Stark broadening

Fig. 6.2 Stark structure and field ionization properties of the m = 1 states of the H atom. The zero field manifolds are characterized by the principal quantum number n. Quasidiscrete states with lifetime r > 10-6 s (solid line), field broadened states 5 x 10 10 s < x < 5 x 10-6 s (bold line), and field ionized states r < 5 x 10 10 s (broken line). Field broadened Stark states appear approximately only for W > ITC. The saddle point limit Wc = -2 /E is shown by a heavy curve (from ref. 3).

Figure 12.5 Electric field-induced broadening (Stark effect) of spectral holes for psendoisocyanineio-dide monomer (a) and aggregate (b). Note the different scales of the applied Stark field for monomer...

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

One of the simplest examples of line interference is impact broadening of H atom La Stark structure, observed in plasmas [176] (Fig. 4.1.(a)). For a degenerate ground state the impact operator is linear in the S-matrix ... 

As charge-dipole interaction between the electron and the atom is small, the perturbation theory expansion may be used to estimate f. The odd terms of this expansion disappear after averaging over impact parameters due to isotropy of collisions. In the second order approximation only those elements of P that are bilinear in V are non-zero. Straightforward calculation showed [176] that all components of the Stark structure are broadened but only those for which m = 0 interfere with each other ... 

In addition to the photoluminescence red shifts, broadening of photoluminescence spectra and decrease in the photoluminescence quantum efficiency are reported with increasing temperature. The spectral broadening is due to scattering by coupling of excitons with acoustic and LO phonons [22]. The decrease in the photoluminescence quantum efficiency is due to non-radiative relaxation from the thermally activated state. The Stark effect also produces photoluminescence spectral shifts in CdSe quantum dots [23]. Large red shifts up to 75 meV are reported in the photoluminescence spectra of CdSe quantum dots under an applied electric field of 350 kVcm . Here, the applied electric field decreases or cancels a component in the excited state dipole that is parallel to the applied field the excited state dipole is contributed by the charge carriers present on the surface of the quantum dots. 

Stark and Zeeman broadening caused by electric and magnetic fields respectively set up within the sample vapour and which perturb atomic energy levels. 

In solid state lasers the fluorescence lines are broadened 26) by statistical Stark fields of the thermal vibrating crystal lattice and furthermore by optical inhomogenities of the crystal. The corresponding laser lines are accordinglyjlarge at multimode operation 22)... 

The autput of a mode-locked ruby laser 729) producing a train of pulses of 5 psec duration with a maximum peak power of 5 GW was focused into a cell pressurized with the sample gas. Pulse-energy conversion efficiencies into the Raman lines of up to 70 % have been obtained. The induced rotational lines are broadened this could be due to a strong optical Stark effect 730)... 

Stark broadening occurs in the presence of an electric field, whereby the emission line is split into several less intense lines. At electron densities above 1013 the field is relatively inhomogeneous, the splitting is different for different atoms and the result is a single broadened line. 

Russian workers have been active recently in this field. Thus [Eu(thenoyltrifluoro-acetate)3(phen)] has been shown to retain its structure in polystyrene or PVC 298 the second order crystal field parameters ° and have been obtained for a series of complexes [EuL phen)] where L was a series of eight /S-diketonates,299 and the temperature broadening has been investigated, for similar adducts and for EuL2(N03)(Ph3P0)2, of the Stark components of the 1F levels.300... 

Fig. 10. Random Stark broadening of a hydrogen atom in a Gaussian random field with different modulation speeds (y/A = 2, 1, 0.2, 0).

Fig. 11. Random Stark broadening of a hydrogen atom in the superposition of a static Gaussian field E, and a fluctuating Gaussian field Ec. The modulation rate of Ee is as large as ye/o> = 10.

Fig. 7.2 Energy levels of the H n = 15, m = 0 Stark levels. The broadening of the levels corresponds to an ionization rate of 106 s-1. The extreme red and blue state ionization rates are taken from the calculations of Bailey et al. (ref. 5), and those of the intermediate states...

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... 

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]. 

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... 

Table 1. (B + C) rotational constants from low resolution microwave spectra of complexes of CF3COOH with various carboxylic acid and amide partners. An estimate of p, from Stark broadening measurements is also given. The (B + Q constants were calculated with O. .. H—O distances of 2.67 A and O. .. H—N distances of 2.71 A.

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