Collisions Fermis model

By virtue of their enormous size and comparatively high stability against radiative decay, high Rydberg states are very susceptible to collisions. Indeed, some of the detectors which are used to observe them, such as the thermionic diode (see section 8.16) depend for their operation on the presence of collisions. Collisions between excited species affect ionisation and recombination rates in such diverse environments as gaseous nebulae [41], laboratory plasmas [42] and flames [43] their study is therefore of some considerable intrinsic interest. 

---

It is not absolutely necessary to have accurate interatomic potentials to perform reasonably good calculations because the many collisions involved tend to obscure the details of the interaction. This, together with the fact that accurate potentials are only known for a few systems makes the Thomas-Fermi approach quite attractive. The Thomas-Fermi statistical model assumes that the atomic potential V(r) varies slowly enough within an electron wavelength so that many electrons can be localized within a volume over which the potential changes by a fraction of itself. The electrons can then be treated by statistical mechanics and obey Fermi-Dirac statistics. In this approximation, the potential in the atom is given by ... 

Step 3. The next problem is to choose (by chance) the momentum of the nucleon (in the target) which has been struck. The uniform density model of the nucleus has a concomitant Fermi momentum sphere whose size is fixed by the number of particles in the nucleus and the radius of the nucleus. The momentum intervals must be equally subdivided taking into account the probability (i.e. cross-section) for a nucleon-nucleon collision for particles with various momenta with the incoming particle. 

Next we briefly discuss how other models of collision-induced ISC can be applied to intermolecular magnetic quenching. According to Selwyn and Steinfeld (1969) and Thayer and Yardley (1972,1974), the transition rate due to collisional quenching can be calculated by using the Fermi golden rule. 

The experimental observables ascribed to the preequilibrium mechanism have usually been interpreted in the context of the exciton model (Griffin et al. 1966 Blann et al. 1975). In the basic model, the nucleus is treated as a Fermi gas in which the projectile initiates a series of sequential N-N collisions, generating unstable particle-hole states, or excitons exciton = a particle-hole pair). The number of excitons is thus proportional to the degree of thermalization. 

For heavy-ion collisions well above the Fermi energy, models predict a low probability for composite-nucleus formation. Instead, most of the cross section is predicted to go into reactions that can be generalized as "participant—spectator reactions (O Fig. 3.44). In the participant-spectator scenario, the participant source is defined by those nucleons that occupy the geometrical overlap volume of the target and projectile, which is impact-parameter dependent. 

S A point source in an infinite medium is emitting neutrons of zero lethargy isotropically at a constant rate in time. Assume that the slowing-down process may be described by means of the Fermi age model once the first collision has occurred. Thus at points of first collision, the neutrons enter a continuous slowing-down process. 

These results are entirely consistent with those of our previous analysis of the bare reactor using the Fermi age model (refer to Sec. 6.3). In this formulation, Eq. (8.281a) describes the neutron-energy spectrum and is easily recognized as the integral equation for the collision density in an infinite homogeneous system. If we select, for example [cf. Eq. (4.36)],... 

The observed first power relation between resistivity and temperature implies that the collision velocity must not only be independent of the applied field and be much greater than the drift velocity but must also be independent of temperature, which rules out the thermal velocity as the motion responsible for the observed collision rate. With the discovery of quantum mechanics, the difficulties encountered by the classical electron gas model are resolved by having the electrons travel at the Fermi velocity. 

In order to evaluate the influence of phonon versus electron friction it is necessary to have models which include both aspects. Although many models for electron-hole pair excitation are available, most of these do not also consider the phonon excitation, and they are therefore not able to discriminate between the two processes. The model which is proposed by Metiu and coworkers [256] as well as Billing [262] assumes that the effective charge on the incoming molecule or adsorbate through Coulomb interaction with the metal-electrons excites these from levels below to levels above the Fermi level. Below we describe the semiclassical model proposed by Billing. This model has a collision-oriented aspect and treats the excitation processes to infinite order. 

---