Doppler broadening effect

The second perturbation, namely the thermal motion of emitter nuclei, produce a Doppler-effect broadening of the emission line and causes it to extend in part beyond the energy Eq even though centered at Ey (= Eq—Er). The y-ray energy will be broadened into a distribution by the Doppler-effect energy, E = MvV, which is proportional to the initial velocity, Vx. from the random thermal motion of the atom, and v from the recoil of the nucleus. 

In heavy-particle collisions it is often not the resolving power of the electron spectrometer that limits the accuracy with which structures in ejected electron spectra can be measured, but the Doppler effect broaden-ings and shifts of the electron peaks severely influence the spectra and have to be taken into account in the analysis, or to be avoided by special means in the experimental setup. Since electron spectra due to heavy-particle collisions are treated in some detail in the following sections, we will briefly discuss the various kinematical effects. 

The Doppler effect broadens absorption or emission lines from atoms in the gas phase at thermal equilibrium. Assume that an atom at rest is excited by a photon with wave vector k and de-excited to emit light with angular frequency coq. If the atom is moving at a velocity v the angular frequency of the emitted light is shifted to a value coq according to the formula,... 

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. 

The spectral linewidths of fluorescence lines are determined in most spectral lamps by Doppler effect and pressure broadening and are therefore normally much broader than the natural linewidth, which is approached only by low-pressure hollow cathode lamps 23) operated at liquid helium temperatures. 

Experimental details for the cross-section measurements were presented in the literature. Briefly, after the irradiation by electron beam pulse for a few nanoseconds, the time-dependent absorption for the atomic line transition Rg Rg -i-/zv was measured to observe the time-dependent population of the excited rare gas atoms Rg. The population of excited Rg was determined using an absorption law for the atomic lines, where the broadening of the absorption profile due to the thermal Doppler effect and due to the attractive interatomic potentials was reasonably taken into consideration. The time-dependent optical emission from energy transfer products, such as ... 

These line shapes are generally not very useful for collision-induced absorption work, because pressure broadening, Doppler effect and instrumental resolution are here of no great concern. In Chapters 5 and 6 we will consider a number of other ad hoc model functions that have acquired a certain significance in collision-induced absorption. 

Linewidth is also affected by pressure broadening from collisions between atoms. Collisions shorten the lifetime of the excited state. The uncertainty in the frequency of atomic absorption and emission lines is roughly numerically equal to the collision frequency between atoms and is proportional to pressure. The Doppler effect and pressure broadening are similar in magnitude and yield linewidths of 10-3 to I0-2 nm in atomic spectroscopy. 

Doppler and pressure effects broaden the atomic lines by one to two orders of magnitude relative to their inherent linewidths. 

Explain what is meant by the Doppler effect. Rationalize why Doppler broadening increases with increasing temperature and decreasing mass in Equation 21-5. 

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. 

To observe a 7s — 9 transition requires that there be a 9p admixture in the 9 state. For odd this admixture is provided by the diamagnetic interaction alone, which couples states of and 2, as described in Chapter 9. For even states the diamagnetic coupling spreads the 9p state to all the odd 9( states and the motional Stark effect mixes states of even and odd (. Due to the random velocities of the He atoms, the motional Stark effect and the Doppler effect also broaden the transitions. Together these two effects produce asymmetric lines for the transitions to the odd 9t states, and double peaked lines for the transitions to even 9( states. The difference between the lineshapes of transitions to the even and odd 9i states comes from the fact that the motional Stark shift enters the transitions to the odd 9( states once, in the frequency shift. However, it enters the transitions to the even 9( states twice, once in the frequency shift and once in the transition matrix element. Although peculiar, the line shapes of the observed transitions can be analyzed well enough to determine the energies of the 9( states of >2 quite accurately.25... 

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 thermal motion of the atoms in the source volume leads to a broadening of the observed line, because the thermal velocity vth of the electron-emitting atom is added to the electron velocity v0. For an estimation of the resulting disturbance by this kinematical effect it is sufficient to select for the thermal velocity the two directions at which the Doppler effect becomes extreme, i.e.,... 

If the sample moves toward or away from the detector at speed V, then the linewidth of an absorption or emission at wavelength 10 is broadened by Doppler effect ... 

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... 

Another effect is due to the vibration of atoms in solids. At room temperature, this vibration leads to a Doppler effect and line broadening of the order of D x 10 eV. 

Figure 10.2. Absorption of y-ray photons by free atoms E = excitation energy E = recoil energy D = line broadening by the Doppler effect.

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