Quantum-Information Theoretic Properties of Nuclei and Trapped Bose Gases

Fermionic (atomic nuclei) and bosonic (correlated atoms in a trap) systems are studied from an information-theoretic point of view. Shannon and Onicescu information measures are calculated for the above systems comparing correlated and uncorrelated cases as functions of the strength of short range correlations. One-body and two-body density and momentum distributions are employed. Thus the effect of short-range correlations on the information content is evaluated. The magnitude of distinguishability of the correlated and uncorrelated densities is also discussed employing suitable measures of distance of states i.e. the well known Kullback-Leibler relative entropy and the recently proposed Jensen-Shannon divergence entropy. It is seen that the same information-theoretic properties hold for quantum many-body systems obeying different statistics (fermions and bosons).Comment: 24 pages, 9 figures, 1 tabl

Information entropy and nucleon correlations in nuclei

The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator model and with the short-range correlated distributions. It is found that $S_r$ depends strongly on $\ln A$ and does not depend very much on the model. The behaviour of $S_k$ is opposite. The various cases we consider can be classified according to either the quantity of the experimental data we use or by the values of $S$, i.e., the increase of the quality of the density and of the momentum distributions leads to an increase of the values of $S$. In all cases, apart from the linear relation $S=a+b\ln A$, the linear relation $S=a_V+b_V \ln V$ also holds. V is the mean volume of the nucleus. If $S$ is considered as an ensemble entropy, a relation between $A$ or $V$ and the ensemble volume can be found. Finally, comparing different electron scattering experiments for the same nucleus, it is found that the larger the momentum transfer ranges, the larger the information entropy is. It is concluded that $S$ could be used to compare different experiments for the same nucleus and to choose the most reliable one.Comment: 14 pages, 4 figures, 2 table

Effects of Short Range Correlations on Ca Isotopes

The effect of Short Range Correlations (SRC) on Ca isotopes is studied using a simple phenomenological model. Theoretical expressions for the charge (proton) form factors, densities and moments of Ca nuclei are derived. The role of SRC in reproducing the empirical data for the charge density differences is examined. Their influence on the depletion of the nuclear Fermi surface is studied and the fractional occupation probabilities of the shell model orbits of Ca nuclei are calculated. The variation of SRC as function of the mass number is also discussed.Comment: 11 pages (RevTex), 6 Postscript figures available upon request at [email protected] Physical Review C in prin

Systematic study of the effect of short range correlations on the form factors and densities of s-p and s-d shell nuclei

Analytical expressions of the one- and two-body terms in the cluster expansion of the charge form factors and densities of the s-p and s-d shell nuclei with N=Z are derived. They depend on the harmonic oscillator parameter b and the parameter $\beta$ which originates from the Jastrow correlation function. These expressions are used for the systematic study of the effect of short range correlations on the form factors and densities and of the mass dependence of the parameters b and $\beta$. These parameters have been determined by fit to the experimental charge form factors. The inclusion of the correlations reproduces the experimental charge form factors at the high momentum transfers ($q\geq 2 1/fm$). It is found that while the parameter $\beta$ is almost constant for the closed shell nuclei, $^4$He, $^{16}$O and $^{40}$Ca, its values are larger (less correlated systems) for the open shell nuclei, indicating a shell effect in the closed shell nuclei.Comment: Latex, 21 pages, 6 figures, 1 tabl

Bose-Einstein condensation of correlated atoms in a trap

The Bose-Einstein condensation of correlated atoms in a trap is studied by examining the effect of inter-particle correlations to one-body properties of atomic systems at zero temperature using a simplified formula for the correlated two body density distribution. Analytical expressions for the density distribution and rms radius of the atomic systems are derived using four different expressions of Jastrow type correlation function. In one case, in addition, the one-body density matrix, momentum distribution and kinetic energy are calculated analytically, while the natural orbitals and natural occupation numbers are also predicted in this case. Simple approximate expressions for the mean square radius and kinetic energy are also given.Comment: 14 pages, 19 figures, 1 Table, RevTe

Calculations of 8^{8}He+p Elastic Cross Sections Using Microscopic Optical Potential

