Configuration mixing within the energy density functional formalism: pathologies and cures

Configuration mixing calculations performed in terms of the Skyrme/Gogny Energy Density Functional (EDF) rely on extending the Single-Reference energy functional into non-diagonal EDF kernels. The standard way to do so, based on an analogy with the pure Hamiltonian case and the use of the generalized Wick theorem, is responsible for the recently observed divergences and steps in Multi-Reference calculations. We summarize here the minimal solution to this problem recently proposed [Lacroix et al, arXiv:0809.2041] and applied with success to particle number restoration[Bender et al, arXiv:0809.2045]. Such a regularization method provides suitable corrections of pathologies for EDF depending on integer powers of the density. The specific case of fractional powers of the density[Duguet et al, arXiv:0809.2049] is also discussed.Comment: 5 pages, Proceedings of the French-Japanese Symposium, September 2008. To be published in Int. J. of Mod. Phys.

Pairing correlations beyond the mean field

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys. E, in prin

Constraints on galaxy formation from alpha-enhancement in luminous elliptical galaxies

We explore the formation of alpha-enhanced and metal-rich stellar populations in the nuclei of luminous ellipticals under the assumption of two extreme galaxy formation scenarios based on hierarchical clustering, namely a fast clumpy collapse and the merger of two spirals. We investigate the parameter space of star formation time-scale, IMF slope, and stellar yields. In particular, the latter add a huge uncertainty in constraining time-scales and IMF slopes. We find that -- for Thielemann, Nomoto & Hashimoto nucleosynthesis -- in a fast clumpy collapse scenario an [alpha/Fe] overabundance of approx. 0.2 dex in the high metallicity stars can be achieved with a Salpeter IMF and star formation time-scales of the order 10^9 yr. The scenario of two merging spirals which are similar to our Galaxy, instead, fails to reproduce alpha-enhanced abundance ratios in the metal-rich stars, unless the IMF is flattened during the burst ignited by the merger. This result is independent of the burst time-scale. We suggest that abundance gradients give hints to distinguish between the two extreme formation scenarios considered in this paper.Comment: Accepted for publication in MNRAS, LaTex 2.09 with mn.sty, 13 pages, 5 figure

Pion Loop Contribution to the Electromagnetic Pion Charge Radius

A phenomenological Dyson-Schwinger equation approach to QCD, formalised in terms of a QCD based model field theory, is used to calculate the electromagnetic charge radius of the pion. The contributions from the quark core and pion loop, as defined in this approach, are identified and compared. It is shown explicitly that the divergence of the charge radius in the chiral limit is due to the pion loop and that, at the physical value of the pion mass, this loop contributes less than 15\% to $\langle r^2_\pi\rangle$; i.e. the quark core is the dominant determining characteristic for the pion. This suggests that quark based models which fail to reproduce the $\ln\,m_\pi$ divergence of $\langle r^2_\pi\rangle$ may nevertheless incorporate the dominant characteristic of the pion: its quark core.Comment: 22 Pages, 5 figures uuencoded and appended to this file, REVTEX 3.0. ANL-PHY-7663-TH-93, UNITUE-THEP-13/199

Guidance, flight mechanics and trajectory optimization. Volume 12 - Relative motion, guidance equations for terminal rendezvous

Equations of relative motion and guidance for orbital transfer and docking maneuvers in spacecraft rendezvou

Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable

In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N+1)-st harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f=0) but also a normalizable (N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge

The structure of supersymmetry in PT{\cal PT} symmetric quantum mechanics

The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one dimensional shape invariant potentials.Comment: 15 pages, some explanations included, references adde

Comparison of LISA and Atom Interferometry for Gravitational Wave Astronomy in Space

One of the atom interferometer gravitational wave missions proposed by Dimopoulos et al.1 in 2008 was called AGIS-Sat. 2. It had a suggested gravitational wave sensitivity set by the atom state detection shot noise level that started at 1 mHz, was comparable to LISA sensitivity from 1 to about 20 mHz, and had better sensitivity from 20 to 500 mHz. The separation between the spacecraft was 1,000 km, with atom interferometers 200 m long and shades from sunlight used at each end. A careful analysis of many error sources was included, but requirements on the time-stability of both the laser wavefront aberrations and the atom temperatures in the atom clouds were not investigated. After including these considerations, the laser wavefront aberration stability requirement to meet the quoted sensitivity level is about 1\times10-8 wavelengths, and is far tighter than for LISA. Also, the temperature fluctuations between atom clouds have to be less than 1 pK. An alternate atom interferometer GW mission in Earth orbit called AGIS-LEO with 30 km satellite separation has been suggested recently. The reduction of wavefront aberration noise by sending the laser beam through a high-finesse mode-scrubbing optical cavity is discussed briefly, but the requirements on such a cavity are not given. Unfortunately, such an Earth-orbiting mission seems to be considerably more difficult to design than a non-geocentric mission and does not appear to have comparably attractive scientific goals.Comment: Submitted to Proc. 46th Rencontres de Moriond: Gravitational Waves and Experimental Gravity, March 20 - 27, 2011, La Thuile, Ital

On the eigenproblems of PT-symmetric oscillators

We consider the non-Hermitian Hamiltonian H= -\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \geq 1 with all nonnegative real coefficients (possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\prime and we find some other interesting properties of eigenfunctions.Comment: 21pages, 9 figure

Interpretation of satellite images of the Republic of Niger

Interpretations of LANDSAT pictures were carried out for an area located in the west of the Niger Republic in the geological, hydrogeological and pedological sectors. Checking of the extent of vegetation and use of the soils and effects of desertification for the purpose of yearly map making was carried out. The proposed control of land use may be optimized by the direct reception of LANDSAT data by the receiving station planned for Ouagadougou. Since that station will not be operating before 1983, the establishment of a mobile reception station in the Republic of Niger to enable the installation of the required control system is advised