Continuous-wave threshold

Ter Haar, G. R., Daniels, S., and Morton, K. (1986). Evidence for acoustic cavitation in vivo thresholds for bubble formation with 0.75-MHz continuous wave and pulsed beams. IEEE Trans. UFFC 33,162—4. [173]... 

Although (jpg = 0 for energies below EPs, the expression for An given by equation (3.105) can nevertheless be analytically continued below the threshold by replacing the positronium wave number n by i n and so replacing aPs(n) by i(-l)z<7Ps(H), see equation (3.97). Consequently, just above the positronium formation threshold, An is of the form given in equation (3.105), but just below this threshold it is given by... 

The elastic scattering cross section must fall as the positron energy is increased above the threshold, and it will either rise or fall as the threshold is approached from below, depending on the value of l and on the phase shift at the threshold. Furthermore, because the s-wave contribution to crPs, considered as a function of the positron energy, has an infinite slope at the threshold energy EPs, equation (3.99), so too does energy dependence has the shape of either a cusp or a downward rounded step. All other partial-wave contributions to aei, however, continue through the threshold with no discontinuity of slope. 

Several different approximation methods have been used to investigate excitation in positron-helium scattering, but in all cases rather simple uncorrelated wave functions have been used to represent the ground and excited states of helium. All the reported results, which relate almost exclusively to the excitation of 2 S and 21 P states, exhibit a steady rise from the threshold followed by a gentle fall, which continues up to a few... 

Cavitation begins at much smaller intensities when low sound frequencies are applied. Fig. 5 describes how the threshold intensity increases with increasing frequency. Drawing a vertical line at approximately 20 kHz, as one moves up this vertical line, wave intensity increases [W/cm2]. The first thing one encounters as the intensity is increased is the curve for aerated water, or water saturated with air. The intensity at this point is sufficient to produce cavitation as desorbed air contributes to bubble nucleation. As one continues to increase intensity, one will encounter the curve for degassed cavitation. This intensity is the absolute maximum intensity allowed (at standard conditions) for sound traveling in water at this frequency. Most of sonochemistry are performed at intensity levels between these two values. 

Einstein s hypothesis, then, led to two definite predictions. In the first place, there should be a photoelectric threshold frequencies less than a certain limit, equal to 4>/h, should be incapable of ejecting photoelectrons from a metal. This prediction proved to be verified experimentally, and with more and more accurate determinations of work function it continues to hold true. It is interesting to see where this threshold comes in the spectrum. For this purpose, it is more convenient to find the wave length X = c/v corresponding to the frequency /h. If we express in electron volts, as is commonly done, (see Eq. (1.1), Chap. IX), we have the relation... 

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