Width of spectral line

Paper [16] reported unusual behaviour of the widths of rotational components of the P-R doublet of HC1 dissolved in SFg. They decreased with increasing temperature. The widths of spectral lines, obtained with (7.73), really must decrease with increasing temperature, because tc decreases due to intensification of thermal motion, and V[ due to thermal expansion. 

Hydrogen is the most abundant chemical element in the universe, and in its various atomic and molecular forms furnishes a sensitive test of all of experimental, theoretical and computational methods. Vibration-rotational spectra of dihydrogen in six isotopic variants constituting all binary combinations of H, D and T have nevertheless been recorded in Raman scattering, in either spontaneous or coherent processes, and spectra of HD have been recorded in absorption. Despite the widely variable precision of these measurements, the quality of some data for small values of vibrational quantum number is still superior to that of data from electronic spectra [106], almost necessarily measured in the ultraviolet region with its concomitant large widths of spectral lines. After collecting 420... 

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. 

Each spectral line is characterized by an absorption coefficient kp which exhibits a maximum at some central characteristic wavelength or wave number r 0 = l/ o and is described by a Lorentz probability distribution. Since the widths of spectral lines are dependent on collisions with other molecules, the absorption coefficient will also depend upon the composition of the combustion gases and the total system pressure. This brief discussion of gas spectroscopy is intended as an introduction to the factors controlling absorption coefficients and thus the factors which govern the empirical correlations to be presented for gas emissivities and absorptivities. 

Atomic spectral lines have finite widths. With ordinary measuring spectrometers, the observed line widths are determined not by the atomic system but by the spee-trometer properties. With very-high-resolution spectrometers or with interferometers, the actual widths of spectral lines can be measured. Several factors contribute to atomic spectral line widths. 

Owing to the line broadening mechanisms, the physical widths of spectral lines in most radiation sources used in optical atomic spectrometry are between 1 and 20 pm. This applies both for atomic emission and atomic absorption line profiles. In reality the spectral bandwidth of dispersive spectrometers is much larger than the physical widths of the atomic spectral lines. 

Many absorption experiments on impurities and defects are performed at low temperature or as a function of temperature, especially for the observation of discrete spectra. This is a necessity when the population of the ground state level of a transition or of a series of transitions is thermalized at room temperature. Another reason for using low temperatures is the decrease of the widths of spectral lines with temperature due to the reduced coupling of the levels with lattice phonons. The samples have to be, therefore, cooled in optical cryostats. 

D15.6 The ESR spectra of a spin probe, such as the di-terr-butyl nitroxide radical, broadens with restricted motion of the probe. This suggests that the width of spectral lines may correlate with the depth to which a probe may enter into a biopolymer crevice. Deep crevices are expected to severely restrict probe motion and broaden the spectral lines. Additionally, the splitting and center of ESR spectra of an oriented sample can provide information about the shape of the biopolymer-probe environment because the probe ESR signal is anisotropic and depends upon the orientation of the probe with the external magnetic held. Oriented biopolymers occur in lipid membranes and in muscle fibers. 

One consequence of the high Q attained in these structures is that they become sharply tuned the system described above would show a FWHM of 1.5 MHz, comparable with the Doppler width of spectral lines in this region. Thus spectral lines viewed in a cavity may appear as an increased loss that lowers the Q at high pressures whereas at lower pressures their profile becomes distorted because the incident power density varies markedly with offset from the cavity resonant frequency. 

R.H. Dicke The effect of collisions upon the Doppler width of spectral lines. Phys. Rev. 89, 472 (1953)... 

Isotopic and hypeifine structure, resonance broadening (resulting from interaction between radiating and nonradiating atoms of the same species), and Stark broadening (resulting from interaction with electric fields), contribute to the widths of spectral lines. 

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. 

In addition to this spectral class, stars are also characterized by a luminosity parameter. This luminosity classification is made on the basis of the width of spectral lines. Table 2 summarizes this classification. The width of spectral lines increases as the gas pressure increases. This so-called pressure broadening is due to the perturbation of atomic energy levels by other, nearby species. The physically largest stars have the lowest surface densities and pressures. Lines from these stars are therefore broader than from smaller stars (Figure 1 and Table 2). This difference in size, which results in a difference in stellar luminosity, has led to the naming scheme from supergiants to dwarfs. 

Along this sequence, the width of spectral lines increases from supergiants to white dwarfs. 

With a traveling fellowship awarded by Harvard, Slater spent his first postdoctoral year at Cambridge. There, he developed a theory on radiative transitions in atoms. On discussing this idea with Neils Bohr and Hans Kramers, a joint paper on the quantum theory of radiation was published in 1924. However, Bohr and Kramers altered Slater s original idea by ascribing a virtual existence to the photons in the transitions— not the real photons that Slater believed in. In early 1925, Slater was back at Harvard and published further work of his own on radiative transitions. He presented a picture of absorption and emission of real photons coupled with energy conservation in transition processes. He also established a relationship between the width of spectral lines and the lifetimes of states. 

From the variety of different techniques which recently have been developed to outwit the Doppler-width of spectral lines in gas phase spectroscopy only two examples are selected here. They shall illustrate the resolution achieved so far and the gain in information about molecular structures obtainable from resolved features in sub-Doppler spectra, which are completely masked in Doppler-limited spectroscopy. 

Although we have considered the various contributions to the width of spectral lines separately, it is obvious that in any experimental situation several effects will usually be acting simultaneously. Consequently the observed lineshape will not have either a simple Lorentzian or Gaussian profile. To investigate this we consider a moving atom whose resonance frequency is observed to be at Uq. 

Homogeneous broadening. The Doppler width of spectral lines decreases as we go from the visible into the infrared region of the spectrum and eventually the line profile will be dominated by collision or natural broadening. 

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