Photodissociation cross section total

For two Bom-Oppenlieimer surfaces (the ground state and a single electronic excited state), the total photodissociation cross section for the system to absorb a photon of energy ai, given that it is initially at a state x) with energy can be shown, by simple application of second-order perturbation theory, to be [89]... 

B. The Time-Dependent Formulation Total Integral Photodissociation Cross Section... 

The partial cross section gives the probability of absorbing light and producing a particular final product quantum state. The total photodissociation cross section is clearly given by the sum over all partial photodissociation cross sections ... 

Three types of measurements were performed in this study. First, photodissociation cross sections were measured, in which the total photofragment yield was measured as a function of dissociation photon energy. In these experiments, the electron signal generated by the microchannel plates is collected with a flat metal anode, so that only the total charge per laser pulse is measured. The beam block is 3 mm wide for these measurements. 

In the following we will call the a u,n,j) partial photodissociation cross sections.t They are the cross sections for absorbing a photon with frequency u and producing the diatomic fragment in a particular vibrational-rotational state (n,j). Partial dissociation cross sections for several photolysis frequencies constitute the main body of experimental data and the comparison with theoretical results is based mainly on them. Summation over all product channels (n,j) yields the total photodissociation cross section or absorption cross section ... 

The calculation of absolute cross sections requires knowledge of the transition dipole function which, unfortunately, is rarely known. Therefore, all examples which we will discuss in this monograph are relative cross sections and the constant C will be mostly ignored in what follows. As stressed in Section 1.4, the total photodissociation cross section is the... 

Employing the completeness of the spherical harmonics, one derives the following expression for the total photodissociation cross section... 

The time-dependent formalism would be rather limited if it yielded only the total cross section. However, that is not the case all partial photodissociation cross sections a(Ef,n) can be also extracted from the time-dependent wavepacket. We assume that for large times the wavepacket has completely left the interaction zone and moves entirely in the asymptotic region where the interaction potential Vi(R,r) is zero. Then, the asymptotic conditions (2.59) for the stationary continuum wavefunctions can be inserted into (4.3) yielding... 

In the time-independent approach one has to calculate all partial cross sections before the total cross section can be evaluated. The partial photodissociation cross sections contain all the desired information and the total cross section can be considered as a less interesting by-product. In the time-dependent approach, on the other hand, one usually first calculates the absorption spectrum by means of the Fourier transformation of the autocorrelation function. The final state distributions for any energy are, in principle, contained in the wavepacket and can be extracted if desired. The time-independent theory favors the state-resolved partial cross sections whereas the time-dependent theory emphasizes the spectrum, i.e., the total absorption cross section. If the spectrum is the main observable, the time-dependent technique is certainly the method of choice. 

Fig. 6.4. Schematic illustration of the multi-dimensional reflection principle in the adiabatic limit. The left-hand side shows the vibrationally adiabatic potential curves en(R). The independent part of the bound-state wavefunction in the ground electronic state is denoted by

We consider the photofragmentation of a triatomic molecule, ABC — A + BC(j), within the model outlined in Section 3.2. The vibrational coordinate of BC is fixed and the total angular momentum is zero. According to (5.23), the classical approximation of the partial photodissociation cross section for producing BC in rotational state j is given by... 

So far we have considered only the decay of the initial quasi-bound states and the influence on the total spectrum. Recalling that the total rate is the sum of all partial rates we can recast (7.22) as a sum of partial photodissociation cross sections, each being defined by... 

A much clearer picture evolves when one decomposes the total spectrum into the partial photodissociation cross sections a(, n,j) for absorbing a photon with wavelength A and producing NO in a particular vibrational-rotational state with quantum numbers (n,j). Experimentally this is accomplished by measuring so-called photofragment yield spectra. The idea is, in principle, simple the NO product is probed by laser-induced fluorescence (LIF). However, instead of scanning the wavelength Alif of the probe laser (in order to determine the final rotational state distribution) one fixes Alif to a particular transition NO(2n, nj) —>... 

Fig. 7.14. Photofragment yield spectra for the photodissociation of C1NO through the T electronic state. The lower part depicts the total absorption spectrum crt<)t(A) measured at room temperature. The three separate spectra in the upper part correspond to the (unnormalized) partial photodissociation cross sections cr(, n,j) for producing NO in a particular vibrational state n as indicated. The rotational state varies between 1.5 and 4.5 in these three cases. The additional spectrum in the lower part is the n = 0 cross section originating from excitation in the So —> Si electronic band. Recall that the sum of all partial cross sections yields the total spectrum. Adapted from Qian, Ogai, Iwata, and Reisler (1990).

