Photoabsorption cross-sections

Figure B3.4.7. Schematic example of potential energy curves for photo-absorption for a ID problem (i.e. for diatomics). On the lower surface the nuclear wavepacket is in the ground state. Once this wavepacket has been excited to the upper surface, which has a different shape, it will propagate. The photoabsorption cross section is obtained by the Fourier transfonn of the correlation function of the initial wavefimction on tlie excited surface with the propagated wavepacket.

The distinction between photoabsorption and photoionization is important, particularly near threshold, where the probability that ionization will not occur upon photoabsorption is significant. Thus, the ionization efficiency is defined by TJ. = a. /photoionization cross section and absorption coefficient a by a = n(7, n being the absorber density. 

In Eq. (4.9), V is the frequency of radiation and a>. and (Ox are the statistical weights of the initial and final states. It should be remembered that Eq. (4.9) refers to the photoionization cross section, not the total photoabsorption cross section (see Sect. 4.2). 

Photoabsorption cross section, 34 213 Photoactivation, lattice oxygen, 31 123 Photoadsorption, 26 360 of oxygen, 32 106 Photoadsorptive effect... 

The absolute values of the photoabsorption, photoionization, and photodissociation cross sections are key quantities in investigating not only the interaction of photons with molecules but also the interaction of any high-energy charged particle with matter. The methods to measure these, the real-photon and virtual-photon methods, are described and compared with each other. An overview is presented of photoabsorption cross sections and photoionization quantum yields for normal alkanes, C H2 + 2 n = 1 ), as a function of the incident photon energy in the vacuum ultraviolet range and of the number of carbon atoms in the alkane molecule. Some future problems are also given. 

The oscillator-strength distribution dfjdE is proportional to the cross section a for the absorption of a photon of energy E, the so-called photoabsorption cross section. Note that the excitation energy is equivalent to the photon energy. Explicitly, one may write... 

The vertical ionization potentials of the (lt2) and (2ai) ionic states are indicated in Fig. 2, while that of the (lai) ionic state is far away from the range in Fig. 2. Kameta et al. examined their photoabsorption cross sections c in terms of the TKR sum rule for the oscillator-strength distribution dfjdE, Eq. (3), following the conversion of a to dfjdE,... 

In this chapter, we aim at giving an overview of the photoabsorption (c), photoionization (ff ), and photodissociation (cross sections of molecules in the vacuum ultraviolet range, where as stated the significant part of the photoabsorption cross sections lies. 

The double ionization-chamber method [19] provides an excellent means of measuring the photoabsorption cross sections of atoms and molecules in the range of the incident photon... 

The light intensities need not be measured to obtain the photoabsorption cross sections (o ), as will be shown later using Eq. (20). Therefore we do not need to consider the absorption of light by gas that effuses through the entrance and exit apertures of the chamber. 

Photoionization quantum yields ( / ) and, therefore, photoionization cross sections (o ) are obtained together with the photoabsorption cross sections (cr). 

Fig. 4 shows the illustration of a double ionization chamber. We describe the process of measuring the photoabsorption cross sections as follows, /q denotes the incident photon flux coming into the chamber filled with atoms or molecules of the number density n, I and I denote the photon fluxes entering and leaving plate 1, respectively, and I2 and I2 denote the photon fluxes entering and leaving plate 2, respectively. The ion currents q and q collected by plates 1 and 2, respectively, are expressed as... 

According to Eq. (20), we measure only q, q, and the pressure of a gas in the chamber to obtain the absolute values of the photoabsorption cross sections (cr), and then we obtain the values of from a following Eq. (18) or Eq. (19). If we use a rare gas as reference, of which is unity in the whole range above its first ionization potential, then /q is obtained. Thus the relation between Iq and the signal from the incident photon detector,... 

It follows from the above discussion that the fast electron scattering experiments at forward direction is able to simulate the photoabsorption cross sections over a wide range of the energy loss. 

