Linear response strength functions with iterative Arnoldi diagonalization

We report on an implementation of a new method to calculate RPA strength functions with iterative non-hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix. We discuss the treatment of spurious modes, numerical stability, and how the method scales as the used model space is enlarged. We perform the particle-hole RPA benchmark calculations for double magic nucleus 132Sn and compare the resulting electromagnetic strength functions against those obtained within the standard RPA.Comment: 9 RevTeX pages, 11 figures, submitted to Physical Review

Extension of random-phase approximation preserving energy weighted sum rules: an application to a 3-level Lipkin model

A limitation common to all extensions of random-phase approximation including only particle-hole configurations is that they violate to some extent the energy weighted sum rules. Considering one such extension, the improved RPA (IRPA), already used to study the electronic properties of metallic clusters, we show how it can be generalized in order to eliminate this drawback. This is achieved by enlarging the configuration space, including also elementary excitations corresponding to the annihilation of a particle (hole) and the creation of another particle (hole) on the correlated ground state. The approach is tested within a solvable 3-level model.Comment: 2 figure

Neutron-Proton Correlations in an Exactly Solvable Model

We examine isovector and isoscalar neutron-proton correlations in an exactly solvable model based on the algebra SO(8). We look particularly closely at Gamow-Teller strength and double beta decay, both to isolate the effects of the two kinds of pairing and to test two approximation schemes: the renormalized neutron-proton QRPA (RQRPA) and generalized BCS theory. When isoscalar pairing correlations become strong enough a phase transition occurs and the dependence of the Gamow-Teller beta+ strength on isospin changes in a dramatic and unfamiliar way, actually increasing as neutrons are added to an N=Z core. Renormalization eliminates the well-known instabilities that plague the QRPA as the phase transition is approached, but only by unnaturally suppressing the isoscalar correlations. Generalized BCS theory, on the other hand, reproduces the Gamow-Teller strength more accurately in the isoscalar phase than in the usual isovector phase, even though its predictions for energies are equally good everywhere. It also mixes T=0 and T=1 pairing, but only on the isoscalar side of the phase transition.Comment: 13 pages + 11 postscript figures, in RevTe

Fully-Renormalized QRPA fulfills Ikeda sum rule exactly

The renormalized quasiparticle-RPA is reformulated for even-even nuclei using restrictions imposed by the commutativity of the phonon creation operator with the total particle number operator. This new version, Fully-Renormalized QRPA (FR-QRPA), is free from the spurious low-energy solutions. Analytical proof is given that the Ikeda sum rule is fullfiled within the FR-QRPA.Comment: 9 page

Single- and double-beta decay Fermi-transitions in an exactly solvable model

An exactly solvable model suitable for the description of single and double-beta decay processes of the Fermi-type is introduced. The model is equivalent to the exact shell-model treatment of protons and neutrons in a single j-shell. Exact eigenvalues and eigenvectors are compared to those corresponding to the hamiltonian in the quasiparticle basis (qp) and with the results of both the standard quasiparticle random phase approximation (QRPA) and the renormalized one (RQRPA). The role of the scattering term of the quasiparticle hamiltonian is analyzed. The presence of an exact eigenstate with zero energy is shown to be related to the collapse of the QRPA. The RQRPA and the qp solutions do not include this zero-energy eigenvalue in their spectra, probably due to spurious correlations. The meaning of this result in terms of symmetries is presented.Comment: 29 pages, 9 figures included in a Postsript file. Submitted to Physcal Review

Self-Consistent Quasi-Particle RPA for the Description of Superfluid Fermi Systems

Self-Consistent Quasi-Particle RPA (SCQRPA) is for the first time applied to a more level pairing case. Various filling situations and values for the coupling constant are considered. Very encouraging results in comparison with the exact solution of the model are obtained. The nature of the low lying mode in SCQRPA is identified. The strong reduction of the number fluctuation in SCQRPA vs BCS is pointed out. The transition from superfluidity to the normal fluid case is carefully investigated.Comment: 23 pages, 18 figures and 1 table, submitted to Phys. Rev.

Neutrinoless double beta decay within Self-consistent Renormalized Quasiparticle Random Phase Approximation and inclusion of induced nucleon currents

The first, to our knowledge, calculation of neutrinoless double beta decay ($0\nu\beta\beta$-decay) matrix elements within the self-consistent renormalised Quasiparticle Random Phase Approximation (SRQRPA) is presented. The contribution from the momentum-dependent induced nucleon currents to $0\nu\beta\beta$-decay amplitude is taken into account. A detailed nuclear structure study includes the discussion of the sensitivity of the obtained SRQRPA results for $0\nu\beta\beta$-decay of $^{76}$Ge to the parameters of nuclear Hamiltonian, two-nucleon short-range correlations and the truncation of the model space. A comparision with the standard and renormalized QRPA is presented. We have found a considerable reduction of the SRQRPA nuclear matrix elements, resulting in less stringent limits for the effective neutrino mass.Comment: 13 pages, 3 figures, 1 tabl

Making and observing visual representations during problem solving : An eye tracking study

This paper presents a case study of following visual attention during collaborative geometry problem solving. We first analyse the emergence and spread of the incorrect idea of curved lines as the optimal shortest solution. Then, we examine the different visual representations made for solution ideas and how these are observed by the collaborating peers.Peer reviewe

Dyson Equation Approach to Many-Body Greens Functions and Self-Consistent RPA, First Application to the Hubbard Model

An approach for particle-hole correlation functions, based on the so-called SCRPA, is developed. This leads to a fully self-consistent RPA-like theory which satisfies the $f$-sum rule and several other theorems. As a first step, a simpler self-consistent approach, the renormalized RPA, is solved numerically in the one-dimensional Hubbard model. The charge and the longitudinal spin susceptibility, the momentum distribution and several ground state properties are calculated and compared with the exact results. Especially at half filling, our approach provides quite promising results and matches the exact behaviour apart from a general prefactor. The strong coupling limit of our approach can be described analytically.Comment: 35 pages, 18 Figures, Feynman diagrams as 10 additional eps-files, revised and enhanced version, accepted in Phys. Rev.

Magnetic Fluffy Dark Matter

We explore extensions of inelastic Dark Matter and Magnetic inelastic Dark Matter where the WIMP can scatter to a tower of heavier states. We assume a WIMP mass $m_\chi \sim \mathcal{O}(1-100)$ GeV and a constant splitting between successive states $\delta \sim\mathcal{O}(1 - 100)$ keV. For the spin-independent scattering scenario we find that the direct experiments CDMS and XENON strongly constrain most of the DAMA/LIBRA preferred parameter space, while for WIMPs that interact with nuclei via their magnetic moment a region of parameter space corresponding to $m_{\chi}\sim 11$ GeV and $\delta < 15$ keV is allowed by all the present direct detection constraints.Comment: 16 pages, 6 figures, added comments about magnetic moment form factor to Sec 3.1.2 and results to Sec 3.2.2, final version to be published in JHE