Racah represent electron repulsion

Figure 1.1 shows that the stability sequence revealed by chemical reactions and chemical synthesis corresponds to thermodynamic stabilities. An explanation requires a theory that will explain both. To get it we apply the theory of atomic spectra [9]. The energy of the 4f electrons in an ion with the configuration [Xe]4P, F(4P), can be written [nU+E Q-p(4f )] where U, a negative quantity, is the energy of each 4f electron in the field of the positively charged xenon core, and Frep(4P) represents the repulsion between the n 4f electrons. In Table 1.1, rep(4P) is expressed as a function of the Racah parameters and E. The... 

However, as we have already pointed out, the value of Sgg — t2g is quite insensitive to the electronic configuration (2). Therefore, in the present paper, we approximated all of these effective crystal-field splittings by the value of eg — t2g Calculated in the ground state. On the other hand, the Racah parameters represent the electron-electron repulsion interaction and can be calculated by the radial part of the pure 3d atomic orbitals of the impurity chromium ion (1). After evaluating the value of these parameters, the multiplet structure of ruby can be obtained by diagonalizing the Tanabe-Sugemo matrices. 

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