Collisions, elastic phase changing

Figure 4.2 Two common interactions between light and matter, (a) At certain angles, light is refracted when passing from one medium to another (at dashed line), changing direction and velocity, (b) When light hits a particle, elastic collisions result in changes in direction and phase (Rayleigh scattering), whereas inelastic collisions result in frequency changes (Raman effect).

The elastic collisions do not change the amplitude, but the phase of the damped oscillator is changed due to the frequency shift As(jo R) during the collisions. They are often termed phase-perturbing collisions (Fig. 3.11). 

Figure 4.11 depicts the space-time plot of a head-on quasi-elastic collision with positive phase shifts between two waves of unequal velocity. The slower wave experiences the larger change in wave velocity. Both waves travel with higher velocities after the collision. This situation is reminiscent... 

Numerical calculations have also been performed by Eu (1970) with the variable-phase method. He investigated changes of the opacity versus angular momentum curve for various collision energies and imaginary potentials, and for elastic collisions of K + HBr at energy E= 1-49 kcal/mole. Tables of results were presented in terms of reduced variables. 

In the case of the photoproduction of neutral n mesons, some of the mesons are absorbed before they leave the nucleus. One could try to put a complex (real and imaginary) phase factor into the outgoing wave to take care of attenuation. However, it is also necessary to consider multiple collisions within the nucleus and the associated change in direction. The calculation is obviously no longer that of a simple form factor but a quite formidable undertaking. It becomes a many-body problem. Similar considerations are involved in the elastic scattering of nucleons from complex nuclei. 

So far, we have neglected the fact that collisions also change the velocity of both collision partners. If the velocity component of a molecule is altered by an amount during the collision, the molecule is transferred from one subgroup (u Au ) within the Doppler profile to another subgroup vz+Uz EAv ). This causes a shift of its absorption or emission frequency from CO to co- -kuz (Fig. 3.21). This shift should not be confused with the line shift caused by phase-perturbing elastic collisions that also occurs when the velocity of the oscillator does not noticeably change. 

This causes a shift of its absorption or emission frequency from co to co kuz (Fig. 3.20). This shift should not be confused with the line shift caused by phase-perturbing elastic collisions that also occurs when the velocity of the oscillator does not noticeably change. 

The Fourier transform of the oscillation trains with random phase jumps yields again a Lorentzian line profile as derived in Sect.3.3. Summarizing, we can state that elastic and inelastic collisions which only perturb the phase or amplitude of an oscillating atom without changing its velocity cause homogeneous line broadening. 

---