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

Identifying "communities" within energy landscapes

Potential energy landscapes can be represented as a network of minima linked by transition states. The community structure of such networks has been obtained for a series of small Lennard-Jones clusters. This community structure is compared to the concept of funnels in the potential energy landscape. Two existing algorithms have been used to find community structure, one involving removing edges with high betweenness, the other involving optimization of the modularity. The definition of the modularity has been refined, making it more appropriate for networks such as these where multiple edges and self-connections are not included. The optimization algorithm has also been improved, using Monte Carlo methods with simulated annealing and basin hopping, both often used successfully in other optimization problems. In addition to the small clusters, two examples with known heterogeneous landscapes, LJ_13 with one labelled atom and LJ_38, were studied with this approach. The network methods found communities that are comparable to those expected from landscape analyses. This is particularly interesting since the network model does not take any barrier heights or energies of minima into account. For comparison, the network associated with a two-dimensional hexagonal lattice is also studied and is found to have high modularity, thus raising some questions about the interpretation of the community structure associated with such partitions.Comment: 13 pages, 11 figure

Power-law distributions for the areas of the basins of attraction on a potential energy landscape

Energy landscape approaches have become increasingly popular for analysing a wide variety of chemical physics phenomena. Basic to many of these applications has been the inherent structure mapping, which divides up the potential energy landscape into basins of attraction surrounding the minima. Here, we probe the nature of this division by introducing a method to compute the basin area distribution and applying it to some archetypal supercooled liquids. We find that this probability distribution is a power law over a large number of decades with the lower-energy minima having larger basins of attraction. Interestingly, the exponent for this power law is approximately the same as that for a high-dimensional Apollonian packing, providing further support for the suggestion that there is a strong analogy between the way the energy landscape is divided into basins, and the way that space is packed in self-similar, space-filling hypersphere packings, such as the Apollonian packing. These results suggest that the basins of attraction provide a fractal-like tiling of the energy landscape, and that a scale-free pattern of connections between the minima is a general property of energy landscapes.Comment: 4 pages, 3 figure

Nuclear symmetry energy effects on neutron stars properties

We construct a class of nuclear equations of state based on a schematic potential model, that originates from the work of Prakash et. al. \cite{Prakash-88}, which reproduce the results of most microscopic calculations. The equations of state are used as input for solving the Tolman-Oppenheimer-Volkov equations for corresponding neutron stars. The potential part contribution of the symmetry energy to the total energy is parameterized in a generalized form both for low and high values of the baryon density. Special attention is devoted to the construction of the symmetry energy in order to reproduce the results of most microscopic calculations of dense nuclear matter. The obtained nuclear equations of state are applied for the systematic study of the global properties of a neutron star (masses, radii and composition). The calculated masses and radii of the neutron stars are plotted as a function of the potential part parameters of the symmetry energy. A linear relation between these parameters, the radius and the maximum mass of the neutron star is obtained. In addition, a linear relation between the radius and the derivative of the symmetry energy near the saturation density is found. We also address on the problem of the existence of correlation between the pressure near the saturation density and the radius.Comment: 17 pages, 25 figure

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

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

My fear is not, an never will be, your fear: on emotions and feelings in animals

Action Contro

A comparative approach to affect and cooperation

A central premise of the science of comparative affect is that we can best learn about the causes and consequences of affect by comparing affective phenomena across a variety of species, including humans. We take as a given that affect is widely shared across animals, but a key challenge is to accurately represent each species' affective experience. A common approach in the comparative study of behavior and cognition is to develop standardized experimental paradigms that can be used across species, with the assumption that if the same task is being used, we can directly compare behavioral responses. This experimental approach rests on two underlying assumptions: first, that different species' perception of and affective response to these paradigms are the same; and second, that behavioral and physiological (including endocrine and neural) responses to these paradigms are homologous; if either of these assumptions is not true, then the comparison becomes much less straightforward. Our goal in the present paper is to summarize the dominant paradigms that have been used for such comparative research, with a particular focus on paradigms common in the cooperation literature, and to critically discuss dominant assumptions about what affective states these tasks can or should measure. We then consider the advantages and drawbacks of this experimental method, and consider alternatives that may improve our understanding. We hope that this will help scholars recognize and avoid pitfalls inherent in studying affect, and stimulate them to create novel, ecologically relevant paradigms for examining affect across the animal kingdom.Action Contro