Fig. 13.5. Partial photodissociation cross sections a(E,n) following the photodissociation of the 40 ) and the 31 ) vibrational states of H20(X) as functions of the energy in the A state. The quantum number n specifies the vibrational state of the OH product n = 0 (solid line), n = l (dashed line), and n = 2 (dotted line). E = 0 corresponds to three ground-state atoms. The vertical lines mark the total energies in the excited state corresponding to the two photolysis wavelengths A2 = 239.5 and 218.5 nm in the experiment of Vander Wal, Scott, and Crim (1991). Reproduced from Weide, Hennig, and Schinke (1989).

In both cases, la and lb, the total photodissociation cross section is completely determined by the short-time dynamics in the Franck-Condon region. In contrast, the partial cross sections, which determine the vibrational, rotational, and electronic-state distributions of the products, involves longer time dynamics. To obtain all of the relevant information about the reaction, the wavepacket evolution must be followed out into the product region of the potential energy surface and projected onto the various different vibrational and rotational states of the fragments. The partial cross section for scattering... 

Above the ionization threshold (see Chapter 8), the absolute photodissociation cross section can be obtained as the difference between the absolute total absorption cross section and the absolute photoionization cross section (see for example, for N2, Fig. 6 of Shaw, et ai, 1992). Another experimental quantity is the ionization efficiency defined as the total photoionization cross section divided by the total absorption cross section. 

Figure 7.5 Total photodissociation cross sections, for HC1 starting from the v — 1...

TABLE 3 Absolute Total Photodissociation Cross Sections (o), SfP)/S( /)) Branching Ratios aud SfPj, ) Fine-Structure Distributions, for 193-nm Photodissociation of HS and CHjS Initially Formed in the 193-nm Photodissociation of H2S, CHjSH, and CHjSCH,... 

Total photodissociation cross sections of KrN" and KrN were measured between 565 and 670 nm with a drift-tube mass spectrometer and a tunable dye laser. The photodissociation proceeds via KrN hv Kr N and KrNs + hv Kr N2. The absolute cross sections steadily increased for KrN and decreased for KrN towards smaller wavelengths. The maximum absolute cross sections of about 1.0 x 10" cm for KrN and 0.48 x 10" cm for KrNj were obtained at 575 and 655 nm, respectively [35]. 

Fig. 3 Total photodissociation cross section for O2 in the Herzberg states. This work (ab initio) corresponds to the use of ab initio potential energy curves and This work (RKR) to the use of RKR potentials constructed on the experimental data [87], Comparison is made with the works of Shardanand and Prasad Rao [149], Herman and Mental [83], Pirre et al. [129], Johnston et al. [88], Cheung et al. [37], Jenouvrier et al. [86], Yoshino et al. [184], Yoshino et al. [185] and Buijsse et al. [19]...

The overall OD vibrational distribution from the HOD photodissociation resembles that from the D2O photodissociation. Similarly, the OH vibrational distribution from the HOD photodissociation is similar to that from the H2O photodissociation. There are, however, notable differences for the OD products from HOD and D2O, similarly for the OH products from HOD and H2O. It is also clear that rotational temperatures are all quite cold for all OH (OD) products. From the above experimental results, the branching ratio of the H and D product channels from the HOD photodissociation can be estimated, since the mixed sample of H2O and D2O with 1 1 ratio can quickly reach equilibrium with the exact ratios of H2O, HOD and D2O known to be 1 2 1. Because the absorption spectrum of H2O at 157nm is a broadband transition, we can reasonably assume that the absorption cross-sections are the same for the three water isotopomer molecules. It is also quite obvious that the quantum yield of these molecules at 157 nm excitation should be unity since the A1B surface is purely repulsive and is not coupled to any other electronic surfaces. From the above measurement of the H-atom products from the mixed sample, the ratio of the H-atom products from HOD and H2O is determined to be 1.27. If we assume the quantum yield for H2O at 157 is unity, the quantum yield for the H production should be 0.64 (i.e. 1.27 divided by 2) since the HOD concentration is twice that of H2O in the mixed sample. Similarly, from the above measurement of the D-atom product from the mixed sample, we can actually determine the ratio of the D-atom products from HOD and D2O to be 0.52. Using the same assumption that the quantum yield of the D2O photodissociation at 157 nm is unity, the quantum yield of the D-atom production from the HOD photodissociation at 157 nm is determined to be 0.26. Therefore the total quantum yield for the H and D products from HOD is 0.64 + 0.26 = 0.90. This is a little bit smaller ( 10%) than 1 since the total quantum yield of the H and D productions from the HOD photodissociation should be unity because no other dissociation channel is present for the HOD photodissociation other than the H and D atom elimination processes. There are a couple of sources of error, however, in this estimation (a) the assumption that the absorption cross-sections of all three water isotopomers at 157 nm are exactly the same, and (b) the accuracy of the volume mixture in the... 

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