Electron shells, atomic form factor

A.O.Williams Jr. noted in his Hartree-calculations on the closed shell atom Cu as early as 1940 (Phys. Rev. 58, 723) The charge density of each single electron turns out to resemble that for the nonrelativistic case, but with the maxima "pulled in " and raised.. .. The size of the relativistic corrections appear to be just too small to produce important corrections in atomic form factors or other secondary characteristics of the whole atom.. .. However, it must be noticed that copper is a relatively light ion, and the corrections for such an ion as mercury would be enormously greater. S.Cohen in 1955 and... 

The sixth element in the periodic table, carbon, has the electron configuration 2s 2 and, thus, has 4 valence electrons in the unfilled orbitals of its second electron shell. To fill these orbitals to a stable set of 8 valence electrons, a single carbon atom may share electrons with 2, 3, or even 4 other atoms. No other element forms such strong bonds to as many other atoms as carbon does. Moreover, multiple carbon atoms readily link together with single, double, or triple bonds. These factors make element number 6 unique in the entire periodic table. The number of carbon-based compounds is many times greater than the total of all compounds lacking carbon. 

In a typical Doppler measurement only one of the two annihilation photons with on average half of the Doppler shift is observed. With second detector opposite to the first one and operated in coincidence with the first one the full Doppler shift is observed. The signal to noise ratio improves by a factor of-1000. The shell structure of tightly bound core electrons of atoms does not change much when the atoms form a solid. Doppler shifts from these electrons can be detected and permit the identification of specific elements next to the annihilation site [70]. 

We now discuss the analysis of the x-ray intensities. The atoms of the C6o molecule are placed at the vertices of a truncated icosahedron. - The x-ray structure factor is given by the Fourier transform of the electronic charge density this can be factored into an atomic carbon form factor times the Fourier transform of a thin shell of radius R modulated by the angular distribution of the atoms. For a molecule with icosahedral symmetry, the leading terms in a spherical-harmonic expansion of the charge density are Koo(fl) (the spherically symmetric contribution) and KfimCn), where ft denotes polar and azimuthal coordinates. The corresponding terms in the molecular form factor are proportional to SS ° (q)ac jo(qR)ss n(qR)/qR and... 

One factor that favors an atom of a representative element forming a monatomic ion in a compound is the formation of a stable noble gas electron configuration. Energy considerations are consistent with this observation. For example, as one mole of Li from Group LA forms one mole of Li+ ions, it absorbs 520 kj per mole of Li atoms. The IE2 value is 14 times greater, 7298 kj/mol, and is prohibitively large for the formation of Li + ions under ordinary conditions. For LE+ ions to form, an electron would have to be removed from the filled first shell. We recognize that this is unlikely. The other alkali metals behave in the same way, for similar reasons. 

Slater proposes an effective quantum number n = 3.7, the atomic factor can only be presented in the form of a sum with an infinite number of components. The series may be terminated if the effective quantum number for the N shell is taken as 3.5, 4.0, or 4.5. We calculated values of the atomic factor for the neutral Br atom with different values of n. The most satisfactory agreement with the theoretical form factors, calculated according to the Thomas—Fermi—Dirac model, was obtained at n — 4.5 screening coefficients proposed in [11] were used in the calculations. The equation of the atomic scattering function for the N shell in the case of a spherically symmetrical electron density distribution and n — 4.5 has the following form ... 

Interpreted in terms of the symmetrical form of the periodic table (Fig. 3), the quantum numbers that define the radial distances of r = n a specify the nodal surfaces of spherical waves that define the electronic shell structure. Knowing the number of electrons in each shell, the density at the crests of the spherical waves that represent periodic shells, i.e., at 1.5,3, etc. (a), can be calculated. This density distribution, shown in Fig. 7, decreases exponentially with Z and, like the TF central-field potential, is valid for all atoms and also requires characteristic scale factors to generate the density functions for specific atoms. The Bohr-Schrodinger... 

The step structure of as a function of rs is determined by factors of the form Hff(r3)P/p (r3) (see Eq. 88), each factor being approximately a constant if r3 is within atomic shell k. The contribution of this factor to the total function is governed by the constants Cfk describing the coupling of the density perturbation in shell k with an electron in shell i. These constants are largest if i = k. Figure 4 clearly displays the step structure of S, as a function of r3 in the region around T2 = 1 bohr. 

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