Crossed position

It is definitely necessary to extend this kind of theory to a general case in which the ordinary transition state and the potential surface crossing position are separated from each other. 

Now we try to control the transition by sweeping the field parameter F as a function of time striding the avoided crossing position F. First, let us consider n periods of oscillation between Fa and Ft,. The final overall transition amplitude Tn is given by... 

The determination of the phase may be accomplished in quite a number of ways. For crude analyses the displacements can be measured directly by means of a dual-beam oscilloscope. One beam is used to display the pumping light the second displays the fluorescence. The difference in zero-crossing positions is then used to calculate the shift. 

In polarimetry and ORD, the sample is placed between the first polarizing element (the polarizer), which remains fixed, and the second element (the analyzer), which can be rotated about the axis of propagation. Maximum intensity of the transmitted light is observed when the principal axis of the polarizer and analyzer are colinear and exactly parallel. The intensity is zero when they are crossed that is, when the principal axes are orthogonal to each other. The most accurate way to determine the rotation angle a is to set the polarizer and analyzer in the crossed position using an achiral substrate and to measure the extent to which the analyzer has to be turned to restore the optical null position when the achiral sample is replaced by a chiral substrate. 

Figure 1.37 Intensity change of polarized light passing through an analyzer when the elliptically polarized light changes. The polarizer and analyzer are in a crossed position. (Reproduced with permission from D.B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging, Wiley-Liss. 2001 John Wiley Sons Inc.)...

Methemoglobln SC Sulfhemoglobin (cross-positive -10% by co-oximeter) methylene blue (2 mg/kg dose gives transient false-positive 15% methemoglobin level) hyperlipidemia (triglyceride level of 6000 mg/dL may give false methemoglobin of 28.6%). 

V,2 R,t) only minimally. Since the shift of Vi R,t) increases with R and viHR,t) remain almost constant, the crossing position Rx(t) moves in a wide range according to its amplitude at each instant. 

The field shape consists of two symmetric half-cycles with zero field amplitude at the pulse center. The upper panel of Fig. 5.13 shows the effective potential curves Vf R,t) obtained under the control field (to = 51 fs). The plotted curves at t = 44 fs represent the maximum shifts of the PECs in the first half-cycle of the control pulse, and those at t = 58 fs represent the maximum shifts in the later half-cycle of the control pulse. In the first half-cycle of the pulse, the control field, through the positive transition amplitude function /xn(7 ), acts to shift the Vn R) potential curve upwards, and thus the dynamical crossing position Rx t) is first shifted to the left. It reaches the leftmost position R ett at the height of the control field, and then is shifted right and restored to 7 cross by t = to- The lower panel of Fig. 5.13 shows the resulting time-dependence of Rx(t). The fact that the... 

From the measured level-crossing positions the fine-structure splitting can be calculated using the Breit-Rabi formula for the fine structure, (2.31). 

In Chap. 7 we have discussed how hyperfine structure can be determined by level-crossing spectroscopy. Clearly, alkali atom states can readily be studied using this technique after stepwise excitation. We will here instead choose an example illustrating fine-structure measurements. In Fig. 9.17 the example of the inverted sodium 4d 5/2,3/2 state is given. From the measured level-crossing positions the fine-structiue splitting can be calculated using the Breit-Rabi formula for the fine structure, (2.31). 

The set-up is similar to the one used in normal saturation spectroscopy but the probe beam is now blocked by crossed polarizers that are placed at opposite sides of the absorption ceU. The polarizer in front of the cell is used to increase the linear polarization of the laser beam, which is frequently already well polarized. A matched pair of polarizers (frequently Gian-Thompson prisms. Fig. 6.46) can have a rejection ratio of 10 to 10 in the crossed position. The pump beam is circularly polarized and induces an anisotropy... 

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