Accounting for correlations with core electrons by means of the generalized relativistic effective core potentials: Atoms Hg and Pb and their compounds

A way to account for correlations between the chemically active (valence) and innermore (core) electrons in the framework of the generalized relativistic effective core potential (GRECP) method is suggested. The "correlated" GRECP's (CGRECP's) are generated for the Hg and Pb atoms. Only correlations for the external twelve and four electrons of them, correspondingly, should be treated explicitly in the subsequent calculations with these CGRECP's whereas the innermore electrons are excluded from the calculations. Results of atomic calculations with the correlated and earlier GRECP versions are compared with the corresponding all-electron Dirac-Coulomb values. Calculations with the above GRECP's and CGRECP's are also carried out for the lowest-lying states of the HgH molecule and its cation and for the ground state of the PbO molecule as compared to earlier calculations and experimental data. The accuracy for the vibrational frequencies is increased up to an order of magnitude and the errors for the bond lengths (rotational constants) are decreased in about two times when the correlated GRECP's are applied instead of earlier GRECP versions employing the same innercore-outercore-valence partitioning.Comment: 12 pages, 4 tables, the text of the paper was significantly improve

Quasiparticle damping in two-dimensional superconductors with unconventional pairing.

We calculate the damping of excitations due to four-fermionic interaction in the case of two-dimensional superconductor with nodes in the spectrum. At zero temperature and low frequencies it reveals gapless $\omega^3$ behavior at the nodal points. With the frequency increasing the crossover to the normal-state regimes appears. At high frequencies the damping strongly depends on details of a normal-state spectrum parametrization. Two important particular cases such as the models of almost free and tight-binding electrons are studied explicitly and the characteristic scales are expressed through the model-free parameters of the spectrum at the nodal points. The possibility of crossover in temperature dependence of damping in the superconducting phase is discussed.Comment: 16 pages, REVTEX 3, 3 figure