Nuclear electric charge distribution

We start by considering a nuclear electric charge distribution p r) placed in an external inhomogeneous electric field with the potential V(r). The origin, r = 0, is at the centre of gravity of the nucleus. The interaction energy E is given by... 

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... 

Relaxation via quadrupolar coupling. Nuclei with 15= 1 have an electric quad-rupole moment (due to non-spherical nuclear charge distribution) which is capable of interacting with local electric field gradients that occur in tumbling molecules with an asymmetric electric charge distribution. Therefore this relaxation mechanism is... 

At very high resolutions it may be possible to determine pj from hfs, and from this to calculate /. The hyperfine splitting and shifting of optical lines have yielded important information not only about nuclear spins and magnetic moments, but also about the electric charge distribution and radius of the nucleus. 

The total electric charge distribution px(r) for monomer X is the sum of the electronic contribution— which can be obtained from the wave function f— and the nuclear contribution. 

Some appreciation for the nitrogen nuclear characteristics may be obtained from Table 1. Because the relative sensitivities are comparable, the approximately 300-fold higher natural abundance of would seem to make it the nucleus of choice. It is even more sensitive than at natural abundance. However, like all nuclei with spin quantum number I > 1/2, possesses an electric quadrupole moment that arises from a nonspherical electric charge distribution in the nucleus itself. When placed in an electric field gradient, such as that characteristic of most molecular electron distributions, a quadrupolar nucleus experiences random fluctuating electric fields. The characteristic frequencies of these motions have components at the resonance frequency and hence afford an efficient relaxation mechanism. As a result, spin-lattice relaxation times (Tj ) are very short, 0.1-10 ms. Because Tj = To for in most molecules Lie in solution, linewidths are corres-... 

Oil Contamination of Helium Gas. For more than 20 years, helium gas has been used in a variety of nuclear experiments to collect, carry, and concentrate fission-recoil fragments and other nuclear reaction products. Reaction products, often isotropically distributed, come to rest in helium at atmospheric concentration by coUisional energy exchange. The helium is then allowed to flow through a capillary and then through a pinhole into a much higher vacuum. The helium thus collects, carries, and concentrates products that are much heavier than itself, electrically charged or neutral, onto a detector... 

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

For spherically symmetric nuclear charge distribution (Gaussian, Fermi, or point nucleus), the electric field at a point r outside the nucleus can be evaluated from Gauss law as... 

The strength of the quadrupolar interaction is proportional to the quadrupole moment Q of a nucleus and the electric field gradient (EFG) [21-23]. The size of Q depends on the effective shape of the ellipsoid of nuclear charge distribution, and a non-zero value indicates that it is not spherically symmetric (Fig. 1). 

The quadrupolar interaction in term (Id) applies to nuclei having nuclear spin I > 1/2, the so-called quadrupolar nuclei. Such nuclei have a nonspherical distribution of positive electric charge that can be expanded in terms of moments, with... 

Asymmetry in the ligand environment, either geometric or in charge distribution (or both), affect the asymmetry parameter, tp An r = 0 value corresponds to complete axial symmetry, whereas r = 1 corresponds to pure rhombic symmetry. Electric monopole interactions between the nuclear charge distributions and the electrons at the nucleus cause a shift of the nuclear ground and excited states. These interactions are known as the isomer shift, 8. Both the Mossbauer source and the absorber (the sample of interest) experience an isomer shift, and it is customary to quote 8 relative to a standard, usually Fe metal or Na2[Fe(CN)5NO] 2H2O at... 

In other words, isotopes having a spin value equal to, or greater than one exhibit an ellipsoidal charge distribution and have spin. They invariably possess a nuclear electric quadrupole moment, designated as Q ... 

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