Atomic population operators

Since there is no operator that produces the atomic population, it is not an observable and so the procedure for computing N(k) is arbitrary. There are two classes of methods for computing the atomic population those based on the orbital population and those based on a spatial distribution. ... 

A far-off resonance trap (FORT), in contrast, uses tire dipole force ratlier tlian tire spontaneous force to confine atoms and can therefore operate far from resonance witli negligible population of excited states. A hybrid MOT/dipole-force trap was used by a NIST-Maryland collaboration [26] to study cold collisions, and a FORT was... 

Figure lb shows a four-level system. The terminal level, level 2, is ordinarily empty. Atoms are optically pumped to level 4. From level 4, the atoms make a rapid radiationless transition to level 3. The first few atoms to arrive begin to contribute to the population inversion. Therefore, laser operation can begin with much less intense pumping light. After the laser transition, the atoms return to the ground state (level 1) by a radiationless transition. 

Such changes in the defect population can be critical in device manufacture and operation. For example, a thin him of an oxide such as SiO laid down in a vacuum may have a large population of anion vacancy point defects present. Similarly, a him deposited by sputtering in an inert atmosphere may incorporate both vacancies and inert gas interstitial atoms into the structure. When these hlms are subsequently exposed to different conditions, for example, moist air at high temperatures, changes in the point defect population will result in dimensional changes that can cause the him to buckle or tear. 

In Fenske and Hall s parameter-free SCF calculations (80-84), the He1t 1-electron operator is substituted by a model 1-electron operator that has a kinetic energy and potential energy term for each atomic center in the complex. This approach assumes that the electron density may be assigned to appropriate centers. The partitioning of electron density is done through Mulliken population analyses (163) until self-consistency is obtained. The Hamiltonian elements are evaluated numerically, and the energies of the MO s depend only on the choice of basis functions and the intemuclear distance. 

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