Multipole strength function of deformed superfluid nuclei made easy

We present an efficient method for calculating strength functions using the finite amplitude method (FAM) for deformed superfluid heavy nuclei within the framework of the nuclear density functional theory. We demonstrate that FAM reproduces strength functions obtained with the fully self-consistent quasi-particle random-phase approximation (QRPA) at a fraction of computational cost. As a demonstration, we compute the isoscalar and isovector monopole strength for strongly deformed configurations in $^{240}$Pu by considering huge quasi-particle QRPA spaces. Our approach to FAM, based on Broyden's iterative procedure, opens the possibility for large-scale calculations of strength distributions in well-bound and weakly bound nuclei across the nuclear landscape.Comment: 5 pages, 3 figure

Mirror and triplet displacement energies within nuclear DFT : Numerical stability

Isospin-symmetry-violating class II and III contact terms are introduced into the Skyrme energy density functional to account for charge dependence of the strong nuclear interaction. The two new coupling constants are adjusted to available experimental data on triplet and mirror displacement energies, respectively. We present preliminary results of the fit, focusing on its numerical stability with respect to the basis size.Peer reviewe

Nuclear charge-exchange excitations in localized covariant density functional theory

The recent progress in the studies of nuclear charge-exchange excitations with localized covariant density functional theory is briefly presented, by taking the fine structure of spin-dipole excitations in 16O as an example. It is shown that the constraints introduced by the Fock terms of the relativistic Hartree-Fock scheme into the particle-hole residual interactions are straightforward and robust.Comment: 4 pages, 1 figure, Proceedings of INPC2013, Florence, Italy, 2-7 June 201

Self-consistent calculation of nuclear photoabsorption cross section: Finite amplitude method with Skyrme functionals in the three-dimensional real space

The finite amplitude method (FAM), which we have recently proposed (T. Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)), simplifies significantly the fully self-consistent RPA calculation. Employing the FAM, we are conducting systematic, fully self-consistent response calculations for a wide mass region. This paper is intended to present a computational scheme to be used in the systematic investigation and to show the performance of the FAM for a realistic Skyrme energy functional. We implemented the method in the mixed representation in which the forward and backward RPA amplitudes are represented by indices of single-particle orbitals for occupied states and the spatial grid points for unoccupied states. We solve the linear response equation for a given frequency. The equation is a linear algebraic problem with a sparse non-hermitian matrix, which is solved with an iterative method. We show results of the dipole response for selected spherical and deformed nuclei. The peak energies of the giant dipole resonance agree well with measurements for heavy nuclei, while they are systematically underestimated for light nuclei. We also discuss the width of the giant dipole resonance in the fully self-consistent RPA calculation.Comment: 11 pages, 10 figure

Isospin-symmetry breaking in masses of N similar or equal to Z nuclei

Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the N = Z line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the T = 1/2 doublets and T= 1 triplets, and TDEs for the T= 1 triplets. Relative strengths of the obtained isospin-symmetry-breaking terms are not consistent with the differences in the NN scattering lengths, a(nn), a(pp), and a(np). Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections. (C) 2018 The Author(s). Published by Elsevier B.V.Peer reviewe

Microscopic Structure of High-Spin Vibrational Excitations in Superdeformed 190,192,194Hg

Microscopic RPA calculations based on the cranked shell model are performed to investigate the quadrupole and octupole correlations for excited superdeformed bands in 190Hg, 192Hg, and 194Hg. The K=2 octupole vibrations are predicted to be the lowest excitation modes at zero rotational frequency. At finite frequency, however, the interplay between rotation and vibrations produces different effects depending on neutron number: The lowest octupole phonon is rotationally aligned in 190Hg, is crossed by the aligned two-quasiparticle bands in 192Hg, and retains the K=2 octupole vibrational character up to the highest frequency in 194Hg. The gamma vibrations are predicted to be higher in energy and less collective than the octupole vibrations. From a comparison with the experimental dynamic moments of inertia, a new interpretation of the observed excited bands invoking the K=2 octupole vibrations is proposed, which suggests those octupole vibrations may be prevalent in SD Hg nuclei.Comment: 22 pages, REVTeX, 12 postscript figures are available on reques

Isospin-symmetry breaking in masses of N ≃ Z nuclei

Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the N=Z line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton–neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the T=1/2 doublets and T=1 triplets, and TDEs for the T=1 triplets. Relative strengths of the obtained isospin-symmetry-breaking terms are not consistent with the differences in the NN scattering lengths, a nn, a pp, and a np. Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections

Relative spins and excitation energies of superdeformed bands in 190Hg: Further evidence for octupole vibration

An experiment using the Eurogam Phase II gamma-ray spectrometer confirms the existence of an excited superdeformed (SD) band in 190Hg and its very unusual decay into the lowest SD band over 3-4 transitions. The energies and dipole character of the transitions linking the two SD bands have been firmly established. Comparisons with RPA calculations indicate that the excited SD band can be interpreted as an octupole-vibrational structure.Comment: 12 pages, latex, 4 figures available via WWW at http://www.phy.anl.gov/bgo/bc/hg190_nucl_ex.htm

Tilted Rotation and Wobbling Motion in Nuclei

The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with wobbling motion in rotating nuclei lead to the appearance of two- or three-dimensional rotation.Comment: 9 pages, 2 Postscript figures, corrected typo

The nuclear energy density functional formalism

The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a {\it Hamiltonian-based} picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel $E[g',g]$ at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. "mean-field", derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a {\it mathematically} meaningful fashion even if $E[g',g]$ does {\it not} derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making {\it any} reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a {\it physical} standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.Comment: 64 pages, 8 figures, submitted to Euroschool Lecture Notes in Physics Vol.IV, Christoph Scheidenberger and Marek Pfutzner editor