Heisenberg natural linewidth

The earliest attempts to compensate for the energy disparity 2 r involved the provision of a large closing Doppler velocity of about 2v. 

This was first successfully achieved by Moon [2] in 1950 using an ultracentrifuge. A mercury absorber was used, together with a Au /5-active source to generate an excited state of The required velocity was 

One of the most important influences on a y-ray energy distribution is the mean lifetime of the excited state. The uncertainties in energy and time are related to Planck s constant h = 2nh) by the Heisenberg uncertainty principle 

The ground-state nuclear level has an infinite lifetime and hence a zero uncertainty in energy. However, the excited state of the source has a mean life T of a microsecond or less, so that there will be a spread of y-ray energies of width Fs at half height where 

Whence, substituting numerical values and remembering that the mean life T is related to the half-life by the relation t = In 2 x 

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Lattice vibration phonon energies Heisenberg natural linewidths (C,)... 

The natural linewidth F AE of y rays is given by the Heisenberg uncertainty principle,... 

The natural width of a spectral line is determined by the Heisenberg uncertainty principle and the lifetime of the excited state. The Heisenberg principle states that the position and velocity of an electron cannot be specified with complete accuracy. Since the lifetime of an excited electronic state is of the order ofl0" -10" sec, there must therefore be associated with the electron sufficient energy uncertainty to provide for slight broadening of the spectral line. The natural linewidth is very small and of the order of... 

Assume that all other line-broadening effects except the natural linewidth have been eliminated by one of the methods discussed in the previous chapters. The question that arises is whether the natural linewidth represents an insurmountable natural limit to spectral resolution. At first, it might seem that Heisenberg s uncertainty relation does not allow outwit the natural linewidth (Vol. 1, Sect. 3.1). In order to demonstrate that this is not true, in this section we give some examples of techniques that do allow observation of structures within the natural linewidth. It is, however, not obvious that all of these methods may realty increase the amount of information about the molecular structure, since the inevitable loss in intensity may outweigh the gain in resolution. We discuss under what conditions spectroscopy within the natural linewidth may be a tool that really helps to improve the quality of spectral information. 

Continuing from remarks ( 62)-( 63), the following conclusion can be drawn The formula t F = h is often used for the estimation of the natural linewidth. This formula is sometimes interpreted as the time-energy equivalent of the Heisenberg relation, where r is the uncertainty (standard deviation) of the lifetime and F (FWHM) is that of the energy state. It should be stressed, however, that while r can play the assigned role (because the standard deviation is equal to the expected value in the case of the exponential distribution), the quantity F cannot be interpreted as standard deviation, since the Cauchy distribution does not have any. 

The ultimate (minimum) linewidth of an optical band is due to the natural or lifetime broadening. This broadening arises from the Heisenberg s uncertainty principle, AvAt < U2jt, Av being the full frequency width at half maximum of the transition and the time available to measure the frequency of the transition (basically, the life-... 

Due to the contribution of various broadening mechanisms, the linewidths typically observed in atomic spectrometry are significantly broader than the natural width of a spectroscopic line which can be theoretically derived. The natural width of a spectral line is a consequence of the limited lifetime r of an excited state. Using Heisenberg s uncertainty relation, the corresponding half-width expressed as frequency is ... 

The linewidth caused solely by the energy level broadening because of the Heisenberg uncertainty principle (i.e., not subjected to the influence of an instrumental imperfection), is called a natural spectral linewidth. 

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