Solid Angle Coverage

The lay-out of the detector is shown in Fig. 6. Two layers of 16 silicon strip detector modules each for charged particle tracking and vertex reconstruction are surrounded by a cylinder constructed of 16 rows of 12 Csl (pure) crystals for the detection of the two 511 keV 7-rays. This arrangement gives a large solid angle coverage for both particle types and a sufficiently fine resolution for vertex reconstruction. 

Fig. 3 The newly upgraded SXD at ISIS provides an instrument with 11 area PSDs arranged around a sphere surrounding the sample and over 50% solid angle coverage. Shown here arc an exploded view of the detector array (l ft) a view of the detector assembly prior to installation (right).

The boost has a substantial effect on solid angle coverage. Figure 1.4 shows the single track efficiency as a function of maximum polar angle 9 in the forward and backward directions for B meson decays at the T(4S) with a boost of 7 = 0.56. Since it is necessary to reconstruct a minimum of three tracks for a measurement of sin 2a using + 7r "7r, and at least five tracks for a measurement of sin 2/ using B there... 

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. 

The importance of contact angle is that it determines the extent of (solid) surface coverage by a liquid. It is intuitively clear that the interfacial area covered by a sessile drop of given, fixed volume Vof liquid increases as contact angle decreases, but this maybe readily written formally in the case of a spherical, cap-shaped drop, of contact radius r, and height h. Writing t = tan(0o/2) = h/r, and with a standard trigonometric formula for the volume, V, of... 

Fig. 9. Correlation of contact angle, flotation recovery, surface coverage by collector, and 2eta potential. Solid, quart2, collector reagent, 4 x 10 Af dodecylammonium acetate. = recovery, % A = zeta potential, mV Q — contact angle, degrees and = surface coverage, % of one monolayer. Ref.

Figure 3. ARUPS energy distribution curves taken with Hel radiation at normal incidence and an electron emission angle of 52" shown as a function of copper coverage. The intensity of the various curves has been normalized at the Fermi level Ef The individual curves are matched to their corresponding copper coverages in monolayers by the solid lines and the saturation behavior of the interface state at approximately —1.5 eV is identified by the dashed lines. (Data from ref. 8.) (Reprinted with permission from ref. 43. Copyright 1987 American Association for the Advancement of Science.)...

Figure 8 shows schematically how the contact angle depends on the adsorption. In the absence of adsorption, the solid surface is wet by aqueous phases that spread over the surface. In Region I of the adsorption isotherm, the surface coverage by the surfactant is too small to significantly affect the wettability. 

A second principle applying to these model systems is derived from their colloidal nature. With the usual thermodynamic parameters fixed, the systems come to a steady state in which they are either agglomerated or dispersed. No dynamic equilibrium exists between dispersed and agglomerated states. In the solid-soil systems, the particles (provided they are monodisperse, i.e., all of the same size and shape) either adhere to the substrate or separate from it. In the liquid-soil systems, the soil assumes a definite contact angle with the substrate, which may be anywhere from 0° (complete coverage of the substrate) to 180° (complete detachment). The governing thermodynamic parameters include pressure, temperature, concentration of dissolved... 

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