In most cases, except those in earlier comparative studies between the real-photon method and the dipole-simulation method, the absolute cross-section values obtained by both methods agree with each other [27]. Comparison of obtained cross-section values between the two methods were discussed in detail [27, 2, and references therein] and summarized in conclusion [5]. It should be noted, at least briefly, that it is essentially difficult to accurately obtain the absolute values of photoabsorption cross sections (u) in the dipole-simulation experiments, and it is necessary to use indirect ways in obtaining those values as the application of the TKR sum rule, Eq. (3), to the relative values of the cross sections obtained partly with theoretical assumptions. Moreover, in some cases, in relatively earlier dipole-simulation experiments, particularly of corrosive molecules upon their electron optics with poorer energy resolutions, serious discrepancy from the real-photon experiments was clearly pointed out in the obtained absolute values of photoabsorption cross sections [5,20,25-28]. 

In case of simple diatomic molecules such as H2 and N2, sharp peaks are observed with large photoabsorption cross sections, especially in the lower energy range. In real-photon experiments, if the peak shape is narrower in energy than the bandpass of the incident... 

The real-photon method is essentially more direct and easier compared to the dipole-simulation method in obtaining absolute values of photoabsorption cross sections (o ), photoionization cross sections and photoionization quantum yields (t],). In the real-photon method, however, there is a practical need to use the big and dedicated facilities of synchrotron radiation where, in many cases, one should change the beam lines equipped with different types of monochromators depending on used photon-wavelengths—and to develop some specific new experimental techniques in the range from the vacuum ultraviolet radiation to soft X-ray. 

In Fig. 6 [7], the photoabsorption cross sections (u) of CH4, C2Hg, C3H8, and n-C iQ are compared, which were measured by our group by using the double ionization chamber and synchrotron radiation, as described in Section 2.1. Those in the range below the first ionization potentials were measured by the photon-beam attenuation method using the ionization chamber as a conventional gas cell. The following features can be noted [7]. 

The features in C1-C4 normal alkanes discussed in Section 3 seem to be generalized to a wide range of molecules, and thus we conclude that the major part of the photoabsorption cross sections of molecules (cr) is associated with the ionization and excitation of the outer-valence electrons. Hence, there is a strong need to measure the absolute values of a in the vacuum ultraviolet range, particularly in the range of the incident photon energy 10-30 eV, which is covered by the normal incidence monochromator used to monochromatize synchrotron radiation. The photoionization (cr ) and photodissociation (cd) cross sections. 

Figure 17 The ratios of the experimental cross sections to the theoretical ones (

Figure 1. Photoabsorption cross section for the dipole plasmon in axially deformed sodium clusters, normalized to the number of valence electrons N - The parameters of quadrupole and hexadecapole deformations are given in boxes. The experimental data [39] (triangles) are compared with SRPA results given as bars for RPA states and as the strength function (49) smoothed by the Lorentz weight with A = 0.25 eV. Contribntions to the strength function from p =0 and 1 dipole modes (the latter has twice larger strength) are exhibited by dashed curves. The bars are given in eVA. ...

Burley, J. D and H. S. Johnston, Ionic Mechanisms for Heterogeneous Stratospheric Reactions and Ultraviolet Photoabsorption Cross Sections for N02, HNO, and NO( in Sulfuric Acid, Geophys. Res. Lett., 19, 1359-1362 (1992b). 

According to Ref. [32], the (weak field) photoabsorption cross section is given by... 

The periodic-orbit quantization can be used to calculate not only the resonances but also the full shape of the photoabsorption cross section using (2.26) and (2.27). This semiclassical formula for the cross section separates in a natural way the smooth background from the oscillating structures due to the periodic orbits. In this way, the observation of emerging periodic orbits by the Fourier transform of the vibrational structures on top of the continuous absorption bands can be explained. 

R, D. Hudson, Critical Review of Ultraviolet Photoabsorption Cross Sections lor Molecules of Astrophysical and Aeronomic Interest, Null. Stand. Ref. Data Ser., Natl. Bur. Stand. (U.S.) 38 (1971). 

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