Interaction time

Figure Al.6.17. Double-sided Feymnan diagrams, showhig the interaction time with the ket (left) and the bra (right). Time moves forward from down to up (adapted from [36]).

The dynamics of ion surface scattering at energies exceeding several hundred electronvolts can be described by a series of binary collision approximations (BCAs) in which only the interaction of one energetic particle with a solid atom is considered at a time [25]. This model is reasonable because the interaction time for the collision is short compared witii the period of phonon frequencies in solids, and the interaction distance is shorter tlian the interatomic distances in solids. The BCA simplifies the many-body interactions between a projectile and solid atoms to a series of two-body collisions of the projectile and individual solid atoms. This can be described with results from the well known two-body central force problem [26]. 

Laser cooling can efficiently reduce the velocity of the atoms but cannot circumvent the acceleration due to gravity. On the ground the 1-g gravity level sets clear limitations to the ultimate sensitivities. The HYPER project (Hyper precision cold atom interferometry in space) will follow precisely this line and will benefit from the space environment, which enables very long interaction time (few seconds) and low spurious vibrational level. The sensitivity of the atomic interferometer can achieve few 10 rad.s. Hz to rotation and to acceleration. This very sensitive and accurate apparatus... 

Figure 20. Secular variation in 5 U(0) for Bahamas flowstone sequence. Changes in 5 U(0) are related to uranium-series disequilibrium conditions in host limestone, periodic addition of new material with elevated (marine) 5 U(0), alpha recoil effects and variation in recharge, and hence water-rock interaction times (see text for details).

Equation (65) illustrates that in the limit of ultrashort pulses the two-pathway method loses its value as a coherence spectroscopy 8s is fixed at it/2 irrespective of the system parameters. From the physical perspective, when the excitation is much shorter than the system time scales, the channel phase carries no imprint of the system dynamics since the interaction time does not suffice to observe dynamical processes. 

To estimate the available interaction time in a free-fall droplet experiment the steady-state balance between gravity and Stokes drag can be analyzed. A free-falling droplet will be subject to both gravitational and drag forces. Assuming that... 

Analytical Continuation of the Polynomial Representation of the Full, Interacting Time-Independent Green Function. 

We examine the time dependence of the charge transfer P,(t) in Fig. 5a for the wide band and Fig, 5b for the narrow band. Both curves show some oscillation, indicating there can be a series of transfers between the atom and the band. We have used A = 0.1, so the atom is moving slowly and is in the vicinity of the surface for a sufficiently long time for these multiple transfers to occur. The graphs show that the effective interaction time, when transfers take place, is about [ — 4A, 4A] for the narrow band and [ — 2A, 2A] for the wide band. It has been suggested that it is only the outward (r > 0) part of the atom s trajectory which is important for the charge-transfer process, but that is certainly not true for the cases shown in Fig. 5. 

Circulate at low flow rates to allow sufficient interaction time between the antibody and the hapten. Generally three complete passes through the column are adequate for most purposes. 

In both cases (i. e. emission or absorption saturation) the halfwidth of this/Lamb dip is slightly dependent on laser power but mainly determined by the interaction time of the individual molecules with the standing light wave in the cavity. This time may be limited by the finite lifetimes rb of upper or lower states, by the average time l/aup between two disturbing collisions, or by the transit time Tt of the gas molecules across the laser beam. This last limitation becomes important at low pressures of the absorbing gas and for transitions between long-lived states (see Section IV.3). 

Shorter <-----Change (reaction/interaction) time---> Longer... 

The model was fit to experimental planarization data with good success. Divergence from experimental results was explained by viscoelastic deformation of pad asperities. Incomplete elastic recovery reduces penetration of the trench and improves selectivity. This may be due to velocity effects (i.e., the interaction times are below the relaxation time for the material). 

Another possible solution that has been under development for three decades is to use a pulsed laser and time-resolved detection to allow the Raman photons to be discriminated from the broad luminescence background. The Raman interaction time is virtually instantaneous (less than 1 picosecond), whereas luminescence emission is statistically relatively slow, with minimum hundreds of picoseconds elapsing between electronic excitation and radiative decay. If we illuminate a sample with a very short (= 1 ps) laser pulse, all of the Raman... 

When an electron resonance occurs, the temporary capture of an electron at an atomic or molecular site increases the interaction time of the electron at that site in proportion to the resonance lifetime (xa sec) and the inverse of the electron... 

For gas-liquid combinations with relatively small uptake coefficients ( 10 4-10-7), longer interaction times between the gas and liquid are needed than can be obtained with the falling-droplet apparatus. These are provided in a bubble apparatus, a typical example of which is shown in Fig. 5.24. The gas of interest as a mixture with an inert carrier gas is introduced as a stream of bubbles into the liquid of interest. The interaction time is varied by moving the gas injector relative to the surface. The composition of the gas exiting the top of the liquid is measured as a function of the interaction time (typically 0.1-1 s), e.g., by mass spectrometry. The interaction time is limited by the depth in the liquid at which the bubbles are injected and their buoyancy. Longer interaction times and better control over them have been achieved using a modified apparatus in which the bubbles are generated and transported horizontally (Swartz et a.l., 1997). 

Enhancement of the Hght-matter interaction in a microscopic optical cavity is achieved because Hght trapped in the cavity has longer effective interaction time with absorbers. For short laser pulses, cavity length exceeding CTp allows avoidance of the interference between the pulses incident and reflected from the mirrors. Spectral selectivity of planar Fabry-Perot cavities can be used to achieve the localization at the resonant wavelength of the cavity. 

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