Oscillating particle distributions

The use of more realistic potentials, including both repulsive and attractive contributions, results in the more smooth intermediate order curves G(r). As previously, they reveal oscillations thus reflecting the specific law of mutual particle distribution in dense systems. 

The behaviour of the correlation functions shown in Fig. 8.5 corresponds to the regime of unstable focus whose phase portrait was earlier plotted in Fig. 8.1. For a given choice of the parameter k = 0.9 the correlation dynamics has a stationary solution. Since a complete set of equations for this model has no stationary solution, the concentration oscillations with increasing amplitude arise in its turn, they create the passive standing waves in the correlation dynamics. These latter are characterized by the monotonous behaviour of the correlations functions of similar and dissimilar particles. Since both the amplitude and oscillation period of concentrations increase in time, the standing waves do not reveal a periodical motion. There are two kinds of particle distributions distinctive for these standing waves. Figure 8.5 at t = 295 demonstrates the structure at the maximal concentration... 

Figurell.8 The parabola shows the harmonic oscillator potential. The horizontal lines show the energy levels, which are equally spaced for the quantum harmonic oscillator. The lowest level has energy liv/2. This is called the zero-point energy. The curve on each horizontal line shows tp x), the particle distribution probability for each energy level.

Inelastic collisions of swift, charged particles with matter are completely described by the distribution of generalized oscillator strengths (GOS s) characterizing the collision. These quantities, characteristic of excitation in the N-electron target (or, in fact, of a dressed projectile as well [1]) from some initial state 0) to a final state n) and concomitant momentum transfer, can be written... 

The opportunity of creation of oscillating system in the structure with braking potential field, which were made by the distributed potentials and accelerating potential, is shown. The particle in such the field will make fourfold process of braking and accelerating. 

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