Siegert functions

However, the Siegert function of eqn. (10) is divergent / V rei ad r oo and the number of particles is not conserved. This non-L2 nature of ipTet has given rise to difficulties in the direct application of Siegert s method to resonant scattering /55/. 

N. Fernandez-Garcia, O. Rosas-Ortiz, Gamow-Siegert functions and Darboux-deformed short range potentials, Ann. Phys. 323 (2008) 1397. 

The Siegert relation is valid except in the case of scattering volumes with a very small number of scatterers or when the motion of the scatterers is limited. We ignore the exceptions, which are rare in common uses of DLS, and consider only autocorrelations of the type shown in Equation (104). As mentioned above, modern DLS instruments use computer-controlled correlators to calculate the intensity autocorrelation function automatically and to obtain the results in terms of the function gi(s,/rf) therefore we only need to concern ourselves here with the interpretation of gi(s,td). 

Solution The given DLS data can be used to obtain the intensity autocorrelation function g,(s,td) by rewriting the Siegert relation as follows ... 

Wendler J, Siegert C, Schelhorn P, Klinger G, Gurr S, Kaufmann J, Aydinlik S, Braunschweig T. The influence of Microgynon and Diane-35, two sub-fifty ovulation inhibitors, on voice function in women. Contraception 1995 52(6) 343-8. 

The normalized electric field autocorrelation function gift), which can be calculated from the normalized intensity autocorrelation function g2(t) = (1(0) 7(f)) (I(0)/2 according to the Siegert relation [56]... 

O.I. Tolstikhin, V.N. Ostrovsky, H. Nakamura, Siegert pseudo-states as a universal tool Resonances, S matrix, Green function, Phys. Rev. Lett. 79 (1997) 2026. 

In a dynamic light scattering experiment, the measured intensity-intensity time-correlation function g<2)(tc), where tc is the delay time, is related to the normalized electric field correlation function g(1)frc), representative of the motion of the particles, by the Siegert relation [18] ... 

Building of a correct Siegert ratio when starting from the inverse of the Siegert ratio. Same parameters as in Table 1. Coluom (a) number of steps. Column (b) ratios of the wave function at two adjacent points. 

If a homodyne method is used, the measured autocorrelation function (g,x) can be interpreted by using the Siegert relation. Equation 5.454. The translational and rotational diffusion coefficients for several specific shapes of the particles are given in Table 5.9. The respective power spectrum functions can be calculated by using the Fourier transform. Equation 5.449b. 

Faaji, R.A., Burgaaf, J., Schoemaker, H.C., Stiekema, J.C.J., Siegert, C., and Cohen, A.F. The influence of renal function on the pharmacokinetics (PK) and pharmacodynamics of the novel antithrombotic agent Org31540/ SR90107A. British Journal of Clinical Pharmacology 1998 45 21 IP. 

In this section we shall see that the incorporation of polarization into the formulation for PCS enables the shape of the particles to be inferred. This is achieved by a modest augmentation of PCS equipment that facihtates the measurement of the cross-correlation of the scattered intensity that has been resolved into different polarization states. The temporal decay of the polarized intensity cross-correlation function is identical to that of the intensity autocorrelation function used in PCS, however it decays from value less than 2, and the difference from 2 is related to the particles departure from a sphere. Before demonstrating precisely how this occurs, it is first necessary to see how polarization generalizes the Siegert relation. 

Since q, T, and q are known, we determine R from the measurement of t. Actually, most commercial software calculate the size assuming that the object is spherical. As mentioned before, the digital correlator gives directly G2(q, t), and therefore, after subtracting the baseline and dividing by baseline, we get by the Siegert relationship a correlation function C(t) given by... 

As proved by Siegert [939] for optical fields with a Gaussian intensity distribution (7.60), the second-order correlation function G x) is related to G x) by the Siegert relation... 

If the light fluctuation is caused by Brownian motion, one can relate the normalised autocorrelation function of the detected light intensity to that of the scattered field by the following equations (Siegert 1943 Xu 2000, pp. 86-89) ... 

The two normalized correlation functions are related by the Siegert equation ... 

The experimentally accessible quantity is the intensity line correlation function g2(t) which is connected to the theoretically simpler correlation function of the electric field, gi(t) via the Siegert relation... 

In most PCS experiments the intensity autocorrelation function G2(0,t) is measured at one or several scattering angles 0 as a function of time delay x. In the first step of the interpretation procedure G2(0,x) is related to the modulus of the normalized field autocorrelation function gi(0,x) by a Siegert relation ... 

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