Coulomb distortion

The effects of the Coulomb distortion can be seen in the measured spectra from the decay of 64Cu shown in Figure 8.2. This odd-odd nucleus undergoes both (3 and (3+ decay to its even-even neighbors with very similar Q values. 

If the potential V(r) is a pure Coulomb potential the asymptotic partial wave is given by the regular Coulomb function (4.64), apart from a constant phase factor. We strictly have no incident plane wave since the Coulomb potential modifies the wave function everywhere. We make the normalisation of the Coulomb distorted wave t/j,j(k,r) analogous to that of (4.83) by choosing the phase factor to be the Coulomb phase shift [Pg.95]

Coulomb distortion effects [14], a spectroscopic factor of 0.65 for the 3si/2 proton with occupation number 0.75 has been obtained [15,16]. 

In the calculations done by us and presented here we account for the static Coulomb term, vf, and the electromagnetic spin-orbit part of t, cn,m> where, cn,m is the free nucleon-nucleon Coulomb distorted nuclear t-matrix. Estimates of the (G2. - g) term, representing medium corrections, are also given. Electromagnetic effects are usually ignored in the second-order optical potential. 

Recently Elster, Liu and Thaler (ELT) [El 91] proposed a novel method for dealing with the momentum space Coulomb problem, which is, in principle, exact and may be less prone to numerical difficulties than the VP method. Their approach is based on the separation of the optical potential in eq. (3.63) and employs the two-potential formula [Ro 67] to express the full scattering amplitude as a sum of the point Coulomb amplitude and the point Coulomb distorted nuclear amplitude. The latter is obtained by numerically solving an integral equation represented in terms of Coulomb wave function basis states rather than the usual plane wave states. 

In eqs. (3.101)-(3.103) (vf) is the local, static Coulomb term and should include the relativistic correction factor, rj (see section 3.4). In eq. (3.101) ( ,cn,m) interpreted as the empirical, on-shell Coulomb distorted nuclear t-matrix obtained from phase shift analyses. The (, cn.m) contain... 

In the Hamiltonian Eq. (3.39) the first term is the harmonic lattice energy given by Eq. (3.12). It depends only on A iU, i.e., the part of the order parameter that describes the lattice distortions. On the other hand, the electron Hamiltonian Hcl depends on A(.v), which includes the changes of the hopping amplitudes due to both the lattice distortion and the disorder. The free electron part of Hel is given by Eq. (3.10), to which we also add a term Hc 1-1-1 that describes the Coulomb interne-... 

Fig. 10. Formation of the bipolaron (= diion) state in poly-p-phenylene upon reduction In the model it is assumed that the ionized states are stabilized by a local geometric distortion from a benzoid-like to a chinoid-Iike structure. Hereby one bipolaron should thermodynamically become more stable than two polarons despite the coulomb repulsion between two similar charges...

The activation energy for the charge reduction reaction is due to two factors the bond stretching and distortions of the originally near linear complex, so as to achieve the internal proton transfer and the increase of energy due to the Coulombic repulsion between the two charged products, a repulsion that leads to a release of kinetic energy on their separation. 

It follows from the above X-ray data that betaines I and II have some structural peculiarities. Two main peculiarities are especially pronounced for betaines I. These compounds have the sterically strained gauche-conformation of the main chain due to the intramolecular Coulomb interaction of the cationic and anionic centers and noticeable distortions of the bond lengths in it. In Section 5 we discuss how these peculiarities of the betaine structure reflect their reactivity. 

To obtain an estimate for the energy of reorganization of the outer sphere, we start from the Born model, in which the solvation of an ion is viewed as resulting from the Coulomb interaction of the ionic charge with the polarization of the solvent. This polarization contains two contributions one is from the electronic polarizability of the solvent molecules the other is caused by the orientation and distortion of the... 

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