Atomic quadrupole moments

The five second-moment spherical tensor components can also be calculated and are defined as the quadrupolar polarization terms. They can be seen as the ELF basin equivalents to the atomic quadrupole moments introduced by Popelier [32] in the case of an AIM analysis ... 

Whitehouse and Buckingham have recently measured the atomic quadrupole moment of graphite and made a correlation with the moment by simply adding up the quadrupole moments of all the carbon atoms. It is interesting to note that the quadrupole moment of benzene is roughly six times the quadrupole moment of the individual carbon atom. Thus one can postulate that the ions observed in Figure 23 are the result of quadrupole-bound electrons to Cn clusters present in the laser ablation plume. Possible polycyclic structures for the carbon clusters observed in the negative ion spectrum produced by RET are... 

Calculations of atomic quadrupole moments are still of interest, particularly for heavier atoms where relativistic accuracy is required. Sundholm102 has reported a finite-element MCSCF method to calculate the quadrupole of Ar+ and finds a final value of —0.5271 au in comparison with a recent experimental determination of —0.5208 au. The Hartree-Fock value is —0.57213 au and the valence shell correlation correction, amounting to 0.04844 au, accounts for most of the additional contribution, a result which may be of some significance for molecular calculations involving atoms in the intermediate range of atomic numbers. 

Yakobi, H., Eliav, E. and Kaldor, U. (2007) Nuclear quadrupole moment of 197Au from high-accuracy atomic calculations. Journal of Chemical Physics, 126, 184305-1-184305-4. 

The experimentally observed quadrupole splitting AEq for Fe in inorganic compounds, metals, and solids reaches from 0 to more than 6 mm s [30, 32]. The range of AEq for other Mossbauer isotopes may be completely different because of the different nuclear quadrupole moment Q of the respective Mossbauer nucleus, and also because the EFG values may be intrinsically different due to markedly different radial distributions of the atomic orbitals (vide infra). As Q is constant for a given isotope, variations in the quadrupole coupling constants eQV can only arise from... 

Element Atomic Weight Spin, I Natural Abundance (%) Receptivity (13C =1.00) Quadrupole Moment (10-30m2) (MHz) at 2.348 T (23.48 kG)... 

Another parameter that one can extract from a Mossbauer spectrum is the quadrupole splitting. The 3/2 state in either iron or tin is degenerate with respect to an asymmetric electrostatic field, and in such a field these levels will be split into dz 3/2 and 1/2 levels. One can observe transitions either to or from these two levels to the ground state, and this is the quadrupole splitting. It is actually e qQ, where eq is the electrostatic field gradient—i,e., the second derivative of the potential with respect to the coordinate—and eQ is the nuclear quadrupole moment. The typical quadrupole split spectrum for iron is shown in Figure 6, in which the cubic (octahedral) symmetry around the iron atom is de-... 

Because the interactions measured in Mossbauer experiments are products of atomic and nuclear factors, experiments on iodine isotopes have yielded values of the change of nuclear radius between the ground state and the excited state, AR/R, quadrupole moment values Q, and magnetic moment values, fi, as well as electric field gradients and internal magnetic fields. 

In Formulas (19) and (20) the actual value of the quadrupole moment Q that occurs is not that of the bare nucleus, but the bare nucleus value multiplied by a parameter 1 — This is necessary because the electron distribution of the atom is distorted when the atom is in an electric field gradient, due to the interaction of the electrons with the field gradient. This distortion produces an additional gradient which is —7 times the... 

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