typical frequency width of 1 GHz, and the width of the light source can be anywhere from 1 kHz to 30 GHz. We assume that these widths are larger than the radiative width. The photoionization cross sections from the ground states of H, alkali, and the alkaline earth atoms are given in Table 3.3. 20... 

Absorption of electromagnetic radiation by monatomic gases leads either to production of atoms in excited states or, if the wavelength is short enough, to ionization. Absorption lines have widths which depend on the following factors1 (a) the temperature, i.e. there will be a Doppler effect which will broaden the line if the absorbing atoms are in motion (b) an intrinsic factor dependent on the nature of the electronic state and on the extent of perturbations by other states ... 

The limitation in the determination of the strong interaction width is mainly given by the Doppler effect caused by the so-called Coulomb deexcitation acceleration. 

The situation is more complicated in the applications of the statistical method to radiation phenomena. Some of the older attempts have not as yet yielded clear results. Among these are the connection of the interference limit for large path differences with the average time between collisions undergone by the center of emission,2,6 or the remark that, on account of the corresponding Doppler effect, the thermal motion of the sources of emission creates a lower limit for the width of fine spectral lines.218... 

Dynamic light scattering (DLS), also called photon correlation spectroscopy (PCS) or laser light scattering (LLS) is a technique based on the principle that moving objects cause a frequency shift due to the Doppler effect. If a solution of macromolecules with random Brownian motion is illuminated with monochromatic laser light, the scattered light should contain a distribution of frequencies about the incident frequency the spectral line is virtually broadened. The width of the distribution is related to the MMD. 

Since At is of the order of 10-8 s, it can be calculated that the natural line width is about (10 -s nm). In practice this natural line width is broadened by several effects. These include the Doppler effect caused by the motion of absorbing atoms in their environment (usually a flame). At any given instance... 

The line widths in vibrational spectroscopy are a function of the measuring conditions and of the state of the sample. The natural line width of about 10 cm is not usually re.solved. The Doppler effect at room temperature contributes 10 cm. The contribution due to impacts and intermolecular interactions for a gas at 1 mbar is 10 cm and for 1 bar it is 10 cm. The resulting line width in the spectra of crystals is of the order 1 - 5 cm and for a liquid it may reach 20 cm. ... 

The effect of atmospheric gas on the emission of an LIB plasma [146] exhibits selfabsorption in He compared to Ar as a result of increased free atom populations in the outer regions of the plasma. Spectral line widths do not correlate well with atmospheric gas. This rules out Doppler effects as a major source of broadening in the laser-induced plasma. The use of a low pressure (ca. 1 torr) to examine the influence of this variable on the shock wave or secondary plasma revealed an increased emission intensity, which confirmed the assumption that the secondary plasma was excited by the shock wave. 

The accuracy with which the wavenumber of the center of a symmetrical isolated line can be measured is of the line width. For a gas at a sufficiently low pressure so that pressure broadening is unimportant, the width of the line is determined by the Doppler effect and is... 

It is appropriate here to consider the spectroscopic conditions necessary for the investigation of Ha. The smallest interval in Fig. 2 is 0036 cm-"1, between components (l) and (4). Since the intensities of these components are unequal, their resolution would require a spectroscopic resolving power considerably in excess of 5 x IG5. This presents no difficulty with interference techniques a serious difficulty, however, is presented by the width of the components due to the Doppler effect. Other causes of line broadening are considerably less important,... 

Thus, the Doppler broadening is directly proportional to frequency of the line (v) and to the square root of the absolute temperature (T), and inversely proportional to the square root of the atomic mass (M). The Doppler effect accounts for most of the line width. 

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