Spatially separated fields

Atomic clocks represent one of the basic applications of atom physics, for the precise measurement of time is one of the most important needs of present-day civilization. The most familiar are atomic clocks using a microwave transition in Cs. In 1967, an international standard was introduced for the second 1 second = 9192631770 cycles of the standard Cs transition. Cesium atomic clocks use the magnetic sorting of sublevels in Cs and the method of spatially separated fields (Ramsey 1987) to... 

Ri does not show any phase transition. This should not be terribly surprising, since, in the deterministic limit, Ri exhibits either class 2 behavior (i.e. periodicity) or class 4 behavior (spatially separated propagating structures with an ill-defined statistical limit). The density p therefore has no well-defined statistical mean for p = 1 and the periodicity and/or propagating structures are rapidly destroyed (and thus p — 0) whenever p < 1. Moreover, from the above mean-field... 

Fig. 13.12 Photographs of sonoluminescence from sulfuric acid solution of Na2SC>4, illustrating the spatial separation of sodium (orange) and continuum (blue-white) emissions using a horn-type transducer at 20 kHz (a) [38] (Reprinted from American Chemical Society. With permission) and using standing-wave fields at 28 kHz in a cylindrical beaker (b) [39]...

Hardness and softness as chemical concepts were presaged in the literature as early as 1952, in a paper by Mulliken [138], but did not become widely used till they were popularized by Pearson in 1963 [139]. In the simplest terms, the hardness of a species, atom, ion or molecule, is a qualitative indication of how polarizable it is, i.e. how much its electron cloud is distorted in an electric field. The adjectives hard and soft were said to have been suggested by D.H. Busch [140], but they appear in Mulliken s paper [138], p. 819, where they characterize the response to spatial separation of the energy of acid-base complexes. The analogy with the conventional use of these words to denote resistance to deformation by mechanical force is clear, and independent extension, by more than one chemist, to the concept of electronic resistance, is no surprise. The hard/soft concept proved useful, particularly in rationalizing acid-base chemistry [141]. Thus a proton, which cannot be distorted in an electric field since it has no electron cloud (we ignore the possibility of nuclear distortion) is a very hard acid, and tends to react with hard bases. Examples of soft bases are those in which sulfur electron pairs provide the basicity, since sulfur is a big fluffy atom, and such bases tend to react with soft acids. Perhaps because it was originally qualitative, the hard-soft acid-base (HSAB) idea met with skepticism from at least one quarter Dewar (of semiempirical fame) dismissed it as a mystical distinction between different kinds of acids and bases [142]. For a brief review of Pearson s contributions to the concept, which has been extended beyond strict conventional acid-base reactions, see [143],... 

The lessened value of dV/dx within the semiconductor in the high surface state case tends to increase the loss of active electrons by means of hole—electron pair recombination because the rate of spatial separation of the electron from its hole, which was formerly encouraged by the electric fields sending the oppositely charged entities in die opposite directions, is now diminished. 

When piezoelectric fields are taken into consideration, the oscillator strength of GalnN/GaN quantum wells decreases strongly with increasing well width or increasing magnitude of the field [6], This is due to the spatial separation of the electron and hole wavefimctions in the case of wide wells and strong fields. 

Time-resolved photoluminescence was also used to show that the spatial separation of the electron and hole wavefunctions due to the piezoelectric fields in GalnN/GaN QWs leads to a dramatic reduction in oscillator strength, particularly for thick quantum wells [6]. Due to the reduced oscillator strength for the lowest energy state, the optical absorption spectrum of the quantum wells is expected to be dominated by highly excited states close to the strained bulk bandgap. 

In contrast to the recoil-stopping methods, as used in He-jet systems or mass separators, where ion sources are utilized, recoil-separation techniques use the ionic charge and momentum of the recoiling fusion product obtained in the reaction process. Spatial separation from the projectiles and other reaction products is achieved by combined electric and magnetic fields. The... 

When charges of opposite sign are spatially separated, a potential difference develops. This potential difference between two unit volumes at Xj and x, opposes the attempt at charge segregation. The faster-moving positive ions face strong opposition from the electroneutrality field and they are slowed down. In contrast, the slower-... 

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