Coherent tunnelling in Cu2+- and Ag2+-doped MgO and CaO: Cu2+ explored through ab initio calculations

The observation of coherent tunnelling in Cu2+ - and Ag2+ -doped MgO and CaO:Cu2+ was a crucial discovery in the realm of the Jahn-Teller (JT) effect. The main reasons favoring this dynamic behavior are now clarified through ab initio calculations on Cu2+ - and Ag2+ -doped cubic oxides. Small JT distortions and an unexpected low anharmonicity of the eg JT mode are behind energy barriers smaller than 25 cm-1 derived through CASPT2 calculations for Cu2+ - and Ag2+ -doped MgO and CaO:Cu2+ . The low anharmonicity is shown to come from a strong vibrational coupling of MO610- units (M=Cu,Ag) to the host lattice. The average distance between the d9 impurity and ligands is found to vary significantly on passing from MgO to SrO following to a good extent the lattice parameter.

Semiclassical evaluation of average nuclear one- and two-body matrix elements

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results, and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elements it is shown how the Thomas-Fermi approach can be projected on good parity and also on good angular momentum. For the two-body case, the pairing matrix elements are considered explicitly.

Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.