Universal trend of the information entropy of a fermion in a mean field

We calculate the information entropy of single-particle states in position-space $S_{r}$ and momentum-space $S_{k}$ for a nucleon in a nucleus, a $\Lambda$ particle in a hypernucleus and an electron in an atomic cluster. It is seen that $S_{r}$ and $S_{k}$ obey the same approximate functional form as functions of the number of particles, $S_{r}$ ({\rm or} $S_{k}) = a+bN^{1/3}$ in all of the above many-body systems in position- and momentum- space separately. The net information content $S_{r}+S_{k}$ is a slowly varying function of $N$ of the same form as above. The entropy sum $S_{r}+S_{k}$ is invariant to uniform scaling of coordinates and a characteristic of the single-particle states of a specific system. The order of single-particle states according to $S_r +S_k$ is the same as their classification according to energy keeping the quantum number $n$ constant. The spin-orbit splitting is reproduced correctly. It is also seen that $S_{r}+S_{k}$ enhances with excitation of a fermion in a quantum-mechanical system. Finally, we establish a relationship of $S_r +S_k$ with the energy of the corresponding single-particle state i.e. $S_r +S_k = k \ln (\mu E +\nu)$. This relation holds for all the systems under consideration.Comment: 9 pages, latex, 6 figure

Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

The analytic properties of Nilsson's Modified Oscillator (MO), which was first introduced in nuclear structure, and of the recently introduced, based on quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator (3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce correctly in terms of only one parameter the magic numbers of alkali clusters up to 1500 (the expected limit of validity for theories based on the filling of electronic shells), are considered. Exact expressions for the total energy of closed shells are determined and compared among them. Furthermore, the systematics of the appearance of supershells in the spectra of the two oscillators is considered, showing that the 3-dim q-HO correctly predicts the first supershell closure in alkali clusters without use of any extra parameter.Comment: 25 pages LaTeX plus 21 postscript figure

Unified description of magic numbers of metal clusters in terms of the 3-dimensional q-deformed harmonic oscillator

Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of several metal clusters. The Taylor expansions of angular momentum dependent potentials approximately producing the same spectrum as the 3-dimensional q-deformed harmonic oscillator are found to be similar to the Taylor expansions of the symmetrized Woods-Saxon and wine-bottle symmetrized Woods-Saxon potentials, which are known to provide successful fits of the Ekardt potentials.Comment: 23 pages including 7 table

Rotationally Invariant Hamiltonians for Nuclear Spectra Based on Quantum Algebras

The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational nuclear spectra is explicitly proved and a connection of this Hamiltonian to the formalisms of Amal'sky and Harris is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITO) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved, a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced, and its connection to the Harris formalism is established. Numerical tests in a series of Th isotopes are provided.Comment: 34 pages, LaTe

Two approximate formulae for the binding energies in Lambda hypernuclei and light nuclei

Two approximate formulae are given for the binding energies in Lambda-hypernuclei and light nuclei by means of the (reduced) Poeschl-Teller and the Gaussian central potentials. Those easily programmable formulae combine the eigenvalues of the transformed Jacobi eigenequation and an application of the hypervirial theorems.Comment: Accepted for publication in Europhysics Letter

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. In the framework of the spin and pseudospin symmetry concept, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of the two Dirac particles are obtained, in closed form, by means of the Nikiforov-Uvarov method which is based on solving the second-order linear differential equation by reducing it to a generalized equation of hypergeometric type. The special cases $\kappa =\pm 1$ ($l=\widetilde{l}=0,$ s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. Also, the non-relativistic results are compared with the other works.Comment: 25 page

Comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry (GC x GC-TOFMS) for drug screening and confirmation

Comprehensive two-dimensional gas chromatography (GC×GC) is applied to analysis of drug standard mixtures containing 78 drugs of interest in forensic samples. For this study, underivatised drugs were employed. While several of the drugs were not detected at the low concentrations employed in the samples, most could be satisfactorily assigned their first and second dimension retentions in the GC×GC retention plane. For this study, time-of-flight mass spectrometry (TOFMS) detection was used. The enhanced separation possible in GC×GC is demonstrated, and typical linearity and apparatus precision are shown for tramadol, diazepam, olanzapine and desipramine using selected qualifier ions. Mass spectral library search quality for the detection of drugs in a selection of authentic forensic cases, along with retention position in the 2D retention plane, is used to support positive identification of the presence of the drugs. The analysis of [`]difficult' drugs paracetamol and phenytoin is shown to produce anomalous chromatographic peak shape in the 2D plane, whereas most drugs gave acceptable peak shapes. The GC×GC technique was applied to screening drugs in forensic samples, with either flame ionisation (FID) or TOFMS detection, and compared favourably with conventional single column GC-MS analysis when tested for diazepam in an authentic forensic study

Sesquiterpene lactones from Staehelina fruticosa

The phytochemical analysis of Staehelina fruticosa led to the isolation of four germacranolide-type sesquiterpene lactones (1-4), including two new glycosides. The structures of these sesquiterpene lactones were elucidated using spectroscopic techniques, and enzymatic hydrolysis was carried out to confirm the nature of the two glycoside derivatives. Molecular modeling was incorporated to substantiate their relative configuration. © 2008 American Chemical Society and American Society of Pharmacognosy

Cooking plant foods in the northern Aegean: microbotanical evidence from Neolithic Stavroupoli (Thessaloniki, Greece)

Intensive archaeobotanical research in northern Greece and other circum-Mediterranean regions over the last two decades has demonstrated an extensive spectrum of domestic and wild plants consumed by Neolithic communities. However, macrobotanical remains are seldom associated with the artefact in which they were cooked, and therefore we know the list of ingredients but not what ingredients were cooked together or how were they cooked. By focusing on remains recovered from cooking vessels, this paper explores the culinary practices of the inhabitants of the Neolithic settlement at Stavroupoli (Thessaloniki, Greece) through combined starch grain and phytolith analyses from charred food crusts adhering to the inner walls of 17 late Middle and early Late Neolithic vessels (ca. 5600-5000 cal. BC). The results show that the food represented by burnt remains included domestic wheat(s) and lentils, as well as weedy Setaria sp. and other wild plants. The presence of Setaria weeds suggests high soil fertility and disturbed growing conditions. These results further indicate that the inhabitants of different areas of the settlement had differential access to food resources (more vs. less valued food), which might be related to a) different types of meals being prepared in separated areas of the site, or b) different preferences or economic status of its inhabitants expressed through culinary practices. Further research at Stavroupoli and other contemporary sites will help to unravel the role of food in shaping social identity and human-environment interactions in the Neolithic northern Aegean