Landau-Migdal vs. Skyrme

The magnitude and density-dependence of the non-spin dependent Landau-Migdal parameters are derived from Skyrme energy functionals and compared with the phenomenological ones. We perform RPA calculations with various approximations for the Landau-Migdal particle-hole interaction and compare them with the results obtained with the full Skyrme interaction. For the first time the next to leading order in the Landau-Migdal approach is considered in nuclear structure calculations.Comment: Dedicated to the memory of G.E. Brow

Large-scale nuclear structure studies

The problem of microscopic nuclear structure theory in large single particle basis systems is reviewed. Several approaches are discussed, which attempt to approximate the large model spaces numerically inaccessible in complete shell model expansions of the nuclear wavefunctions. All of them use symmetry projected Hartree-Fock- Bogoliubov quasiparticle configurations as basic building blocks of the theory. They differ, however, in the degree of sophistication of the variational procedures which are used to determine the corresponding mean fields as well as the configuration mixing, up to a level, on which the construction of the configuration space itself is entirely left to the dynamics of the considered system. The mathematical formalism underlying these models is briefly summarised and the steps towards a numerical realisation are discussed. In several examples the possibilities and the power of the models are demonstrated and their limitations are shown. The models may provide a powerful tool for the analysis of experimental data as well as for predictions in still unexplored regions. On the other hand they may lead to a much better theoretical understanding of effective nuclear interactions as well as the underlying fundamental forces

Spontaneous fission modes and lifetimes of super-heavy elements in the nuclear density functional theory

Lifetimes of super-heavy (SH) nuclei are primarily governed by alpha decay and spontaneous fission (SF). Here we study the competing decay modes of even-even SH isotopes with 108 <= Z <= 126 and 148 <= N <= 188 using the state-of-the-art self-consistent nuclear density functional theory framework capable of describing the competition between nuclear attraction and electrostatic repulsion. The collective mass tensor of the fissioning superfluid nucleus is computed by means of the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov approach. Along the path to fission, our calculations allow for the simultaneous breaking of axial and space inversion symmetries; this may result in lowering SF lifetimes by more than seven orders of magnitude in some cases. We predict two competing SF modes: reflection-symmetric and reflection-asymmetric.The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow corridor formed by $^{280}$Hs, $^{284}$Fl, and $^{284}_{118}$Uuo that separates the regions of SH nuclei synthesized in "cold fusion" and "hot fusion" reactions. The region of long-lived SH nuclei is expected to be centered on $^{294}$Ds with a total half-life of ?1.5 days.Comment: 6 pages, 4 figure

Self-consistent calculations within the Extended Theory of Finite Fermi Systems

The Extended Theory of Finite Fermi Systems(ETFFS) describes nuclear excitations considering phonons and pairing degrees of freedom, using experimental single particle energies and the effective Landau-Migdal interaction. Here we use the Skyrme interactions in order to extend the range of applicability of the ETFFS to experimentally not yet investigated short-lived isotopes. We find that Skyrme interactions which reproduce at the mean field level both ground state properties and nuclear excitations are able to describe the spreading widths of the giant resonances in the new approach, but produce shifts of the centroid energies. A renormalization of the Skyrme interactions is required for approaches going beyond the mean field level.Comment: 7 pages, 5 figures, corrected typo

Log-periodic self-similarity: an emerging financial law?

A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor lambda=2, which indicates that its real value should be close to this number. This applies even to a declining decelerating log-periodic phase. Crucial in this connection is identification of a "super-bubble" (bubble on bubble) phenomenon. Identifying a potential "universal" preferred scaling factor, as undertaken here, may significantly improve the predictive power of the corresponding methodology. Several more specific related results include evidence that: (i) the real end of the high technology bubble on the stock market started (with a decelerating log-periodic draw down) in the begining of September 2000; (ii) a parallel 2000-2002 decline seen in the Standard & Poor's 500 from the log-periodic perspective is already of the same significance as the one of the early 1930s and of the late 1970s; (iii) all this points to a much more serious global crash in around 2025, of course from a level much higher (at least one order of magnitude) than in 2000.Comment: Talk given by S. Drozdz at International Econophysics Conference, Bali, August 28-31, 2002; typos correcte

Neutron rich nuclei in density dependent relativistic Hartree-Fock theory with isovector mesons

Density dependent relativistic Hartree-Fock theory has been extended to describe properties of exotic nuclei. The effects of Fock exchange terms and of pi - and rho - meson contributions are discussed. These effects are found to be more important for neutron rich nuclei than for nuclei near the valley of stability.Comment: 10 pages, 5 figures, LaTeX, macro packages graphicx and time

Self-consistent calculations of the electric giant dipole resonances in light and heavy mass nuclei

While bulk properties of stable nuclei are successfully reproduced by mean-field theories employing effective interactions, the dependence of the centroid energy of the electric giant dipole resonance on the nucleon number A is not. This problem is cured by considering many-particle correlations beyond mean-field theory, which we do within the "Quasiparticle Time Blocking Approximation". The electric giant dipole resonances in $^{16}$O, $^{40}$Ca, and $^{208}$Pb are calculated using two new Skyrme interactions.Comment: 4 pages, 4 figure

Decomposing the stock market intraday dynamics

The correlation matrix formalism is used to study temporal aspects of the stock market evolution. This formalism allows to decompose the financial dynamics into noise as well as into some coherent repeatable intraday structures. The present study is based on the high-frequency Deutsche Aktienindex (DAX) data over the time period between November 1997 and September 1999, and makes use of both, the corresponding returns as well as volatility variations. One principal conclusion is that a bulk of the stock market dynamics is governed by the uncorrelated noise-like processes. There exists however a small number of components of coherent short term repeatable structures in fluctuations that may generate some memory effects seen in the standard autocorrelation function analysis. Laws that govern fluctuations associated with those various components are different, which indicates an extremely complex character of the financial fluctuations.Comment: 15 pages, 13 PostScript figure

Quantifying dynamics of the financial correlations

A novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented. This formalism allows to quantify the memory effects as well as some potential repeatable intradaily structures in the financial time-series. The present study is based on the high-frequency Deutsche Aktienindex (DAX) data over the time-period between November 1997 and December 1999 and demonstrates a power of the method. In this way two significant new aspects of the DAX evolution are identified: (i) the memory effects turn out to be sizably shorter than what the standard autocorrelation function analysis seems to indicate and (ii) there exist short term repeatable structures in fluctuations that are governed by a distinct dynamics. The former of these results may provide an argument in favour of the market efficiency while the later one may indicate origin of the difficulty in reaching a Gaussian limit, expected from the central limit theorem, in the distribution of returns on longer time-horizons.Comment: 10 pages, 7 PostScript figures, talk presented by the first Author at the NATO ARW on Econophysics, Prague, February 8-10, 2001; to be published in proceedings (Physica A