Collision times

When relaxation of the internal motion during the collision is fast compared with the slow collision speed v, or when the relaxation time is short compared with the collision time, the kinetic energy operator... 

In the derivation of the Boltzmann equation, it was noted that the distribution function must not change significantly in times of the order of a collision time, nor in distances of the order of the maximum range of the interparticle force. For the usual interatomic force laws (but not the Coulomb force, which is of importance in ionized gases), this distance is less than about 10 T cm the corresponding collision times, which are of the order of the force range divided by a characteristic particle velocity (of the order of 10 cm/sec for hydrogen at 300° C), is about 10 12 seconds. 

In the derivation of the Boltzmann equation it is assumed that the distribution function changes only in consequence of completed collisions, i.e., the effect of partial collisions is neglected. We shall, therefore, consider the single-particle distribution function averaged23 over a time r, which will (later) be taken large compared with a collision time ... 

Here 0(a) is the density of distribution over a after collision and tc is the average collision time. The popular Keilson-Storer model, presented in Eq. (1.6) and Fig. 1.2, uses the single numerical parameter y to characterize the strength of inelastic collisions. It will be discussed in Section 1.3. 

The validity conditions of the models given in (1.5) and (1.6) are also of great importance [4], though seldom taken into account. Transition between rotational states j and j + 1 is induced only when the product of the transition frequency and the collision time rc is less than 1 ... 

Impact processes with finite collision time 27... 

However, only the left-hand side of the inequality has a clear, although qualitative, physical meaning. As far as collision time tc is concerned, its evaluation as p/ v) in Eq. (1.58) is rather arbitrary. Alternatively, it may be defined as the correlation time of the collisional processes which modulate the rotation. Using the mechanical equation of motion... 

From the above discussion, it is apparent that the exponential asymptotic behaviour of KmU) characterizes the correlation between collisions rather than collision itself. Hence the quantity tm defined in Eq. (1.67) cannot be considered as a collision time. To determine the true duration of collision let us transform Eq. (1.63) to the integral-differential equation as was done in [51] ... 

The latter is negligible in the centre of the spectrum (at < 1) which looks like a pure Lorentzian, as in the impact approximation with HWHH 1/t. Only far wings are affected at finite collision time tc. When, however, k > 1 /4 (fc2 = ), the situation changes drastically. To describe it let us... 

It clearly shows that perturbation theory is valid and the Mori approach is identical to it in this limit. However, the impact approximation is unacceptable since the collision time tc exceeds ij. This is a fact of principal importance in understanding Poley absorption and related phenomena. At such a condition, the libration maxima appear in spectra... 

Burshtein A. I., McConnell J. Spectral estimation of finite collision times in liquid solutions, Physica A157, 933-54 (1989). 

Sodium-molecule collision time 150 /LIS Peak D2 cross section for natural linewidth 1.1 IQ- m ... 

Luminescence lifetime spectroscopy. In addition to the nanosecond lifetime measurements that are now rather routine, lifetime measurements on a femtosecond time scale are being attained with the intensity correlation method (124), which is an indirect technique for investigating the dynamics of excited states in the time frame of the laser pulse itself. The sample is excited with two laser pulse trains of equal amplitude and frequencies nl and n2 and the time-integrated luminescence at the difference frequency (nl - n2 ) is measured as a function of the relative pulse delay. Hochstrasser (125) has measured inertial motions of rotating molecules in condensed phases on time scales shorter than the collision time, allowing insight into relaxation processes following molecular collisions. 

When particle impacts with a solid surface, the atoms of the surface layer undergo crystal lattice deformation, and then form an atom pileup on the outlet of the impacted region. With the increase of the collision time, more craters present on the solid surface, and amorphous transition of silicon and a few crystal grains can be found in the subsurface. 

The soft-core model may be more convenient in molecular dynamics simulation, since a continuously differentiable potential is available to calculate the force. In the case of a hardcore potential, collision times of all atom pairs have to be monitored and used to control the time step. 

Particles are moved along their current velocity vectors without undergoing interactions for a time At which is chosen smaller than the mean collision time. If a particle hits the domain boundary, its velocity vector is modified according to the corresponding boundary condition (for example specular or diffuse reflection if a particle hits a wall) ... 

Cross-sections for reactive scattering may exhibit a structure due to resonance or to other dynamical effects such as interference or threshold phenomenon. It is useful to have techniques that can identify resonance behavior in a system and distinguish it from other sorts of dynamics. Since resonance is associated with dynamical trapping, the concept of the collision time delay proves quite useful in this regard. Of course since collision time delay for chemical reactions is typically in the sub-picosecond domain, this approach is, at present, only useful in analyzing theoretical scattering results. Nevertheless, time delay is a valuable tool for the theoretical identification of reactive resonances. 

Treating the free electrons in a metal as a collection of zero-frequency oscillators gives rise51 to a complex frequency-dependent dielectric constant of 1 - a>2/(co2 - ia>/r), with (op = (47me2/m)l/2 the plasma frequency and r a collision time. For metals like Ag and Au, and with frequencies (o corresponding to visible or ultraviolet light, this simplifies to give a real part... 

---