Uncertainty broadening

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. 

Uncertainty, 10 Uncertainty broadening, 134 Uncertainty principle, 10 for energy and time, 10,133,134 Unitary matrix, 85-86, 87 Unitary operator, 108 Unit matrix, 83 Unit operator, 12 Units, 23... 

Another radical which should give interesting information from fluorine nuclei is NF2, which is formed by dissociation of N2F4 at relatively low temperatures (37). The ESR spectrum for these radicals in the gas phase is very broad and structureless, either because of rotational interactions, or possibly because the rate of dimerization was sufficient, under the conditions used (37), to give uncertainty broadening. This radical should have a structure comparable with that of N02 , so that the spectrum from radicals randomly trapped may well... 

Because a 100-fs IR pulse has a bandwidth of approximately 150 cm , uncertainty broadening is a potential concern with ultrashort IR pulses. However, spectral resolution lost to uncertainty broadening can be recovered by dispersing a spectrally broad pulse through a monochromator after it has passed through the sample [25]. 

In ion spectroscopy, however, the ions are under acceleration between collisions and, depending on the condition, the resonance may not last for the whole collision interval. This fact introduces a new source of uncertainty broadening which I call here transit" broadening (the quotation mark is to discriminate this effect from the usual transit time broadening which is much smaller). 

Line widths due to uncertainty broadening are sometimes called natural line widths and are generally about 10 nm (10" A), as shown in Example 8-1. 

Lifetime broadening is also called uncertainty broadening. 

Various suggestions for the likely effects of anhar-monicity include very short lifetime of the excited vibrational state (uncertainty broadening) and breakdown of the Born-Oppenheimer approximation (i.e. motion of electrons and nuclei are no longer independent, which might be viewed as leading to a multiplicity of potential functions). Special factors may operate in the liquid state in water the combination of distribution of bond lengths and... 

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