Nuclear Charge Form Factor

This quantity is also obtainable from experimental data, e.g. from the short-range behaviour of the nuclear charge form factor F(g), compare Eq. 

To include contributions to the total nuclear charge form factor due to the electric form factor of the neutron and the magnetic contributions from nucleons in unfilled n, I, j = I subshells [Be72b], Pch,p(9 ) i replaced with the empirical nuclear charge form factor, Pc iq ), where 1- Using this substitution and eqs. (3.51) and (3.55), the momentum space Coulomb potential becomes... 

The general result for the nuclear charge radius and the Darwin-Foldy contribution for a nucleus with arbitrary spin was obtained in [9]. It was shown there that one may write a universal formula for the sum of these contributions irrespective of the spin of the nucleus if the nuclear charge radius is defined with the help of the same form factor for any spin. However, for historic reasons, the definitions of the nuclear charge radius are not universal, and respective formulae have different appearances for different spins. We will discuss here only the most interesting cases of the spin zero and spin one nuclei. 

Nuclear size corrections of order (Za) may be obtained in a quite straightforward way in the framework of the quantum mechanical third order perturbation theory. In this approach one considers the difference between the electric field generated by the nonlocal charge density described by the nuclear form factor and the field of the pointlike charge as a perturbation operator [16, 17]. 

The relationship between nuclear charge and atomic wave functions is of the form Z oc Core-charge imbalance could therefore be compensated for with an effective charge of Ze = re2/3 on one of the atoms. For p-block atomic pairs, this screening factor does indeed lead to the correct solution. For hydrides of p-block elements in periodic row n, compensating charge is defined as Ze = (knx/n)2/3, with screening constants / g = 0.84 and kz = 0.70. 

When the platinum nucleophilicity scale was first proposed it was implied that one np, scale was applicable to all substrates and that plots of logk2 against npt°(Y) were linear, taking the form log 10 2 = S np, (Y) + C, where S is termed the nucleophilic discrimination factor of the substrate and C its intrinsic reactivity. Discussions of mechanism based on a comparison of nucleophilic discrimination factors are frequently encountered. Nucleophiles that do not retain their positions in the nucleophilicity scale, e.g. NO2", SeCN and SC(NH2)2, were termed biphilic by Cattahni since their behaviour could be explained by their n-acceptor properties. When the Pt reaction centre had a greater n-basicity than the standard complex (for example a smaller effective nuclear charge) the substrate was more reactive than predicted and vice versa. This concept had been deduced some years earlier by Bosnich from his work with octahedral Ru complexes... 

At higher energies a simple form factor calculation (see Sect. 7) of the diffraction will show that one should obtain minima and maxima if the charge distribution is uniform and cuts off sharply. With such a nuclear model, the simple form factor calculation (Born approximation) leads to minima which go to zero at 7 ... 

Finally, for hydrogenic systems it has been notedt33] that dominant uncertainty in the nuclear size contribution arises from the normalisation of the electron scattering form factors F(q) which are used to determine the proton and deuteron charge radii. However, if... 

Electron configurations in molecules can also be related to bond distances and bond enthalpies, aao (Section 8.8) As bond order increases, bond distances decrease and bond enthalpies increase. N2, for example, whose bond order is 3, has a short bond distance and a large bond enthalpy. The N2 molecule does not react readily with other substances to form nitrogen compounds. The high bond order of the molecule helps explain its exceptional stability. We should also note, however, that molecules with the same bond orders do not have the same bond distances and bond enthalpies. Bond order is only one factor influencing these properties. Other factors include nuclear charge and extent of orbital overlap. 

The nuclear radii are Rj - and the parameters encode the diffuseness of the nuclear surface. The subscript (i) allows these constants to be different for the different terms in the potential. The spin-orbit form is analogous to the Thomas form for atoms. Relativistic treatments generate such a term, but do not provide insight into the strength or even its sign. The Coulomb potential can be taken to be that for uniformly charged spheres or calculated numerically assuming form factors for the density similar to that for the potential. 

For the calculations discussed in ref. [Ra 85], and for those shown here, the proton vector densities were obtained by unfolding the single proton (free space) electric form factor from the nuclear charge densities [Fr 77, Si 70, Si 79]. The contributions to the apparent total nuclear charge density due to the neutron electric form factor and the nucleon magnetic form factor (in the case of Pb) were taken into account [Be 72b, Ra79]. The neutron vector densities used in the RIA predictions were assumed to be... 

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