Point-particle interaction

Fuzzy spheres. Radially varying dielectric response, 79 "Point-particle" interactions, 79 Point-particle substrate interactions, 85 Particles in a dilute gas, 86 Screening of "zero-frequency" fluctuations in ionic solutions, 89 Forces created by fluctuations in local concentrations of ions, 90 Small-sphere ionic-fluctuation forces, 91... 

By virtue of simplifications similar to those permitted in formulating point-particle interactions, many results can be derived for the interaction of thin cylinders. It is even possible to include the anisotropy of material within the rod, for example putting ecl and eC for the dielectric response perpendicular and parallel to the rod axis. There are then two kinds of A s [see Table C.4 and Eqs. (L2.224)] ... 

Screening factor for point-particle interaction + I rn) energy. 

Table S.8. Point-particle interaction in vapor, like particles without retardation screening...

The [ct i n)f if )]/ [A7tem(ifn) 2 in expressions for point particles becomes a3b3 ((eea 2em)) fo+20 Irksome mks-cgs worries disappear because of canceling s0 s and 4jt s. From gap (l) derived for point-particle interactions, the interaction between spheres at relatively large center-to-center separation z a, b becomes... 

Expanding the integrand to lowest order in N and then integrating in p yields a point-particle interaction that consists of three terms,... 

Let denote the set of vectors that locate each center of mass of each of the atoms in the system, = ri, F2,. .., r/v. The particles in the system each have d degrees of freedom. We assume that the N point particles interact through... 

Here a denotes the maximum field amplitude, rj is the ellipticity together with the pulse-shape function g(rj), which depends on the phase rj = (ot — k r. The laser beam is characterized by the frequency co and the wave vector k with ck = co. The transversality condition implies k A — 0. For a charged point particle interacting with this external electromagnetic field, the Hamilton-Jacobi equation reads... 

Furthermore, we can extend the theorem to a collection of point particles interacting with each other in any desired way but influenced by external forces only through a spherically symmetric potential function. If we describe such a system by using the polar coordinates of each particle, the Lagrangian function is... 

RICHMOND [5.103] and IMURA and OKANO [5.98] have discussed the nonretarded interaction of a rod (or ellipsoid) and a half-space. The more restricted cases of point particles interacting with a half-space has been given by PARSEGIAN [5.40] and of a point particle with a multilayered half-space, as in physical absorption, by MAHANTY and NINHAM [5.104]. 

The definition of z depends on the explicit choice of the electron-nucleus attraction potential energy. If it is of the form of point particle interactions as in Eq. (6.3), V r) = —Ze lr, the choice for z is as given above. In general, one may write z = — -i (compare section 6.9). These substitutions help to rewrite the system of coupled differential equations as. 

The model chosen for the liquid solvents is an immiscible mixture of two atomic liquids whose intra- and interspecies interaction potential energies are different. The A and B liquids are modelled by point particles interacting through a Lennard-Jones potential ... 

Here Az is the thickness of a narrow layer adjacent to the wall in which the momentum transfer occurs. This layer is ill defined, because we consider point particles interacting with a completely smooth wall. Fortunately the final result does not require to specify Az assumed to be the same for all particles. We define the collision time, i.e. the time a particle spends inside the layer. At, via = 2Az/Af, i.e. 

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