Long-range fields

With regard to your second remark I would like to say this The calculations I showed for CaF and BaF Rydberg states are examples where the core field is a Coulomb field but where a very strong dipole field is superimposed. Here we have used the generalized version of quantum defect theory, which takes account of this modified long-range field. 

The motion of particles is affected by the short-range interparticle forces such as the van der Waals force, electrostatic force, and collision force. It is also affected by the long-range field forces such as the gravitational force, electric force, and magnetic force. This section discusses the basic relationships which quantify these interparticle and field forces. 

The excess collision-induced pair polarizability of molecules A and B results as a self-consistent solution of a set of equations for local fields polarizing molecules A and B and the multipolar moments induced in molecules A and B. In a first approximation, the long range field-induced change in the pair polarizability, related to the linear multipolar polarizabilities of molecules, is [27] ... 

Let us introduce the Weiss (long-range) field constant W( > 0 which generates an internal field Hm proportional to the magnetisation... 

Arcus and Hall reported long range field effects in a kinetic study of quaternization of poly(4-N,N-dimethylamino-styrene) with methyl iodide in DMF. Two homopolymers with different molecular weights, and one copolymer composed of a 2 1 styrene 4-N,N-dimethy1-aminostyrene monomer mixture were quaternized along with gj-isopropyl N,N-dimethylaniline and N,N-dimethylaniline as low molecular weight analogues. The two model compounds exhibited normal Sj 2 kinetics. However, a rate deceleration was observed when the extent of quaternization of each of the three polymers reached 20 25%. The initial... 

Any element of a liquid experiences forces across its surface that arise from the presence of the surrounding liquid. These forces are the contact or surface forces and arise from the molecular action between adjacent elements or particles of liquid. There may also be forces produced by the effects of long-range fields such as the gravitational field. These forces act throughout the liquid on all its elements and are called body forces. 

The use of Lamb waves offers the possibility of rapid long-range in-service inspection. Receiver and transmitter probes are positioned single sided - access is only required from one side of the specimen - in a pitch-catch-arrangement, the receiver being outside tbe field of the specular reflection. 

A related phenomenon with electric dipoles is ferroelectricity where there is long-range ordermg (nonzero values of the polarization P even at zero electric field E) below a second-order transition at a kind of critical temperature. 

Figure A3.14.13. Further examples of the various Turing patterns observable in a 2D gel reaetor. (a) and (b) spots, (e) and (d) stripes, (e) and (1) wider field of view showing long-range defeets in basie stnietine. The seale bar alongside eaeh figure represents 1 nnu. (Reprinted with pemrission from [39], The Ameriean Institute of Physios.)...

Two colliding atoms approach on tire molecular ground-state potential. During tire molasses cycle witli tire optical fields detuned only about one line widtli to tire red of atomic resonance, tire initial excitation occurs at very long range, around a Condon point at 1800 a. A second Condon point at 1000 takes tire population to a 1 doubly excited potential tliat, at shorter intemuclear distance, joins adiabatically to a 3 potential, drought to be die... 

Oq, and, if die trap cycle field couples to die 0 long-range molecular state [57], die second Condon point occurs at 60 <3q. Survival against radiative relaxation improves greatly because die optical coupling occurs at much shorter... 

But the methods have not really changed. The Verlet algorithm to solve Newton s equations, introduced by Verlet in 1967 [7], and it s variants are still the most popular algorithms today, possibly because they are time-reversible and symplectic, but surely because they are simple. The force field description was then, and still is, a combination of Lennard-Jones and Coulombic terms, with (mostly) harmonic bonds and periodic dihedrals. Modern extensions have added many more parameters but only modestly more reliability. The now almost universal use of constraints for bonds (and sometimes bond angles) was already introduced in 1977 [8]. That polarisability would be necessary was realized then [9], but it is still not routinely implemented today. Long-range interactions are still troublesome, but the methods that now become popular date back to Ewald in 1921 [10] and Hockney and Eastwood in 1981 [11]. 

The function /(r) is a force-switching function that goes smoothly from 1 ar r = 0 to 0 at r = Tc. The long-range part of the field, i.e., what remains from the complete Coulomb field ... 

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