Cross Section Measurement

In situ measurement of the concentration of radioactive tracers in the different phases requires that the phases are separated and arranged according to density difference over the measurement cross section in a horizontal pipe. In general, the measurements are performed with two spectral gamma radiation detectors placed on top and bottom of the pipe respectively. 

Theorists calculate cross sections in the CM frame while experimentalists usually measure cross sections in the laboratory frame of reference. The laboratory (Lab) system is the coordinate frame in which the target particle B is at rest before the collision i.e. Vg = 0. The centre of mass (CM) system (or barycentric system) is the coordinate frame in which the CM is at rest, i.e. v = 0. Since each scattering of projectile A into (v[i, (ji) is accompanied by a recoil of target B into (it - i[/, ([) + n) in the CM frame, the cross sections for scattering of A and B are related by... 

The measured cross section data for are shown in Figure 4b. The dominant resonance at 2.13 MeV offers a powerful enhancement to sensitivity for deuterium detection, exceedii the Rutherford cross section by two orders of magnitude. 

Because all measurement methods and instruments are sensitive to the velocity profile, the choice of the measurement cross-section is of vital importance. In most ventilation systems there is seldom enough straight duct to allow a fully developed velocity profile to develop, which is the most favorable for flow measurement. Thus, the principle in selecting the measurement cross-section is to find the place where the velocity profile is as near to the fully developed profile as possible. In practice the distance from the nearest source of disturbance upstream is maximized, ensuring that the distance to the nearest downstream disturbance is at least 3 to 5 duct diameters. 

Let us note that this definition of y breaks the limits of the Kielson-Storer model and can cause a few contradictions in interpretation of results. If the measured cross-section oj appears to be greater than oo, then, according to (3.45), the sought y does not exist. To be exact, this assertion is valid relative to the cross-section of the rotational energy relaxation oe = (1 — y2)oot since y2 is always positive. As to oj, taking into account the domain of negative values of y, corresponding to the anticorrelated case (see Chapter 2), formula (3.45) fails to define y when oj > 2co. 

N2 - NO+ + N, compared with a theory (7) based on classical trajectories subject to an ion-induced dipole potential. The assumptions involved in calculating the measured cross-sections are noted in the text... 

The curve marked ion-dipole is based on the classical cross-section corresponding to trajectories which lead to intimate encounters (9, 13). The measured cross-sections differ more dramatically from the predictions of this theory than previously measured cross-sections for exothermic reactions (7). The fast fall-off of the cross-section at high energy is quite close to the theoretical prediction (E 5 5) (2) based on the assumption of a direct, impulsive collision and calculation of the probability that two particles out of three will stick together. The meaning of this is not clear, however, since neither the relative masses of the particles nor the energy is consistent with this theoretical assumption. This behavior is, however, probably understandable in terms of competition of different exit channels on the basis of available phase space (24). 

There does not seem to be any selection rule such as conservation of spin or orbital angular momentum which this reaction does not satisfy. It is also not clear that overall spin conservation, for example, is necessary in efficient reactions (5, 16, 17, 20). Further, recent results (21) seem to show a greatly enhanced (20 times) reaction rate when the N2 is in an excited vibrational state (vibrational temperature 4000 °K. or about 0.3 e.v.). This suggests the presence of an activation energy or barrier. A barrier of 0.3 e.v. is consistent with the low energy variation of the measured cross-section in Figure 1. 

Obviously, experiments designed to measure cross-sections as a function of energy are needed. At present, tandem experiments are not capable of high precision at low energies because one must assume details of collision mechanics and because it is difficult to estimate collection efficiencies in forward scattering geometry (15). The extension of all known techniques to lower energy (64, 65) and the further development of pulse methods (58) offer the possibility for advances in this area. 

Electron correlations show up in two ways in the measured cross sections. If the initial target state is well described by the independent particle Hartree-Fock approximation, the experimental orbital (6) is the Hartree-Fock orbital. Correlations in the ion can then lead to many transitions for ionisation from this orbital, rather than the expected single transition, the intensities of the lines being proportional to the spectroscopic factors S K... 

