Breit-Wigner distribution

Lorentz, Cauchy, or Breit-Wigner distribution h(r) = j (nb ( 1 + (r-r0)2 /b2 at r0 with a full width at half-maximum b. 

As a result, the energy E of photons emitted by an ensemble of identical nuclei, rigidly fixed in space, upon transition from their excited states (e) to their ground states (g), scatters around the mean energy Eq = E. Eg. The intensity distribution of the radiation as a function of the energy E, the emission line, is a Lorentzian curve as given by the Breit-Wigner equation [1] ... 

In Mhssbauer spectroscopy (see Chap. 25 in Vol. 3), the density function of Cauchy distribution is called a Lorentzian curve. In nuclear physics, the same function is also called the Breit-Wigner curve (Lyons 1986). (See also Chap. 2 in this Volume.) This curve is characteristic of the energy uncertainty of excited (nuclear) states, which follows from the fact that excited states have exponential distribution with a finite mean life t. The natural linewidth T, i.e., the FWHM of the Lorentzian energy density, is twice of the parameter y(F = 2y). 

This equation gives the very important fact that the energy of decaying state is not a constant and is distributed over a region with a width determined by the decay constant. The width is called natural line width. The shape of the distribution is called a Lorentzian or Breit-Wigner curve as shown in Fig. 1.3. 

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