Heisenberg natural line width

Fig. 2.2 Intensity distribution /( ) for the emission of y-rays with mean transition energy Eq. The Heisenberg natural line width of the distribution, F = S/t, is determined by the mean lifetime T of the excited state (e)...

The natural line width is determined by Heisenberg s uncertainty relation... 

Following Eq. 4 there are three different sources of line broadening adding to the natural line width AB, which reflects the lifetime of the final state (Heisenberg uncertainty principle) and in some cases an unresolved spin orbit splitting. In first approximation, 7)... 

Natural Broadening The natural line width of an atomic spectral line is determined by the lifetime of the excited state and Heisenberg s uncertainty principle. The shorter the lifetime, the broader the line, and vice versa. Typical radiative lifetimes of atoms are on the order of 10 s, which leads to natural line widths on the order of 10 nm. 

The natural line width F is also referred to sometimes as the Heisenberg line width because it obeys the following equation (see also O Eq. (2.36) in Chap. 2, Vol. 1, as well as remarks 62-64 in Chap. 9, Vol. 1.) ... 

The natural line width (or intrinsic fine width in the absence of external influences) of an energy level is determined by the lifetime due to the Heisenberg uncertainty principle ... 

A uniform ab.sorber with randomly oriented crystallites can be prepared easily by sandwiching the finely ground material between the thin windows of a Perspex holder. In order to obtain undistorted line shapes it is desirable that the absorber is thin . The natural line width r a, of the Mossbauer line having Lorentzian shape [see Section 19.2.1, Eq. (3)] is determined, as already discussed, by the half-life of the excited nuclear state and the Heisenberg uncertainty principle. The ex-... 

While radiative relaxation can produce relatively narrow spectral lines (e.g. 0.0001 nm or less, depending on the source and line), the lines are not truly monochromatic. At the very least each spectral line exhibits a natural line width that is governed by the Heisenberg uncertainty principle... 

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. 

Many of the processes which determine line widths can be removed by appropriately designed experiments, but it is almost impossible to avoid so-called natural line broadening. This arises from the spontaneous emission process (governed by the Einstein A coefficient) described in the previous section. Spontaneous emission terminates the lifetime of the upper state involved in a transition, and the Heisenberg uncertainty principle states that the lifetime of the state (At) and uncertainty in its energy (A E) are related by the expression... 

Natural broadening occurs because of the finite lifetime (x) of the atom in the excited state. Heisenberg s uncertainty principle states that if we know the state of the atom, we must have uncertainty in the energy level. We assume that x for the ground state is infinity and therefore for a resonance line the natural width Av = IAtxx. 

According to the Bohr model of the atom, atomic absorption and emission linewidths should be infinitely narrow, because there is only one discrete value for the energy of a given transition. However, there are several factors that contribute to line broadening. The natural width of a spectral line is determined by the Heisenberg uncertainty principle and the lifetime of the excited state. Most excited states have lifetimes of s,... 

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 ... 

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