Forward scatter geometry

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. 

Figure 2. Typical V(d) curves for different ff angles. Forward scatter geometry.

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... 

Figure 7 Schematic diagram of a DCEM spectrometer based on the electrostatic cylindrical mirror analyser. Forward scattering geometry is used. 6- and O2, minimal and maximal angles for the input slit edge positions Pb, lead shielding.

Forward scattering, 281-282, 291-293, 296-297 Fox, D. L., 233 Fractal geometry, 8-11 Fraunhofer diffraction, 296 Free energy and ions, 233-237 Free molecule region, thermophoresis in, 166-169... 

The appearance of the forward scattering amplitude in Equation 29 enables us to give a conceptually appealing interpretation of the attenuation coefficient associated with k. Using the forward scattering theorem, which is valid for any scatterer geometry, one finds (27-30)... 

Fig. 3.26 Trajectories in (Q,a>) space for a direct geometry spectrometer with detectors at angles 3, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120 and 135° and with an incident energy of 4000 cm. The dashed lines are the trajectories of an indirect geometry instrument (low-bandpass) using scattering angles of 45 (long dashes, forward scattering)) and 135° (short dashes, backscattering) and a final energy of 28 cm". ...

The MAPS spectrometer at ISIS [2], Fig. 12.1(a), is a third generation instrument that demonstrates the future direction of direct geometry instruments. The principal innovation is the use of large area, position sensitive He detectors ( 3.3.1.1). An area of 16 m. Fig. 12.1(b), of the sample environment tank is covered by 576 detectors that provide ahnost continuous coverage over a large solid angle in the forward scattering direction. 

For simple geometries-, the variation of b from, element to element can be approximated by a simple mathematical expression and the total intensity found by integration. Otherwisie the easiest approach is to measure the actual thickness of shield. material traversed along a straight line from each source element and add algebraically the separate intensity contributions. The total intensity should be multiplied by a fi factor to allow for tbe forward scattering in the shield. This is usually about a factor of 10 for thick shields. 

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