Partial production cross sections

In order to measure cross sections, a beam of electrons of known energy is directed through a gas sample of known pressure and the resulting ion and electron currents measured.63 If mass selective ion detection is used, then partial ionization cross sections oz may be determined. These cross sections correspond to the production of z electrons and an ion or ions having total charge +ze. Some instruments allow the counting cross section oc, also known as the ion production cross section, to be determined ... 

Since the summation method allows absolute partial ionization cross sections to be determined, it is straightforward to extract the counting or ion production cross section from the data. Since this is the quantity which is given by many of the current... 

We will be interested not only in the total absorption cross section [Eqs. (4.1) and (4.2)], which gives us a measure of the total probability that the molecule will absorb light and dissociate, but also in the probability that different product quantum states will be formed. This probability is given by a partial cross section cj/( ). From Eq. (4.1) we see that this partial integral cross section may be written as... 

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 ... 

FIGURE 3. Total ionization cross section of diethylzinc and partial ionization cross sections for the production of the Zn-containing ions. Reproduced by permission of Elsevier from Reference 27... 

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 ... 

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. 7.7. Comparison of the different energy behavior of partial dissociation cross sections a(E,j) for the production of NO(j) in indirect, HONO(iS i), and in direct, ClNO(Si), photofragmentation. Note the quite different energy scales The results for HONO are obtained from a two-dimensional model (Schinke, Untch, Suter, and Huber 1991) and the cross sections for C1NO are taken from a three-dimensional wavepacket calculation (Untch, Weide, and Schinke 1991b).

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. 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 order to evaluate partial photodissociation cross sections (vibrational and rotational product distributions) i.e. ABC + hv A + BC n,K) the wave function can be projected onto the different rovibrational eigenstates of the molecular fragment BC at fixed distance R between the two fragments. The chosen R should be on the asymptote of the potential energy surface where the two fragments do not interact. Balint-Kurti et at [87] have shown that the partial cross section is given by... 

The determination of the total ionization cross section of a molecule requires in principle a careful measurement of all quantities in Eq. (2). Partial ionization cross sections can be obtained if the detection of the ion current is restricted to a particular product ion. In the latter case, a mass selective device—e.g., a mass spectrometer—has to be employed. The most commonly used mass spectrometers for this purpose are magnetic, radio-frequency, quadrupole, and time-of-flight mass spectrometers. In all cases, the detection sensitivity of the instrument may vary with the mass of the detected ions and must be known accurately. 

The formation probability of each product corresponds to a partial reaction cross-section. The total reaction cross-section is the sum of all the partial cross-sections and measures the probability that the projectile causes a nuclear reaction indqjendent of the products formed. Thus, the decrease in intoisity of the particle flux is proportional to oT. The amount of an individual product formed is proportional to where a,- corresponds to the partial reaction cross-section for the formation of the th product. 

Energy, half-life and partial gamma-ray production cross section of the most important prompt and decay gamma lines of elements... 

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