Splitting frequencies

The magnetic interaction of the Is electron in the nucleus causes a hyperfine splitting in the ground state of hydrogen and heavier isotopes. In particular, the 1.4 GHz splitting frequency in hydrogen, corresponding to a transition... 

The method takes advantage of an excite and probe technique with polarization selective detection. A circularly polarized pxnnp pulse of ps duration generates a coherent superposition of atomic substates. The coherence induces an optical anisotropy in the atomic sample, which oscillates exactly with the splitting frequency of the respective substates. 

The relaxations for the ground and excited state are included by Yg and Ye- w° is the population difference generated by the pump pulse and and are the hyperfine splitting frequencies of the respective states. 

Fig. 3a shows a measurement of the beat structure in the Di-line of cesium. The two hyperfine splitting frequencies of the ground and excited state clearly show up. The fast oscillation corresponds to the splitting of the ground state, while the envelope with the smaller frequency results frran the splitting in the excited state. The difference between the measured and calculated oscillating depths can be explained by the finite pulse duration. 

The Fourier transformed signal in Fig. 3b clearly shows the hyperfine splitting frequencies of the excited state with 1.2 GHz and the ground state with 9.2 GHz. Since the beat structure can be described as an amplitude modulation of the fast oscillation with the excited state split-... 

The measurement on the Dg-line in Fig. shows fast beats at 9.2 GHz and only one period of slow oscillation at 200 MHz, which is due to the hyperfine splitting frequencies of the 6p P3 -state. 

The applied method is an extension of a previously described technique [I] of time-resolved polarization spectroscopy into the femtosecond range. It relies on the creation of a coherent superposition of adjacent states or substates by an optical pulse, which is short compared to the reciprocal of the frequency splitting of the respective states. Such an atomic coherence causes an optical anisotropy in the sample, oscillating exactly with the splitting frequency of the coherently excited states. 

Comparison of measured and calculated signal shows that a very satisfactory explanation of the observed signal form is achieved. The beat structure can be understood in terms of atomic coherence between substates yielding an amplitude modulation of optical coherence. The fast decay is mainly determined by Doppler dephasing, however, is also slightly influenced by the excited state splitting frequency. 

In a second experiment, using the same technique, the hyperfine splitting frequencies of the metastable 4s4p P2 state of Ca were measured. They provided the spectroscopic B factor which contains the electric quad-rupole moment of the nucleus (see also Section 5.3). 

Ezekiel and co-workersstabilized a 1772-MHz microwave oscillator with reference to the Na ground state hyperfine structure splitting frequency via a resonance Raman transition in a beam of sodium atoms. The experiment involved a dye laser beam with frequency a>i, from which a laser field of frequency 0)2 was generated by an acousto-optic frequency shifter driven with the oscillator. 

Choi et al. (1998) proposed a generalized bubble-growth model on mean bubble size and frequency for Geldart s Group A, B, and D particles. The model made use of empirical correlations for volumetric bubble flux and bubble splitting frequency. The proposed model correlated well with the extensive data reported in the literature on mean bubble size and frequency. They also found that the equilibrium bubble diameter increased linearly with the ratio of volumetric bubble flux to the splitting frequency of a bubble. 

The scaling up from one bed size to another was based by Horio et al. [1986] on the following similarity conditions, derived from their bubbling bed model. Eor identical bubble fraction, size distribution, and splitting frequency, the following condition has to be satisfied ... 

Fig. 57. The evolution of LA phonon peak position as a function of the temperature and the unnormalized phonon energy (Liu 1989b). It gives qualitatively the shape of the LA phonon dispersion curve near the mode splitting frequency. All frequencies are in units of t].

Doublet patterns were observed for 2,6 and 3,5 protons with a splitting frequency of 9.7 kHz. Doublet patterns were also seen in 2 , 6 and 3 , 5 protons, although they were mixed with the dipolar patterns of the a methyl and 7 protons by spin exchange. It is noted that the doublet patterns for 2 , 6 and 3 , 5 protons have splitting frequencies slightly different from those of 2,6 and 3,5 protons. 

Line broadening is included by convoluting I(Av) with a narrow Gaussian distribution function. If necessary, motional averaging can be included by considering instantaneous values of the quadrupole splitting frequency. 

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