Quadrupole shape oscillations

An original method involves quadrupole oscillations of drops K The drop (a) in a host liquid (P) is acoustically levitated. This can be achieved by creating a standing acoustic wave the time-averaged second order effect of this wave gives rise to an acoustic radiation force. This drives the drop up or down in p, depending on the compressibilities of the two fluids, till gravity and acoustic forces balance. From then onwards the free droplet is, also acoustically, driven into quadrupole shape oscillations that are opposed by the capillary pressure. From the resonance frequency the interfacial tension can be computed. The authors describe the instrumentation and present some results for a number of oil-water interfaces. 

In recent years, several theoretical and experimental attempts have been performed to develop methods based on oscillations of supported drops or bubbles. For example, Tian et al. used quadrupole shape oscillations in order to estimate the equilibrium surface tension, Gibbs elasticity, and surface dilational viscosity [203]. Pratt and Thoraval [204] used a pulsed drop rheometer for measurements of the interfacial tension relaxation process of some oil soluble surfactants. The pulsed drop rheometer is based on an instantaneous expansion of a pendant water drop formed at the tip of a capillary in oil. After perturbation an interfacial relaxation sets in. The interfacial pressure decay is followed as a function of time. The oscillating bubble system uses oscillations of a bubble formed at the tip of a capillary. The amplitudes of the bubble area and pressure oscillations are measured to determine the dilational elasticity while the frequency dependence of the phase shift yields the exchange of matter mechanism at the bubble surface [205,206]. 

Conclusions We have established that the light Br and Rb isotopes presented here have very large quadrupole deformations of s 0.4 and moments of inertia close to the rigid body values. The odd proton in the 431 3/2+ Nilsson orbit polarizes and stabilizes the y-soft, shape coexistent Se and Kr cores into definite prolate triaxial shapes. This effect sets in at rather low spin and seems to be intimately connected with the suppression of pairing correlations near the N = Z = 38 gap developing at 82 = 0.4. We thus face a cumulative suppression of both proton and neutron pairing correlations in the same oscillator shell, a fairly unique feature in the periodic table. 

The intensity of the absorption process is then proportional to the square of the transition matrix element connecting the initial ((pi) and final (delta function which ensures that it satisfies the conservation of energy theorem. The elimination of the spatial dependence of the electric field corresponds to a series expansion of its /l7rz/x dependence up to the first term (linear dependence in r equation (1)) this yields the dipole approximation of the interaction energy between the atom electronic cloud and the X-ray radiation field. Better approximations will include quadrupole, octupole and so forth terms. However, except in few cases, some of them here detailed, the dipole approximation gives a quantitative analysis of the XANES shape and EXAFS oscillations. 

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