Nucleus/nuclear uniform charge distribution

Fnuc is the nuclear attraction potential. In the uniform charge distribution model used here, the charge of a nucleus of atomic mass A is distributed uniformly over a sphere with radius R = 2.2677 x 10 . The nuclear potential for a nucleus with charge Z is then... 

Isomer Shift (IS). The shift observed in the Mossbauer lines with respect to zero velocity is produced by the electrostatic interaction of the nuclear and electron charge distributions inside the nuclear region. One assumes the nucleus is a uniformly charged sphere of radius R, and the electronic charge density is taken to be uniformly distributed over the nucleus. Then the difference between the electrostatic interaction of a point nucleus and a nucleus with radius R is given by... 

If one naively pictures the nucleus as having a uniform (charge) density distribution up to a certain radius, it now appears that the nuclear radius is somewhat smaller than earher measurements indicated. If the nuclear radius is taken to vary as R — r A for heavy nuclei, the constant is now beheved to be about 1.2 X10" cm whereas previously was thought to be 1.4 X10 cm. 

Wheeler 2 has pointed out that further information about the nucleus can be obtained from more precise measurements of the X-ray spectrum especially of the fine structure that should be present. The things that one can study include nuclear quadrupole moments, the non-uniformity of the nuclear charge distribution, and nuclear polarizability. 

Many model potentials (pnuc f) have been used [131] but two have become most important in electronic structure calculations. These are the homogeneous and the Gaussian charge distributions. The homogeneously or uniformly charged sphere is a simple model for the finite size of the nucleus. It is piecewise defined, because the positive charge distribution is confined in a sphere of radius R. The total nuclear charge -f-Ze is uniformly distributed over the nuclear volume 4 rR /3,... 

In Chapter 3 we observed that the binding energy per nucleon is almost constant for the stable nuclei (Fig. 3.3) and that the radius is proportional to the cube root of the mass number. We have interpreted this as reflecting fairly uniform distribution of charge and mass throughout the volume of the nucleus. Other experimental evidence supports this interpretation (Fig. 3.4). This information was used to develop the liquid drop model, which successfully explains the valley of stability (Fig. 3.1). This overall view also supports the assumption of a strong, short range nuclear force. 

Several physical and chemical properties of the elements depend on effective nuclear charge. To understand the trends in these properties, it is helpful to visualize the electrons of an atom in shells. Recall that the value of the principal quantum number (n) increases as the distance from the nucleus increases Section 6.7]. If we take this statement literally, and picture all the electrons in a shell at the same distance from the nucleus, the result is a sphere of uniformly distributed negative charge, with its distance from the nucleus depending on the value of n. With this as a starting point, we will examine the periodic trends in atomic radius, ionization energy, and electron affinity. 

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