Electromagnetic selection rules in the triangular alpha-cluster model of 12C

After recapitulating the procedure to find the bands and the states occurring in the $\mathcal{D}_{3h}$ alpha-cluster model of $^{12}$C in which the clusters are placed at the vertexes of an equilateral triangle, we obtain the selection rules for electromagnetic transitions. While the alpha cluster structure leads to the cancellation of E1 transitions, the approximations carried out in deriving the roto-vibrational hamiltonian lead to the disappearance of M1 transitions. Furthermore, although in general the lowest active modes are E2, E3, $\cdots$ and M2, M3, $\cdots$, the cancellation of M2, M3 and M5 transitions between certain bands also occurs, as a result of the application of group theoretical techniques drawn from molecular physics. These implications can be very relevant for the spectroscopic analysis of $\gamma$-ray spectra of $^{12}$C

The egalitarian effect of search engines

Search engines have become key media for our scientific, economic, and social activities by enabling people to access information on the Web in spite of its size and complexity. On the down side, search engines bias the traffic of users according to their page-ranking strategies, and some have argued that they create a vicious cycle that amplifies the dominance of established and already popular sites. We show that, contrary to these prior claims and our own intuition, the use of search engines actually has an egalitarian effect. We reconcile theoretical arguments with empirical evidence showing that the combination of retrieval by search engines and search behavior by users mitigates the attraction of popular pages, directing more traffic toward less popular sites, even in comparison to what would be expected from users randomly surfing the Web.Comment: 9 pages, 8 figures, 2 appendices. The final version of this e-print has been published on the Proc. Natl. Acad. Sci. USA 103(34), 12684-12689 (2006), http://www.pnas.org/cgi/content/abstract/103/34/1268

Electric and magnetic response to the continuum for A=7 isobars in a dicluster model

Mirror isobars $^7$Li and $^7$Be are investigated in a dicluster model. The magnetic dipole moments and the magnetic dipole response to the continuum are calculated in this framework. The magnetic contribution is found to be small with respect to electric dipole and quadrupole excitations even at astrophysical energies, at a variance with the case of deuteron. Energy weighted molecular sum rules are evaluated and a formula for the molecular magnetic dipole sum rule is found which matches the numerical calculations. Cross-sections for photo-dissociation and radiative capture as well as the S-factor for reactions of astrophysical significance are calculated with good agreement with known experimental data.Comment: Accepted in EPJ

The electron screening puzzle and nuclear clustering

Accurate measurements of nuclear reactions of astrophysical interest within, or close to, the Gamow peak, show evidence of an unexpected effect attributed to the presence of atomic electrons in the target. The experiments need to include an effective "screening" potential to explain the enhancement of the cross sections at the lowest measurable energies. Despite various theoretical studies conducted over the past 20 years and numerous experimental measurements, a theory has not yet been found that can explain the cause of the exceedingly high values of the screening potential needed to explain the data. In this letter we show that instead of an atomic physics solution of the "electron screening puzzle", the reason for the large screening potential values is in fact due to clusterization effects in nuclear reactions, in particular for reaction involving light nuclei.Comment: 6 pages, 2 figures, accepted for publication in Physics Letters

Center clusters in the Yang-Mills vacuum

Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory at finite temperature are analyzed. We show that spatial clusters can be identified where the local Polyakov loops have values close to the same center element. For a suitable definition of these clusters the deconfinement transition can be characterized by the onset of percolation in one of the center sectors. The analysis is repeated for different resolution scales of the lattice and we argue that the center clusters have a continuum limit.Comment: Table added. Final version to appear in JHE

Pairing in the continuum: the quadrupole response of the Borromean nucleus 6He

The ground state and low-lying continuum states of 6He are found within a shell model scheme, in a basis of two-particle states built out of continuum p-states of the unbound 5He nucleus, using a simple pairing contact-delta interaction. This accounts for the Borromean character of the bound ground state, revealing its composition. We investigate the quadrupole response of the system and we put our calculations into perspective with the latest experimental results. The calculated quadrupole strength distribution reproduces the narrow 2+ resonance, while a second wider peak is found at about 3.9 MeV above the g.s. energy.Comment: 5 pages, 5 figure

Electric multipole response of the halo nucleus 6^6He

The role of different continuum components in the weakly-bound nucleus $^6$He is studied by coupling unbound spd-waves of $^5$He by means of simple pairing contact-delta interaction. The results of our previous investigations in a model space containing only p-waves, showed the collective nature of the ground state and allowed the calculation of the electric quadrupole transitions. We extend this simple model by including also sd-continuum neutron states and we investigate the electric monopole, dipole and octupole response of the system for transitions to the continuum, discussing the contribution of different configurations.Comment: 22 pages, 10 figure

On the Consensus Threshold for the Opinion Dynamics of Krause-Hegselmann

In the consensus model of Krause-Hegselmann, opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. A randomly chosen agent takes the average of the opinions of all neighbouring agents which are compatible with it. We propose a conjecture, based on numerical evidence, on the value of the consensus threshold \epsilon_c of this model. We claim that \epsilon_c can take only two possible values, depending on the behaviour of the average degree d of the graph representing the social relationships, when the population N goes to infinity: if d diverges when N goes to infinity, \epsilon_c equals the consensus threshold \epsilon_i ~ 0.2 on the complete graph; if instead d stays finite when N goes to infinity, \epsilon_c=1/2 as for the model of Deffuant et al.Comment: 15 pages, 7 figures, to appear in International Journal of Modern Physics C 16, issue 2 (2005

The Sznajd Consensus Model with Continuous Opinions

In the consensus model of Sznajd, opinions are integers and a randomly chosen pair of neighbouring agents with the same opinion forces all their neighbours to share that opinion. We propose a simple extension of the model to continuous opinions, based on the criterion of bounded confidence which is at the basis of other popular consensus models. Here the opinion s is a real number between 0 and 1, and a parameter \epsilon is introduced such that two agents are compatible if their opinions differ from each other by less than \epsilon. If two neighbouring agents are compatible, they take the mean s_m of their opinions and try to impose this value to their neighbours. We find that if all neighbours take the average opinion s_m the system reaches complete consensus for any value of the confidence bound \epsilon. We propose as well a weaker prescription for the dynamics and discuss the corresponding results.Comment: 11 pages, 4 figures. To appear in International Journal of Modern Physics