Maximum frequency shift

The cornerstone of the recent optical frequency measurements in Paris is the LD/Rb standard laser [51,52,53]. Three identical systems have been built, two at the LPTF and a third in Laboratoire Kastler Brossel. As the two laboratories are linked by two 3 km long optical fibers, it is possible to compare the frequencies of the three systems. The frequency shift due to the fiber has been checked with the highly stabilized titanium-sapphire laser. After a round trip of 6 km through the fibers, a maximum frequency shift of 3 Hz is observed [54]. This shift is completely negligible for the optical frequency measurements. The main metrological features of the LD/Rb laser are a frequency stability (Allan variance) of about 4 X 10-13t-1/2 per laser over 1000 s and a day-to-day repeatability of 400 Hz. 

This rate equation has then to be translated to represent the measured frequency changes. According to the Sauerbrey equation (see Eq.2), the measured frequency difference is proportional to the mass, i.e. the amount, of analyte bound by the ligand [LA. Afm is used to denote the maximum frequency shift upon complete... 

When the maximum frequency shift A/max for an individual experiment, as shown in Fig. 2a, is plotted against the number of cells seeded into the measuring chamber at time zero, we obtained a saturation type relationship that is presented in Fig. 2b. We have interpreted this result as follows as long... 

The maximum mass load over which this linear relation holds corresponds to a maximum frequency shift of about 1% of fq. For fq 5 MHz, this means Af v SOKHz or for example with palladium this yields a deposited thickness of about 7kA. 

Here te, tc are the correlation times of rotational and vibrational frequency shifts. The isotropic scattering spectrum corresponding to Eq. (3.15) is the Lorentzian line of width Acoi/2 = w0 + ydp- Its maximum is shifted from the vibrational transition frequency by the quantity coq due to the collapse of rotational structure and by the quantity A due to the displacement of the vibrational levels in a medium. 

Fig, 3.16. The density-dependence of the frequency shift of the Q-branch maximum. The y values for the curves are in the notation of Fig. 3.15. When plotting the experimental data, the cross-section found in the fitting of the density dependence of the width was employed (Fig. 3.15). 

In the case of gas lasers the discharge conditions, and therefore also the laser intensity, change with the magnetic field strength, and often the maximum Zeeman frequency shift is not limited by technical considerations (greatest possible magnetic fields) but by the fact that the laser intensity drops to zero f... 

One of the most striking features of the scattered spectrum for either neutrons or light in the vicinity of a phase transition is the appearance of a divergent elastic or quasielastic peak centred near zero frequency shift that lies entirely outside the quasiharmonic soft-mode description of the dynamics (Fleury Lyons, 1983). The first observation of a divergence in scattered intensity is due to Yakovlev et ai, (1956), who observed the phenomenon in the a-fi transition of quartz. The scattered intensity increases dramatically, sometimes by a factor of 10000 near and the maximum value of line width of the diverging feature is itself rather small ( 1 cm ). In Fig. 4.7, typical central peaks are shown for the purpose of illustration. 

Fig. 5. Data for frequency shift, Av monomer frequency minus H-bonded frequency), band width at half maximum iq, and integrated molar absorption coefficient per bonded OH minus integrated molar absorption coefficient for monomer, AB. Curves are those...

Fig. 4. The frequency shift Ad of the OH stretching mode over the maximum Ad in linear H-bonds as a function of the H-bond angle /3. This figure also gives the angle dependence of the H-bond energy AH (AH Ad)...

In the case of sbn the phase shift is always exactly = 7t/2 provided that an external electric field is absent (E0 = 0) and there is no frequency shift between the pump and scattered waves. (In the experiments described below, where E0 0, a change of the phase shift <3> of up to 5 % results, which can be neglected. The increase of the space charge field at the maximum field strength of E0 = 4kV/cm is only 15 % in comparison to zero field.)... 

Ac susceptibility measurements performed on the sample with the smallest clusters in a bias field are shown in Fig. 14. x has a maximum that shifts to higher temperature as the bias field increases, while that of x decreases. This apparently contradicts the classical behavior since the bias field reduces the activation energy. This bizarre feature is clarified by the measurements on the larger particles at sufficiently high field (300 Oe), since in that case the maximum, shifted to higher temperature, is not frequency dependent (Fig. 15). Under these conditions, the x response is dominated by the equilibrium susceptibility, and the temperature at the maximum is the temperature of the equilibrium susceptibility Teq 2/uII/kn,... 

Shaped pulses are created from text files that have a line-by-line description of the amplitude and phase of each of the component rectangular pulses. These files are created by software that calculates from a mathematical shape and a frequency shift (to create the phase ramp). There are hundreds of shapes available, with names like Wurst , Sneeze , Iburp , and so on, specialized for all sorts of applications (inversion, excitation, broadband, selective, decoupling, peak suppression, band selective, etc.). The software sets the maximum RF power level of the shape at the top of the curve, so that the area under the curve will correspond to the approximately correct pulse rotation desired (90°, 180°, etc.). When an experiment is started, this list is loaded into the memory of the waveform generator (Varian) or amplitude setting unit (Bruker), and when a shaped pulse is called for in the pulse sequence, the amplitudes and phases are set in real time as the individual rectangular pulses are executed. 

Fig. 10 Representative SLS power spectra from water at 25 °C. The three diffraction orders, 4th, 5th and 6th, correspond to k = 26295, 32431 and 38548 m1, respectively. The frequency shift for the 4th order is indicated by/s while the full width at half-maximum intensity for the 5th order is indicated by Afs...

Fig. 4. Cold collision frequency shift observed in the spectra of a single 120 /rK sample with initial maximum density of 6.6xlO13 cm3. The farthest red shifted spectrum corresponds to the largest density...

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