Propagator heavy particle

We will describe, in some detail, one such modification, an effective Dirac equation (EDE) which was derived in a number of papers [7, 8, 9, 10]. This new equation is more convenient in many applications than the original BS equation, and we will derive some general formulae connected with this equation. The physical idea behind this approach is that in the case of a loosely bound system of two particles of different masses, the heavy particle spends almost all its life not far from its own mass shell. In such case some kind of Dirac equation for the light particle in an external Coulomb field should be an excellent starting point for the perturbation theory expansion. Then it is convenient to choose the free two-particle propagator in the form of the product of the heavy particle mass shell projector A and the free electron propagator... 

A second type of experiment that can give complementary information to that described above is collision-induced two-photon absorption. When we observe collision-induced absorption followed by fluorescence we can study the evolution of the system from the absorption event to the completion of the collision. Re-emission of a photon before completion of the collision is possible, but unlikely, due to the large difference, for a heavy particle collision, between a spontaneous emission decay time, Yn > and a colli-sional duration, Tq typically Yn C 10 . This type of process is easier to observe in absorption to higher lying states. We could as shown in Fig. 5 look for the absorption of a second laser photon before the completion of the collision. This type experiment probes propagation between two regions in a collision complex. This is just about the maximum amount of information one can hope to obtain about a collision complex. Experiments of this type may be the best way to further constrain and test any conclusions from collision dynamics obtained from the single photon experiments. 

Preceding discussions (in this chapter and Chapter 8) relate to problems attending the measurement of propagation rates in heavy-metal azides. The alternative of calculating the maximum, steady-state detonation rates in these azides from first principles is not well established. Nevertheless, a one-dimensional thermohydrodynamic model does exist which can yield reasonable values for detonation properties (velocity, pressure, product density and composition, particle velocity, etc.) [113-119]. 

Neutrons are particles liberated in fission of in nuclear reactors or by pelting heavy nuclei with GeV protons in spallation sources. They propagate with a finite velocity v. and according to the laws of kinematics, a neutron with mass rn= 1.675 g has a kinetic energy... 

As discussed in Sect. 2.2 the diffusion equation has the well-known unrealistic feature that localized disturbances spread infinitely fast, though with heavy attenuation, through the system. In that section we described three approaches to address the unphysical behavior of the diffusion equation and reaction-diffusion equation. Since the Turing instability is a diffusion-driven instability, it is of particular interest to explore how this bifurcation depends on the characteristics of the transport process. In this section, we address the effects of inertia in the dispersal of particles or individuals on the Turing instability. Does the finite speed of propagation of perturbations in such systems affect Turing instabilities We determine the stability properties of the uniform steady state for the three approaches presented in Sect. 2.2. 

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