Stark profile

The shape and width of each absorption line are functions of temperature and pressure of the medium. The Lorenz profile is usually used to define the shape of these lines at moderate temperatures under local thermodynamic equilibrium conditions. Although other profiles, such as Doppler or Stark profiles, can also be used to define the line shapes, the Lorenz profile, which adequately describes collision-broadened lines, is more appropriate for most applications, including those in combustion systems. For more details, the reader is referred to Siegel and Howell [1] or Modest [3]. 

R is independent of F, since both terms go as F, and has no adjustable parameters. We have an / (w) spectrum for R > I and a bleached /(o>) profile for I. The measured linewidth [111], F < 0.010 eV, and oligomer results in Table 6.7 lead to R > 10 and give an / (o>) spectrum. As seen in Fig. 6.12 and Table 6.6, PDA-PTS crystals have both two-photon and linear absorption at 2.00 eV. Stark profiles due to overlapping vibronics depend sensitively on the precise spacing [115] and contain bleaching and induced absorptions that may approximate / (w). 

Fig. 2.96. HPLC profiles of Starking Delicious juice, rose cider, and GPC fractions from rose cider recorded at 520 nm. Each lyophilized sample was dissolved in 10 per cent EtOH (20 mg/ml). Peak 1 with retention time of 27.5min is Cyn-3-gal, which is the main anthocyanin in apple, and peaks 5-9 are unidentified anthocyanins, which may be newly produced during the vinification process. Reprinted with permission from T. Shoji et al. [231],...

Stark P, Fuller R, Wong D. The pharmacologic profile of fluoxetine. J din Psychiatry 1985 46 7-13. 

Fig. 6.10 Calculated SFI profile for diabatic ionization of the H like m a 3 states. Top, extreme members of the n = 31, m = 3 Stark manifold. The crosses represent the points at which each m a 3 Stark state achieves an ionization rate of 10 s I. Bottom, calculated SFI profile for diabatic ionization of a mixture containing equal numbers of atoms in each m a 3 Stark level for n = 31 at a slew rate of 109 V/cm s. (from ref. 26).

For an accurate data analysis, a detailed understanding of systematic effects is necessary. Although they are significantly reduced with the improved spectroscopy techniques described above, they still broaden the absorption line profile and shift the center frequency. In particular, the second order Doppler shift and the ac-Stark shift introduce a displacement of the line center. To correct for the second order Doppler shift, a theoretical line shape model has been developed which takes into account the geometry of the apparatus as well as parameters concerning the hydrogen atom flow. The model is described in more detail in Ref. [13]. 

The method of symmetric points was used to determine the center of the interference curve. Extensive calculations showed that the line profile should be symmetric about the center frequency. The line center was then corrected for the second order Doppler shift, The Bloch-Siegert and rf Stark shifts, coupling between the rf plates, the residual F=1 hyperfine component, and distortion due to off axis electric fields. A small residual asymmetry in the average quench curve was attributed to a residual variation of the rf electric field across the line and corrected for on the assumption this was the correct explanation. Table 1 shows the measured interval and the corrections for one of the 8 data sets used to determine the final result. 

Derivation of Phase-Integral Formulas for Profiles, Energies and Half-Widths of Stark Levels... 

In the present chapter we shall start from the results obtained in Chapter 3 and treat the Stark effect of a hydrogenic atom or ion with the use of the phase-integral approximation generated from an unspecified base function developed by the present authors and briefly described in Chapter 4 of this book. Phase-integral formulas for profiles, energies and half-widths of Stark levels are obtained. The profile has a Lorentzian shape when the level is narrow but a non-Lorentzian shape when the level is broad. A formula for the half-width is derived on the assumption that the level is not too broad. 

Electro-absorption (EA) spectroscopy, where optical absorption is observed under the application of an electric field to the sample, is another method that can distinguish between localised and inter-band excitations. The electric field produces a Stark shift of allowed optical absorptions and renders forbidden transitions allowed by mixing the wavefunctions of the excited states. Excitons show a quadratic Stark (Kerr) effect with a spectral profile that is the first derivative of the absorption spectrum for localised (Frenkel) excitons and the second derivative for charge transfer excitons, i.e. 

In 1996, Nemet and Kozma showed the emission spectrometry of gold laser-produced plasma to be of interest for analytical purposes a delay time of 800-1000 ns was found to ensure nni/-thermal equilibrium and thorough atomization in the plasma. The line profiles obtained under such conditions (both resonant and Stark-broadened) were fitted to a symmetric Lorentzian curve [170]. Recently, LIBS was used in combination with effective chemometric tools to develop a determination method for gold in homogeneous samples that allows the characterization of jewellery products. The results confirmed the LIBS technique as an effective alternative to the hallmark official methods [143,144,171]. 

The l = 2 terms in the multi-pole expansion (8.32), which are linear in the electric field gradient (<9E/dz)r=0, are known as the quadrupole terms [89,90] and they produce a broadening of the shallow impurity lines known as the quadrupole broadening. At a difference with the quadratic Stark broadening, the quadrupole broadening results in a more symmetric profile of the perturbed line [90]. 

Figure 8.38b gives an experimental display of the consequence of the quadratic Stark effect of the profile of the 3p i (P) line in a partially annealed NTD silicon sample. 

Fig. 8.38. Comparison of the profiles of the 3p i P line at LHeT in a NTD natSi sample with [P] —2 x 101Bcm-3 after (a) a post-irradiation 2-h annealing at 650° C and (b) a complementary annealing at 800° C, showing the effect of quadratic Stark effect in (a). The spectral range is 340.37-343.59 cm 1 and the resolution 0.06 cm-1 (7 ueV) (after [67]). Copyright 1981 by the American Physical Society...

K. Gehrmann, M. Busch, S. Meinicke, R. Starke, and A. Krombholz. The influence of fibre geometry of different natural fibres and different PP grades on key properties of composites and extruded hollow profiles. First experiences with the industrial profile... 

M. Bengtsson, N.M. Stark, and K. Oksman. Crosslinked wood-thermoplastic composites—profile extrusion and properties. In Progress in Wood Fibre Plastic Composites 2006 International Conference, Toronto, Canada, May 1-2, 2006. 

This complex relationship means that if the cavity is held at resonance and the spectral line is swept, e.g. by Stark or Zeeman modulation, although other modulation schemes are possible, the cavity impedance changes and the reflected power incident on the Gunn device changes in sympathy with the spectral scan. This causes a current to flow in the Gunn oscillator circuit related to the spectral absorption profile, and therefore to its amplitude and area. That current can be readily transformer-coupled out of the Gunn bias circuit and detected S)mchro-nously with the modulation frequency. 

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