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Multielectron Atoms
Published in Mikhail G. Brik, Chong-Geng Ma, Theoretical Spectroscopy of Transition Metal and Rare Earth Ions, 2019
Mikhail G. Brik, Chong-Geng Ma
It is also worthwhile to note that the (l1l2l3000) 3j-symbol is not zero if and only if the l1 + l2 + l3 sum is an even number. In addition, the following conditions should be also fulfilled in this case l1 + l2 ≥ l3, l2 + l3 ≥ l1, l1 + l3 ≥ l3. Equations (4.12) and (4.13) are widely used in the crystal field theory.
Time-dependent dynamics of nuclear spin symmetry and parity violation in dichlorodisulfane (ClSSCl) during and after coherent radiative excitation
Published in Molecular Physics, 2021
Gunther Wichmann, Georg Seyfang, Martin Quack
One can now write the matrix elements of the nuclear spin Hamiltonian for two equal quadrupolar nuclei () in the symmetric basis functions with the coupling scheme presented in [40]: with the prefactor C being given by and with the Wigner 3-j symbol written with and the 6-j symbol with . As the quadrupole tensor in the principal axis system is symmetric the elements of the spherical quadrupole tensor for the two nuclei 1 and 2 (j = 1, 2) may be expressed as Because the C symmetry axis is the b-axis, we have the following symmetry relations between the quadrupole coupling constants for the two Cl-nuclei Applying a Wang transformation to the matrix elements from Equation (17) gives the possibility to add the matrix elements from the A-reduced Watson Hamiltonian introduced in the previous section, which are usually also given in the Wang basis (see e.g. [71–75]). We have reproduced the effective Hamiltonian from the program SPCAT [77] for the given input parameters and have subsequently used the results for the eigenstate energies and for the dipole transition moments between the coupled basis functions from the output of SPCAT. For further details, we refer to the appendix.