Proton electric charge distribution

Electric quadrupole interaction. Although the magnetic dipole interaction is responsible for the largest contribution to the observed hyperfine structure, the finite extent of the nuclear electric charge distribution is also significant in many cases. We therefore consider the electrostatic interaction between a proton at the point r and an electron at the point r, given by... 

In considering the physical forces acting in fission, use may be made of the Bohr liquid drop model of the nucleus. Here it is assumed that in its uonual energy state, a nucleus is spherical and lias a homogeneously distributed electrical charge. Under the influence of the activation eneigy furnished by the incident nentron, however, oscillations are set up which tend to deform the nucleus. In the ellipsoid form, the distribution of the protons is such that they are concentrated in the areas of the two foci. The electrostatic forces of repulsion between the protons at the opposite ends of the ellipse may then further deform the nucleus into a dumbbell shape. Rrom this condition, there can be no recovery, and fission results. 

Nuclei with a spin number 7 of one or higher have a nonspherical charge distribution. This asymmetry is described by an electrical quadrupole moment, which, as we shall see later, affects the relaxation time and, consequently, the linewidth of the signal and coupling with neighboring nuclei. In quantum mechanical terms, the spin number 7 determines the number of orientations a nucleus may assume in an external uniform magnetic field in accordance with the formula 27+1. We are concerned with the proton whose spin number 7 is 1/2. 

More relevant for our purposes are models for oxides in which, in some way, the affinity of charge-determining ions is related to the surface electric fleld For example, in the theoiy of Hiemstra et al. proton affinities are computed in terms of bond distances, coordinations and charge distribution in the solid surface, i.e. it is essentially an energy Interpretation. For several oxides there are arguments that this is an acceptable approximation. This model also showed that not all potentially available sites are titrated in the usual pH range. 

The quadrupolar nature of deuterium is due to the nonspherical charge distribution at the nucleus, caused by the presence of the neutron next to the proton. The quadrupolar Hamiltonian Hq arises from the electrostatic interaction of the nuclear quadrupole moment with the electric field gradient... 

The variation of the data from the point charge theory can be accounted for on the assumption that both the charge and magnetic moment of the proton are spread out over a finite distance. On the assumption that the magnetic moment and electric charge have the same distribution, they find that a root mean square ra us of about 7X10" cm fits the data they have obtained at several energies up to 236 Mev. 

Using exotic atoms, one can separately study the distributions of protons and neutrons in the nucleus by comparing muon and pion absorption. Muons are absorbed by the protons only, whereas the strong interaction is independent of the electric charge, so hadrons (pions, kaons, and antiprotons) interact equally with protons and neutrons. 

In 1961, some experimental results providing support for this picture of the proton and the neutron were reported by Robert Hofstadter and his CO workers at Stanford University and by a group of investigators at Cornell University. These physicists studied the scattering of high-speed electrons by protons and neutrons, and were able to interpret their experiments to determine the distribution of electric charge with the proton and the neutron. 

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