Local phase shift

The basic scheme for current-density imaging in the laboratory frame is depicted in Fig. 7.4.1 [Seri]. Two current pulses I of total duration tc are applied with opposite polarity in the de- and rephasing periods of a standard spin-echo imaging sequence so that the local phase shifts induced by each of them add constructively. 

In order to realise such a high dynamic range, either a local compensation coil at the location of the SQUID [9] or a gradiometric excitation coil like the double-D coil have to be used. In case of the electronic compensation, the excitation field and the response of the conducting sample is compensated by a phase shifted current in an additional coil situated close to the SQUID-sensor. Due to the small size of this compensation coil (in our case, the diameter of the coil is about 1 mm), the test object is not affected by it. 

For a local potential V(r) which supports bound states of angular momentum i and energy < 0, the phase shift linij Q (Ic)) tends in the lunit of zero collision energy to n. When the well becomes deep enough so as to introduce an additional bound level = 0 at zero energy, then linij ... 

The operation involved in the definition of the EPI is an exchange of atoms on sites i and j and it is a kind of localized perturbation. So the orbital peeling method provides an efficient means for obtaining the generalized phase shifts. 

When experimental results are later introduced, it will be seen that the significance of the final-state scattering in PECO measurements is confirmed by the observation that for C li core ionizations, which must therefore proceed from an initial orbital that is achiral by virtue of its localized spherical symmetry, there is no suggestion that the dichroism is attenuated. The sense of the chirality of the molecular frame in these cases can only come from final-state continuum electron scattering off the chiral potential. Generally then, the induced continuum phase shifts are expected to be of paramount importance in quantifying the observed dichroism. 

The problem now is to determine the derivatives dBz/dx and dBz/dy. This can be done by evaluating the local precession phase shifts caused by the currents, that is... 

By Fourier transforming the EXAFS oscillations, a radial structure function is obtained (2U). The peaks in the Fourier transform correspond to the different coordination shells and the position of these peaks gives the absorber-scatterer distances, but shifted to lower values due to the effect of the phase shift. The height of the peaks is related to the coordination number and to thermal (Debye-Waller smearing), as well as static disorder, and for systems, which contain only one kind of atoms at a given distance, the Fourier transform method may give reliable information on the local environment. However, for more accurate determinations of the coordination number N and the bond distance R, a more sophisticated curve-fitting analysis is required. 

The signal for the 41 amu transient, a measure of the time-dependent rise and fall of BrCH2CH2CH2, rises (xi = 2.5 ps) and then decays (X2 = 7.5 ps), and it shows the same periodic coherent modulation, with a characteristic oscillation time Xc = 680 fs, phased shifted by n radians The local peaks of signal intensity proportionate to the BrCH2CH2CH2 radical concentration match the local troughs of signal decay for the 202 amu periodic modulation they are 180° out of phase. 

In the frame of the theoretical formulation, in which the Penning process is described by the local quantities V+ R), T(/ ), and V+(R), the total cross section can be calculated as either (1) total absorption cross section atotaI from the complex phase shift for scattering by the complex potential V(R)= V (R)- r(R) or (2) as the sum of the partial cross sections a(Pgl), a(AI), and a(QI), into whose calculation also V+(R) enters in the form of matrix elements involving nuclear wave functions in this potential. 

The LS theory was applied to the localization of a Brownian particle in a three-dimensional optical trap [89] a transparent dielectric spherical silica particle of diameter 0.6 pm suspended in a liquid [88]. The particle moves at random within the potential well created with a gradient three-dimensional optical trap—a technique widely used in biophysical studies. The potential was modulated by a biharmonic force. By changing the phase shift between the two harmonics it was possible to localize the particle in one of the wells in very good quantitative agreement with the predictions based on the LS. 

An alternative scheme, which is much easier to handle, is shown in Fig. 2b, where dust or scratches on the cuvette windows serve as local oscillators for the generation of the reference wave. Since the phase of the reference is now fixed with respect to the sample, the phase of the diffracted beam must be controlled instead by shifting the phase of one of the writing beams, and hence of the grating. Due to the first order Bragg condition, the phase shift of the grating translates directly to the phase shift of the diffracted beam. 

Fig. 1 Setup for transient holographic grating measurements. The electro-optic modulators (EOMs) are used for 180°-phase shifts of the holographic grating. The piezo mirror serves for phase matching between the diffracted beam and the coherent reference wave generated by the local oscillator. The setup is a modified version of the one described in [87]...

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