H2O and D2O mixed sample used in the experiment. For the absorption cross-sections, there are probably some small differences among the three isotopomers in reality. Nevertheless, this estimation should be quite realistic. The estimated branching ratios of the H and D productions from HOD at 157 nm excitation should be 2.46 with about 15% estimated error bar. More accurate measurement on the branching ratio should be possible with the experimentally measured cross-section values for H2O and D2O. 

Semiempirical treatments of the electron impact process attempt to formulate fairly simple equations containing parameters determined experimentally in order to reproduce the measured cross section and possibly determine cross sections for... 

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 ... 

Temperature profiles were measured at several axial locations to locate the peak temperatures in the combustor. The axial distance between the nozzle and the temperature-measurement cross-section is denoted by Lf With one insert in place, the peak gas temperature immediately downstream of the insert was lowered but the high-temperature region was extended radially, i.e., the pattern factor was improved, as shown in Fig. 28.2. The peak temperatures at each axial location are shown as a function of the distance from the nozzle, or Lt/D, in Fig. 28.3. For the baseline case the highest temperature of 1418 K was found at 1.8 pipe diameters downstream of the nozzle. With one porous layer present, the peak gas temperature was about 200 K lower at Lt/D = 1.8 2.2 but increased by up to 120 K and 200 K at 0.5 and 3.2 pipe diameters downstream of the nozzle, respectively. The highest flame temperature was lowered but the high-temperature region was extended to upstream and downstream. 

Figure 20 Doubly differential cross sections for ejection of electrons of 219 eV (16 Ry) from He by 2-MeV He ions. The points are measured cross sections and the calculated results are line A— projectile ionization, target remains in the ground state line B—projectile ionization with simultaneous target excitation line C— target ionization, projectile remains in the ground state and line D—target ionization with simultaneous projectile excitation. (From Ref. 70.)...

The elfect of temperature on the absolute values of a, cr,-, and cr as a function of the incident photon energy. All the cross-section data shown in this chapter were measured for molecules in the gas phase at room temperature and thus, the target molecules do not lie in a single energy level as an initial level. This means that the measured cross sections seem to be dependent on gas temperature, which is important in various applications of the cross-section data. 

For harpoon reactions of alkaline metal atoms with iodine molecule I2, the interaction radii, Re, calculated using the formula Re = (ajji) 12 from the experimentally measured cross-sections a, are compared in Table 3 with the distances, Ru, calculated with the help of eqn. (40) and the sums of the gas-kinetic radii i M + i l2 of the reagents. In these calculations, effective radii of alkaline metal atoms have been used as RM, while the radii of the molecule I2, calculated from the data on the viscosity of I2 vapour at T > co and at T = 273 K, have been used as i l2 (the values of RM + i ,2 given in brackets correspond to the latter) [71], It is seen that the values of Re exceed Rm + Rh, i.e. electron transfer occurs at large impact parameters. 

From the size of the measured cross sections it can be concluded that the main contribution comes from large values of /. Therefore, the discrete angular momenta may be replaced as usual by the relation bkQ= (/ +—with b the impact parameter and hk0 = 2nEk(oo) —and by transforming the sum in (II.11) into an integral over b. We then obtain... 

The calculated total elastic cross section for He(2 S) + Ar is given elsewhere.102 There are currently no data for comparison. Trujillo has also measured cross sections for He(23S ) + Ne,Kr.136 Using essentially the same apparatus Harper and Smith138 have extended the cross section measurements to He(23S,) + H2,CO,02,N2 and Ne + He,Ne,Ar,Kr,H2,C0,N2,02. 

Fig. 11.28 Measured cross section for ionization of n = 46 (35 < n < 50) D atoms in collisions with N2 vs the kinetic energy Wu of the deuterium atom (O), measured cross section for destruction of n = 46 D atoms ( ) and n = 71 D atoms (A) in collisions with N2 (ref. 116). For comparison, Kennerly s measured total cross section for free electron-N2...

To explain the shift in current onset.S< cm/sec if o <10 ccm. This is a reasonable number for a neutral surface state,c herefore, this explanation for the observed shift in current onset passes a test of reasonableness. On the other hand, it is hard to be more quantitative without some independent measure of capture cross sections. A method jrf measuring cross sections applicable in some cases has been reported— and will be discussed later in this section. 

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