Potential energy spherically symmetric

In the case of atomic ions scattered by neutral atoms, the potential is spherically symmetric and depends only on the distance between the colliding particles. For polyatomic systems the potential energy is a function of coordinates of all the atoms involved, consequently it is dependent on... 

In cubic close-packing each molecule is surrounded by twelve others, whose interaction with the central molecule can be represented by a potential function of cubic point-group symmetry in case that the twelve molecules are spherically symmetrical or oriented at random. The energy change produced by this potential function,/say, is... 

Under some circumstances the rotationally anisotropy may be even further simplified for T-R energy transfer of polar molecules like HF (41). To explore this quantitatively we performed additional rigid-rotator calculations in which we retained only the spherically symmetric and dipole-dipole terms of the AD potential, which yields M = 3 (see Figures 1, 3, and 4). These calculations converge more rapidly with increasing N and usually yield even less rotationally inelastic scattering. For example Table 2 compares the converged inelastic transition probabilities... 

A much improved description of PE melts is obtained with a more elaborate potential energy function, based on a spherically symmetric potential energy... 

For a Dirac particle in a central field 4> is spherically symmetrical and A = 0. Setting the potential energy V(r) — e(r), the Dirac Hamiltonian becomes... 

Kohn-Sham equations is rather complicated for an arbitrarily selected set of weighting factors, and has to be derived separately for every different case of interest. For a spherically symmetric external potential and equal weighting factors, however, the Kohn-Sham equations have a very simple form, as shown in Ref. [72], In this case the noninteracting kinetic energy is given by... 

Consider tlie mutual approach of two noble gas atoms. At infinite separation, there is no interaction between them, and this defines die zero of potential energy. The isolated atoms are spherically symmetric, lacking any electric multipole moments. In a classical world (ignoring the chemically irrelevant gravitational interaction) there is no attractive force between them as they approach one another. When tliere are no dissipative forces, the relationship between force F in a given coordinate direction q and potential energy U is... 

Another explanation must therefore be found. Now we know that besides forces of an electrical character there are others which act between atoms. Even the noble gases attract one another, although they are non-polar and have spherically symmetrical electronic structures. These so-called van der Waals forces cannot be explained on the basis of classical mechanics and London was the first to find an explanation of them with the help of wave mechanics. He reached the conclusion that two particles at a distance r have a potential energy which is inversely proportional to the sixth power of the distance, and directly proportional to the square of the polarizability, and to a quantity

excitation energies of the atom, so that... 

If the potential energy, U, and the boundary and initial conditions are spherically symmetrical, then the survival and recombination probabilities are, respectively... 

Because of the unknown characteristic of nuclear forces, many different suppositions have been made, using available experimental evidence, regarding the nature of the potential energy V of a nuclear particle as a function of its position in the field of a nucleus, or of another nuclear particle. To a first approximation, the nuclear potential is assumed to be spherically symmetric, such as V is a function only of the distance r from the center of the field, thus being the same in all directions, and is representable by a curve as m Pig. 1 curves (a) to (f). 

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