Spherically averaged potential

Here V(r) is the spherically averaged potential of the electrons and does not contain additional hyperfine operators. The sought matrix element... 

For many potential energy surfaces with barriers, the dominant term in a Legendre polynomial expansion of the interaction potential is the leading term, that is. the spherically averaged potential ... 

The spherically-averaged and collinear distortion potentials can be considered as two limiting cases. Thus, the spherically-averaged potential averages over all possible configurations of the atom with respect to the molecule, leading to a potential that will be too repulsive in general. The collinear distortion potential, on the other hand. 

Figure 7. Spherically averaged potentials, in K, for the O2 - O2 interaction small-dash line, [9j large-dash line, [10] solid line, this work.

Fig. 5. Best-fit spherical average potential (Vq) and anisotropic potential for parallel (V ) and perpendicular (Vj ) configurations (Ref. 48) compared with the corresponding results of Thuis et al- (Ref. 55). ...

Fig. 2. Comparison between the Vq terms of the potential surface (spherical average potential) for Ne-NO, Ne-O and Ne-N2 from this work and the interatomic potential for the corresponding isotropic Ne-Ar system from Ref. 5.

In Fig. 2 we report the spherical average potential Vq(R) for the Ne-N2/ O2 and NO systems compared with the corresponding isotropic Ne-Ar case. The Vq(R) term, i.e., thefirst term in the Legendre expansion or the potential surface, is easily obtained from the full PES by a Gauss-Legendre quadrature, according to the formula ... 

The actual form of the Hamiltonian H assumes that the nucleus can be treated as a point charge. Since exact solutions, i.e. those based on an explicit form of the Coulomb interaction, are only known in the one-electron cases, some method of approximation must be utilized. This is usually the central-field approximation. Each electron is assumed to move independently in the field of the nucleus and an additional central field composed of the spherically averaged potential fields of each of the other electrons in the system. In other words, each electron is treated... 

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