Doppler broadening lineshape

Figure 8.4 Doppler broadening lineshape parameter vs temperature in DyBa2Cu307 Yo.5Pro.5Ba2Cu307 and PrBa2Cu307. The arrow indicates Tc, From Jung et al [34,35].

Figure 8.9 Variation with quenching temperature of, (a) positron lifetime, (b) Doppler broadened lineshape parameter, I, and (c) oxygen deficiency, as obtained from weight loss (+) and Tc (o) measurements. From Bharathi et al. [54].

More frequently g(w) will be given by the Doppler-broadened lineshape (Problem 9.6)... 

For the moment we shall consider the standard method for describing the Doppler-broadened linewidth—i.e. by using a simple lineshape parameter. By far the most common parameters used—called S and W—are defined... 

The linewidth of annihilation from the free-positron state is Doppler-broadening measurements. In lifetime measurements the PsF component hides beneath the o-Ps component which has a similar lifetime. This is a case where the two-dimensional data analysis shows its great advantage As the Doppler broadening of each positron state is determined in its own time regime even positron states with similar features may be seperated from each other. Moreover, a tentative fitting procedure with only the three positron states as in pure water did not come to a satisfactory result with the AMOC histogram of the NaF solution. 

In Ar and even more pronounced, in Kr and Xe, the lineshape functions 5 (t) show indeed a clear shift of the juvenile Doppler broadening to higher positron ages (Figure 14.8). 

To treat predissociation quantitatively, precise measurements of the width (full width at half maximum, FWHM, or T, often misleadingly referred to as the half-width) of each rotational level are necessary. In the absence of Doppler broadening, the lineshape ora(E) is usually Lorentzian,... 

Doppler broadening has a Gaussian lineshape, and its convolution with the Lorentzian natural lineshape yields a Voigt profile. In typical experiments, this effect can be neglected since the Doppler width is usually much smaller than the resolution of the apparatus. Collisional line broadening is also Lorentzian, and the Lorentzian component of measured lines must be carefully extrapolated to zero pressure. 

In this model, the symbols have the following meaning. ( )R(a3) ao(l)HD(a3) is the optical rotation produced by the vapour and depends on the number of absorption lengths ao and on the lineshape function D(o)) which takes the form of a Doppler-broadened dispersion curve for magnetic and electric field induced rotation ( )r will depend on the strength of the field and D(oa) on the direction and type of field (see table 2). The transmitted intensity 1 - Ij exp[-aoG(o))] where the lineshape function G(o)) for a single spectral component can usually be accurately described by a Doppler-broadened Lorentzian curve. Finally the terms B and C in equation (53) represent respectively the finite extinction ratio of the polarisers and a laser independent... 

This is the Gaussian lineshape function, which arises from Doppler broadening. Like the Lorentzian function Pl( )> it maximizes at a> = coq, and approaches zero as to - + oo. The fwhm of Pg o ) is... 

As a final detail, we allow for broadening (e.g., Doppler broadening, which determines the lasing lineshape in He/Ne lasers) of the two-level transition. Assume that the spectral lineshape function is gf(v), normalized so that J g v)dv = 1. Then the negative absorption coefficient in Eq. 9.7 at the lineshape center frequency Vq should be multiplied by (vo), which will be inversely proportional to the lineshape fwhm Av since (v) is normalized the product givojAv will be about unity. This implies that the lasing criterion in Eq. 9.12 should be replaced by [1]... 

To observe a 7s — 9 transition requires that there be a 9p admixture in the 9 state. For odd this admixture is provided by the diamagnetic interaction alone, which couples states of and 2, as described in Chapter 9. For even states the diamagnetic coupling spreads the 9p state to all the odd 9( states and the motional Stark effect mixes states of even and odd (. Due to the random velocities of the He atoms, the motional Stark effect and the Doppler effect also broaden the transitions. Together these two effects produce asymmetric lines for the transitions to the odd 9t states, and double peaked lines for the transitions to even 9( states. The difference between the lineshapes of transitions to the even and odd 9i states comes from the fact that the motional Stark shift enters the transitions to the odd 9( states once, in the frequency shift. However, it enters the transitions to the even 9( states twice, once in the frequency shift and once in the transition matrix element. Although peculiar, the line shapes of the observed transitions can be analyzed well enough to determine the energies of the 9( states of >2 quite accurately.25... 

A high-resolution spectrum of the clock transition is shown in Fig. 2. The clock-laser power was reduced to 30 nW to avoid saturation broadening. The fit with a lorentzian curve results in a linewidth of 170 Hz (FWHM), corresponding to a fractional resolution bv/v of 1.3 10-13. A spectral window of 200 Hz width contains 50% of all excitations. According to our present experimental control of the ion temperature, electromagnetic fields and vacuum conditions, no significant Doppler, Zeeman, Stark or collisional broadening of the absorption spectrum of the ion is expected beyond the level of 1 Hz. The linewidth is determined by the frequency instability of the laser and the lineshape is not exactly lorentzian... 

Here C is a lineshape factor whose value depends on whether the transition is Doppler- or pressure-broadened. 

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