Giant Monopole Resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions

Background: Following the 2007 precise measurements of monopole strengths in tin isotopes, there has been a continuous theoretical effort to obtain a precise description of the experimental results. Up to now, there is no satisfactory explanation of why the tin nuclei appear to be significantly softer than 208Pb. Purpose: We determine the influence of finite-range and separable pairing interactions on monopole strength functions in semi-magic nuclei. Methods: We employ self-consistently the Quasiparticle Random Phase Approximation on top of spherical Hartree-Fock-Bogolyubov solutions. We use the Arnoldi method to solve the linear-response problem with pairing. Results: We found that the difference between centroids of Giant Monopole Resonances measured in lead and tin (about 1 MeV) always turns out to be overestimated by about 100%. We also found that the volume incompressibility, obtained by adjusting the liquid-drop expression to microscopic results, is significantly larger than the infinite-matter incompressibility. Conclusions: The zero-range and separable pairing forces cannot induce modifications of monopole strength functions in tin to match experimental data.Comment: 11 RevTeX pages, 16 figures, 1 table, extended versio

Collective vibrational states with fast iterative QRPA method

An iterative method we previously proposed to compute nuclear strength functions is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasi-particle-random-phase approximation (QRPA) and uses an iterative non-hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method gives substantial advantages over conventional QRPA calculations with regards to the computational cost. The method is used to calculate excitation energies and decay rates of the lowest lying 2+ and 3- states in Pb, Sn, Ni and Ca isotopes using three different Skyrme interactions and a separable gaussian pairing force.Comment: 10 pages, 11 figure

Continuity equation and local gauge invariance for the N3LO nuclear Energy Density Functionals

Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required, as a step preliminary to the adjustment of the coupling constants. Purpose: Determine to which extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, to study the relations between the validity of the continuity equation and invariance of the functional under gauge transformations. Methods: Derive conditions for the validity of the continuity equation in the framework of time-dependent density functional theory. The conditions apply separately to the four spin-isospin channels of the one-body density matrix. Results: We obtained four sets of constraints on the coupling constants of the N3LO energy density functional that guarantee the validity of the continuity equation in all spin-isospin channels. In particular, for the scalar-isoscalar channel, the constraints are the same as those resulting from imposing the standard U(1) local-gauge-invariance conditions. Conclusions: Validity of the continuity equation in the four spin-isospin channels is equivalent to the local-gauge invariance of the energy density functional. For vector and isovector channels, such validity requires the invariance of the functional under local rotations in the spin and isospin spaces.Comment: 12 Latex pages, submitted to Physical Review

Study of odd-mass N=82 isotones with realistic effective interactions

The microscopic quasiparticle-phonon model, MQPM, is used to study the energy spectra of the odd $Z=53 - 63$, N=82 isotones. The results are compared with experimental data, with the extreme quasiparticle-phonon limit and with the results of an unrestricted $2s1d0g_{7/2}0h_{11/2}$ shell model (SM) calculation. The interaction used in these calculations is a realistic two-body G-matrix interaction derived from modern meson-exchange potential models for the nucleon-nucleon interaction. For the shell model all the two-body matrix elements are renormalized by the $\hat{Q}$-box method whereas for the MQPM the effective interaction is defined by the G-matrix.Comment: Elsevier latex style espart, 26 pages, submitted to Nuclear Physics

Self Consistent and Renormalized particle-particle RPA in a Schematic Model

The dynamical effects of ground state correlations for excitation energies and transition strengths near the superfluid phase transition are studied in the soluble two level pairing model, in the context of the particle-particle self consistent Random Phase Approximation (SCRPA). Exact results are well reproduced across the transition region, beyond the collapse of the standard particle-particle Random Phase Approximation. The effects of two-body correlation in the SCRPA are displayed explicitly.Comment: 11 pages, revtex, 3ps figures, to appear in Phys. Rev.

Study of the effect of neutrino oscillation on the supernova neutrino signal with the LVD detector

We present an update of our previous study (astro-ph/0112312) on how $\nu$ oscillations affect the signal from a supernova core collapse observed in the LVD detector at LNGS. In this paper we use a recent, more precise determination of the cross section (astro-ph/0302055) to calculate the expected number of inverse beta decay events, we introduce in the simulation also the $\nu$-{\rm Fe} interactions, we include the Earth matter effects and, finally, we study also the inverted mass hierarchy case.Comment: 4 pages, 4 figures, to appear in the Proceedings of ICRC 200

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

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

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

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