Wigner force

WIGNER FORCE. Short-range nuclear force of noncxchangc type postulated phenomenologically as pait of the interaction between nucleons. Postulated exchange forces are Bartlett, Heisenberg, and Majorana forces. 

Campbell s Theorem, 174 Cartwright, M. L., 388 Caywood, T. E., 313 C-coefficients, 404 formulas for, 406 recursion relations, 406 relation to spherical harmonics, 408 tabulations of, 408 Wigner s formula, 408 Central field Dirac equation in, 629 Central force law... 

Assumes that the driving force for reactions between metals is a function of two factors a negative one, arising from the difference in chemical potential, A y of electrons associated with each metal atom, and a positive one that is the difference in the electron density, Anws, at the boundaries of Wigner-Seitz tvpe cells surrounding each atom. Values of for the metals are approximated by the electronic work functions n ws is estimated from compressibility data. The atomic concentrations in the alloy must be included in the calculation. ... 

Electrostatic. Virtually all colloids in solution acquire a surface charge and hence an electrical double layer. When particles interact in a concentrated region their double layers overlap resulting in a repulsive force which opposes further approach. Any theory of filtration of colloids needs to take into account the multi-particle nature of such interactions. This is best achieved by using a Wigner-Seitz cell approach combined with a numerical solution of the non-linear Poisson-Boltzmann equation, which allows calculation of a configurational force that implicitly includes the multi-body effects of a concentrated dispersion or filter cake. 

Wigner (Figure 1-15) was well known for his legendary politeness and modesty that was perceived by some as somewhat forced and artificial. However, there was nothing forced or artificial when he showed modesty in formulating the principal task of physics and stressed the limitations in its ambitions ... 

We know the Coulomb repulsion between two protons. But this force is certainly small compared with those forces of xmknown origin which keep the particles together their range must be of the order of the nuclear radius (10 cm.). Wigner (1933) assumed these to be ordinary central forces falling off with the distance according to a law Heisenberg (1932) proposed a theory where the forces were... 

The use of Wigner type correlation correction to Hartree-Fock energies [78] and/or the inclusion of dispersion forces [79] and/or the use of Cl energies [80] to define different potentials in Monte Carlo simulations of liquid water, underscores the problem on the reliability of ab initio potentials for force fields. Note that at the time the force fields were obtained only semi-empirically, but I was championing the ab initio banner. 

This relation does not hold exactly for an array of spheres. However, heuris-tically, one might expect that for dilute arrays, the force per unit area between two of the spheres may be related to Tn(rb) where ri, represents the Wigner-Seitz cell boundary. This simple form for the pressure arises because the electric field vanishes on the boundary one is thus left only with the osmotic pressure of the counterions. From the previous discussion, n R) Z R Z

effective charge may be small compared to Z. 

Explain why the force between a periodic array of charged colloidal particles is only approximately related to the charge density at the Wigner-Seitz cell boundaries — i.e., show how the derivation of this relation for charged plates in Chapter 5, breaks down for an array of spheres. When might it be a particularly good or bad approximation ... 

Any general theory of nuclear structure suitable for comparison with experiment should include the properties of nuclear forces so far discussed in successive approximations. The first general discussion along these lines of the level systems of complex nuclei was given by Wigner and his collaborators. 

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