Relativistic Four-Component DFT Calculations of Vibrational Frequencies

We investigate the effect of relativity on harmonic vibrational frequencies. Density functional theory (DFT) calculations using the four-component Dirac–Coulomb Hamiltonian have been performed for 15 hydrides (H2X, X = O, S, Se, Te, Po; XH3, X = N, P, As, Sb, Bi; and XH4, X = C, Si, Ge, Sn, Pb) as well as for HC≡CPbH3. The vibrational frequencies have been calculated using finite differences of the molecular energy with respect to geometrical distortions of the nuclei. The influences of the choice of basis set, exchange–correlation functional, and step length for the numerical differentiation on the calculated harmonic vibrational frequencies have been tested, and the method has been found to be numerically robust. Relativistic effects are noticeable for the heavier congeners H2Te and H2Po, SbH3 and BiH3, and SnH4 and PbH4 and are much more pronounced for the vibrational modes with higher frequencies. Spin–orbit effects constitute a very small fraction of the total relativistic effects, except for H2Te and H2Po. For HC≡CPbH3 we find that only the frequencies of the modes with large contributions from Pb displacements are significantly affected by relativity

Neutrino Interactions in Hot and Dense Matter

We study the charged and neutral current weak interaction rates relevant for the determination of neutrino opacities in dense matter found in supernovae and neutron stars. We establish an efficient formalism for calculating differential cross sections and mean free paths for interacting, asymmetric nuclear matter at arbitrary degeneracy. The formalism is valid for both charged and neutral current reactions. Strong interaction corrections are incorporated through the in-medium single particle energies at the relevant density and temperature. The effects of strong interactions on the weak interaction rates are investigated using both potential and effective field-theoretical models of matter. We investigate the relative importance of charged and neutral currents for different astrophysical situations, and also examine the influence of strangeness-bearing hyperons. Our findings show that the mean free paths are significantly altered by the effects of strong interactions and the multi-component nature of dense matter. The opacities are then discussed in the context of the evolution of the core of a protoneutron star.Comment: 41 pages, 25 figure

Breathing mode in an improved transport approach

The nuclear breathing-mode giant monopole resonance is studied within an improved relativistic Boltzmann-Uehling-Uhlenbeck (BUU) transport approach. As a new feature, the numerical treatment of ground state nuclei and their phase-space evolution is realized with the same semiclassical energy density functional. With this new method a very good stability of ground state nuclei in BUU simulations is achieved. This is important in extracting clear breathing-mode signals for the excitation energy and, in particular, for the lifetime from transport theoretical studies including mean-field and collisional effects.Comment: 33 pages, 11 figures, accepted for publication in Phys. Rev.

Relativistic photoemission theory for general nonlocal potentials

An improved formulation of the one-step model of photoemission from crystal surfaces is proposed which overcomes different limitations of the original theory. Considering the results of an electronic-structure calculation, the electronic (one-particle) potential and the (many-body) self-energy, as given quantities, we derive explicit expressions for the dipole transition-matrix elements. The theory is formulated within a spin-polarized, relativistic framework for general nonspherical and space-filling one-particle potentials and general nonlocal, complex and energy-dependent self-energies. It applies to semi-infinite lattices with perfect lateral translational invariance and arbitrary number of atoms per unit cell.Comment: LaTeX, 18 pages, no figur