Glauber approximation

As we have seen, the Glauber approximation fails to give any interference between odd and even terms in the Bom series for the amplitude. Another way this expected interference might be absent is if all the odd or all the even terms were zero. This happens approximately when we have dipole dominance. 

Another related observation, exploited by Cheshire [5.8], is that in the SCA with a rectilinear trajectory it is actually the projectile, not the electron, that is in an inertial frame as it moves with constant velocity. We can exploit this if, instead of assuming the electron is fixed in position, we allow it to recoil freely. We are then presented with the situation of an electron scattering from the fixed projectile (in the opposite direction). This scattering problem can be treated with the Glauber approximation. Or, as the projectile-electron interaction is most often Coulombic, exactly This is the continuum Distorted Wave Approximation (CDWA). Here the correct off-energy-shell behavior can be inserted. A further important advance is to distort both exit and entrance channels. A last refinement is to recognise that the electron is neither free nor frozen, and to try to incorporate its attachment to the target more realistically. 

Thus this treatment predicts that the cross section for ionization is less than the Bom result for protons at asymptotic energies, see fig. 5.2. Or, equivalently, the ratio of protons to antiprotons is less than unity at high energies. The conventional Glauber approximation, for example Tai et al. [5.9], rotates the Z-axis in an approximate treatment so that Q becomes perpendicular to it. This seems a reasonable approximation for light projectUes where the deflection angle may well be larger. But for heavy projectiles it is a poor approximation. 

A measure of the great practical importance of the charge transfer process is the very considerable experimental and theoretical effort devoted to that process. The areas in which significant progress has very recently been recorded include atom capture as well as electron capture, the eikonal approximation, and versions of the Glauber approximation. Unfortunately, space permits only one topic, an important step in our understanding of asymmetric charge transfer. 

To obtain further insight into the meaning of the inelastic neutron spectra, it is necessary to have specific theoretical models with which to compare the experimental results. In the harmonic approximation it is possible to calculate the incoherent inelastic neutron spectrum i.e., the neutron scattering cross section for the absorption or emission of a specific number of phonons can be obtained with the exact formulation of Zemach and Glauber.481 A full multiphonon inelastic spectrum can be evaluated by use of Fourier transform techniques.482 The availability of the normal-mode analysis for the BPTI136 has made possible detailed one-phonon calculations483 for this system the one-phonon spectrum arises from transitions between adjacent vibrational levels and is the dominant contribution to the scattering at low frequencies for typical experimental conditions.483 The calculated one-phonon neutron en-... 

At the transition point the ratio of sodium sulphate to magnesium sulphate is approximately i i 6. In the case of solutions saturated with respect to both astracanite and Glauber s salt, the relative amount of sodium sulphate increases as the temperature rises, while in the solutions saturated for astracanite and magnesium sulphate, the ratio of sodium sulphate to magnesium sulphate decreases. 

Until Glauber and Schomaker showed that the first Bom approximation is far from valid for molecules with atoms differing considerably in atomic numbers, the expression (10) was used in all electron-diffraction investigations. The calculation of accurate scattering amplitudes by means of equation (4) has greatly contributed to the increased reliability of the electron-diffraction method. This is further discussed below (pp. 21 and 40), but it may be mentioned here that f and vaiues for a series of atoms were first published by Ibers and Hoerni, who used the WKB method. More accurate values, based partly on numerical solution of (1), have recently been published" (c/ Figure 1). 

Discussion of Some Approximations in the Simple ThetHry Application to Molecules with Heavy Atoms.—Introduction. The first Bom approximation is discussed on p. 9. As mentioned, Glauber and Schomaker showed that complex scattering amplitudes must be used at least for molecules with both light and heavy atoms. Figure 6 shows the experimental and two theoretical intensity curves for UFg. Curve B, which agrees quite well... 

Hoemi studied the double scattering in diatomic molecules. He used the second Bora approximation and foimd no contribution to the total intensity which interfered with the molecular intensity. This result has recently been confirmed by Yates and Tenney using a theory for multiple scattering developed by Glauber. 

A third nontrivial approximation can be obtained if we assume the collision is slow. In the Glauber method we assumed that the exponential energy factors could be treated as all the same, and their differences set to zero. In a slow collision exactly the opposite is true and we assume these factors are oscillating very rapidly. If we assume that integrals containing these factors are negligibly small because... 

We return to the approximate methods introduced earlier, and make use of ideas due to Reisenfeld and Watson [7.12] and Glauber [5.2], and those of the crazed maze. In a fast collision the electrons do not have time to move before the collision is over. They therefore do not sense the binding forces which hold them to the target in comparison to the strong shortlived impulse produced by the projectile. They recoil freely because they do not move far during the collision time. TMs is as true of electron-electron correlating forces as it is of the electron-target nuclear forces. 

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