An approach to calculate microscopic optical potential (OP) with the real part obtained by a folding procedure and with the imaginary part inherent in the high-energy approximation (HEA) is applied to study the $^8$He+p elastic scattering data at energies of tens of MeV/nucleon (MeV/N). The neutron and proton density distributions obtained in different models for $^{8}$He are utilized in the calculations of the differential cross sections. The role of the spin-orbit potential is studied. Comparison of the calculations with the available experimental data on the elastic scattering differential cross sections at beam energies of 15.7, 26.25, 32, 66 and 73 MeV/N is performed. The problem of the ambiguities of the depths of each component of the optical potential is considered by means of the imposed physical criterion related to the known behavior of the volume integrals as functions of the incident energy. It is shown also that the role of the surface absorption is rather important, in particular for the lowest incident energies (e.g., 15.7 and 26.25 MeV/nucleon).Comment: 11 pages, 7 figures, accepted for publication in Physical Review

Jastrow-type calculations of one-nucleon removal reactions on open ss-dd shell nuclei

Single-particle overlap functions and spectroscopic factors are calculated on the basis of Jastrow-type one-body density matrices of open-shell nuclei constructed by using a factor cluster expansion. The calculations use the relationship between the overlap functions corresponding to bound states of the $(A-1)$-particle system and the one-body density matrix for the ground state of the $A$-particle system. In this work we extend our previous analyses of reactions on closed-shell nuclei by using the resulting overlap functions for the description of the cross sections of $(p,d)$ reactions on the open $s$-$d$ shell nuclei $^{24}$Mg, $^{28}$Si and $^{32}$S and of $^{32}$S$(e,e^{\prime}p)$ reaction. The relative role of both shell structure and short-range correlations incorporated in the correlation approach on the spectroscopic factors and the reaction cross sections is pointed out.Comment: 11 pages, 5 figures, to be published in Phys. Rev.

Self-similar disk packings as model spatial scale-free networks

The network of contacts in space-filling disk packings, such as the Apollonian packing, are examined. These networks provide an interesting example of spatial scale-free networks, where the topology reflects the broad distribution of disk areas. A wide variety of topological and spatial properties of these systems are characterized. Their potential as models for networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of higher-dimensional packing

In-medium nucleon-nucleon potentials in configuration space

Based on the thermodynamic Green function approach two-nucleon correlations in nuclear matter at finite temperatures are revisited. To this end, we derive phase equivalent effective $r$-space potentials that include the effect of the Pauli blocking at a given temperature and density. These potentials enter into a Schr\"odinger equation that is the $r$-space representation of the Galitskii-Feynman equation for two nucleons. We explore the analytical structure of the equation in the complex $k$-plane by means of Jost functions. We find that despite the Mott effect the correlation with deuteron quantum numbers are manifested as antibound states, i.e., as zeros of the Jost function on the negative imaginary axis of the complex momentum space. The analysis presented here is also suited for Coulombic systems.Comment: 6 pages, 1 table, 4 figure

Dominance relationships and coalitionary aggression against conspecifics in female carrion crows

Funding: European Research Council (ERCStG-336536 FuncSpecGen to J.W.), the Swedish Research Council Vetenskapsrådet (621-2013-4510 to J.W.), Knut and Alice Wallenberg Foundation (to J.W.) and Tovetorp fieldstation through Stockholm University.Cooperation is a prevailing feature of many animal systems. Coalitionary aggression, where a group of individuals engages in coordinated behaviour to the detriment of conspecific targets, is a form of cooperation involving complex social interactions. To date, evidence has been dominated by studies in humans and other primates with a clear bias towards studies of male-male coalitions. We here characterize coalitionary aggression behaviour in a group of female carrion crows consisting of recruitment, coordinated chase, and attack. The individual of highest social rank liaised with the second most dominant individual to engage in coordinated chase and attack of a lower ranked crow on several occasions. Despite active intervention by the third most highly ranked individual opposing the offenders, the attack finally resulted in the death of the victim. All individuals were unrelated, of the same sex, and naive to the behaviour excluding kinship, reproduction, and social learning as possible drivers. Instead, the coalition may reflect a strategy of the dominant individual to secure long-term social benefits. Overall, the study provides evidence that members of the crow family engage in coordinated alliances directed against conspecifics as a possible means to manipulate their social environment.Publisher PDFPeer reviewe