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** Classical turning point definition **

surface interaction potential is not infinitely hard (cf figure A3,9,2. As E increases, the projectile can penetrate deeper into the surface, so that at its turning point (where it momentarily stops before reversing direction to return to the gas phase), an energetic projectile interacts with fewer surface atoms, thus making the effective cube mass smaller. Thus, we expect bE/E to increase with E (and also with W since the well accelerates the projectile towards the surface). [Pg.902]

The physical situation of interest m a scattering problem is pictured in figure A3.11.3. We assume that the initial particle velocity v is comcident with the z axis and that the particle starts at z = -co, witli x = b = impact parameter, andy = 0. In this case, L = pvh. Subsequently, the particle moves in the v, z plane in a trajectory that might be as pictured in figure A3.11.4 (liere shown for a hard sphere potential). There is a point of closest approach, i.e., r = (iimer turning point for r motions) where... [Pg.994]

To integrate this expression, we note that 0 starts at n when r = co, then it decreases while r decreases to its turning point, then r retraces back to oo while 0 continues to evolve back to n. The total change in 0 is then twice the integral... [Pg.998]

outer turning point, whereas at energies above the asymptote, the partiele is no longer eonfmed by an outer turning point (see the figure below). [Pg.32]

energy level with the curve corresponds to a classical turning point of a vibration where the velocity of the nuclei is zero and all the energy is in the form of potential energy. This is in contrast to the mid-point of each energy level where all the energy is kinetic energy. [Pg.25]

As V increases, the two points where j/l, the vibrational probability, has a maximum value occur nearer to the classical turning points. This is illustrated for u = 28 for which A and B are the classical turning points, in contrast to the situation for u = 0, for which the maximum probability is at the mid-point of the level. [Pg.25]

The wavelength of the ripples in ij/ increases away from the classical turning points. This is more apparent as v increases and is pronounced for u = 28. [Pg.25]

The classical turning point of a vibration, where nuclear velocities are zero, is replaced in quantum mechanics by a maximum, or minimum, in ij/ near to this turning point. As is illustrated in Figure 1.13 the larger is v the closer is the maximum, or minimum, in ij/ to the classical turning point. [Pg.248]

Figure 7.21 illustrates a particular case where the maximum of the v = 4 wave function near to the classical turning point is vertically above that of the v" = 0 wave function. The maximum contribution to the vibrational overlap integral is indicated by the solid line, but appreciable contributions extend to values of r within the dashed lines. Clearly, overlap integrals for A close to four are also appreciable and give an intensity distribution in the v" = 0 progression like that in Figure 7.22(b). [Pg.248]

Hydrocarbons and carbon monoxide emissions can be minimised by lean air/fuel mixtures (Fig. 2), but lean air/fuel mixtures maximize NO emissions. Very lean mixtures (>20 air/fuel) result in reduced CO and NO, but in increased HC emissions owing to unstable combustion. The turning point is known as the lean limit. Improvements in lean-bum engines extend the lean limit. Rich mixtures, which contain excess fuel and insufficient air, produce high HC and CO concentrations in the exhaust. Very rich mixtures are typically used for small air-cooled engines, needed because of the cooling effect of the gasoline as it vaporizes in the cylinder, where CO exhaust concentrations are 4 to 5% or more. [Pg.483]

Fan horsepower is obtained from Fig. 12-15. Connecting the point representing 100 percent of standard tower performance with the turning point and extending this straight line to the horsepower scale show that it will require 0.041 hp/fr of actual effective tower area. For a tower area of 1000 ft" 41.0 fan hp is required to perform the necessary cooling. [Pg.1164]

Fig. 19. Cubic parabola potential. Turning points are shown. The dashed line indicates the stable potential with the same well frequency. |

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** Classical turning point definition **

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