Cross forward scattering values

Figure 35 shows the result for the scaled forward scattering from randomly cross linked polyester chains which were prepared by anhydride curing of phe-nylglycidylether in the presence of bisphenol A diglycidylether [173-175]. The data could be fitted with Eq. (91) with values for g and which are collected in Table 5. 

These equations provide useful checks on the consistency of the experimentally measured values of aT with the calculated values of the real part of the forward scattering amplitude, or the scattering length they have been used as such by Bransden and Hutt (1975). For helium, these authors took the measured total cross sections of Coleman et al. (1976b) in the energy range 2-800 eV below 2 eV they used an extrapolation based on a least-squares fit of the functional form... 

Jastrow points out that the real parts of the forward scattering amphtude are not necessarily the square root of the scattering cross-sections at zero degrees. He tries to obtain information about the nucleon-nucleon potential from the values of n obtained from interpreting total neutron cross-sections. He interprets the value of nr. 0 (i.e. at about 300 Mev as evidence favoring a... 

The major application of this technique, principally by Lindholm and co-workers (see Chapter 10), has capitalized on the above limitation in a study of charge-transfer processes, where the products may exhibit a thermal energy distribution. Even in this application, cross sections are difficult to obtain because the sampling volume is not well defined. Lindholm has been careful to quote only Q values which are estimates of the relative reaction efficiencies. There is another reason why any such cross section so measured may be unreliable. It is plausible, and indeed it has recently been demonstrated, that charge-transfer reactions may yield some products which are forward-scattered in the laboratory framework these would result from collisions with small impact parameters. To the extent that these products will not be detected in a transverse tandem machine, the measured cross section will be underestimated. 

We assume that the energy resolution available in the experiment does not allow us to discriminate between states with different A/-values. In this instance, the matrix elements quoted are averaged over M, just as in the calculation of the elastic cross-section. Assembling the results, the cross-section for a near-forward scattering geometry in which an ion is excited between states J and / = 7 -I-1 separated by an energy A is... 

The reason for the large difference between the values of A for positrons and electrons at an energy of 2 eV is that for positrons the s-wave phase shift passes through zero at the Ramsauer minimum and the dominant contribution to the cross section therefore comes from the p-wave, which is quite strongly peaked in the forward and backward directions. In contrast, there is no Ramsauer minimum in electron-helium scattering, and the isotropic s-wave contribution to aT is dominant at this energy. 

Let us turn now to the corresponding inelastic cross-section. The matrix elements (/, M L + 2S J, M) vanish except for / —/ = 1. Hence, near the forward direction we observe only the dipole-allowed transitions, i.e., the /—> / 1 transitions out of the Hund s rule ground state. Beyond the limit of small K, higher-order transitions contribute to the cross-section, and these are the main subject of the subsequent theory valid for arbitrary values of k. The small-K result we present for inelastic events, / = / 1, is of limited practical value since the minimum value of c is usually quite large owing to the kinematic constraints on the scattering process. Even so, the result is a useful guide to the size of the cross-section, and a welcome check on a complete calculation. 

We have studied in Sect. 2.2.1 that there is a finite probability of scattering of a-particle from a target nucleus in a particular directions, the impinging particles can go anywhere after scattering i.e., it can get scattered in the forward direction (0 < 90°) and also in the backward direction (0 > 90°) as shown in Fig. 2.4. The probability value (called differential cross-section) depends on the angle of scattering. 

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