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Excited states in the proton-unbound nuclide $^{177}$Au were populated in the $^92}$Mo($^{88}$Sr, p2n) reaction and identified using the Jurogam-II and GREAT spectrometers in conjunction with the RITU gas-filled separator at the University of Jyvaskyla Accelerator Laboratory. A strongly coupled band and its decay path to the 11/2−α-decaying isomer have been identified using recoil-decay tagging. Comparisons with cranked Hartree-Fock-Bogoliubov (HFB) calculations based on Skyrme energy functionals suggest that the band has a prolate deformation and is based upon coupling the odd 1h11/2 proton hole to the excited 02+ configuration in the $^{178}$Hg core. Although these configurations might be expected to follow the parabolic trend of core Hg(02+) states as a function of neutron number, the electromagnetic decay paths from the strongly coupled band in $^{177}$Au are markedly different from those observed in the heavier isotopes above the midshell. This indicates that a significant change in the structure of the underlying A+1Hg core occurs below the neutron midshell.

Electron scattering provides a powerful tool to determine charge distributions and transition densities of nuclei. This tool will soon be available for short-lived neutron-rich nuclei. [Purpose] Beyond mean-field methods have been successfully applied to the study of excitation spectra of nuclei in the whole nuclear chart. These methods permit to determine energies and transition probabilities starting from an effective in-medium nucleon-nucleon interaction but without other phenomenological ingredients. Such a method has recently been extended to calculate the charge density of nuclei deformed at the mean-field level of approximation [J. M. Yao et al., Phys. Rev. C86, 014310 (2012)]. The aim of this work is to further extend the method to the determination of transition densities between low-lying excited states. [Method] The starting point of our method is a set of Hartree-Fock-Bogoliubov wave functions generated with a constraint on the axial quadrupole moment and using a Skyrme energy density functional. Correlations beyond the mean field are introduced by projecting mean-field wave functions on angular-momentum and particle number and by mixing the symmetry restored wave functions.[Results] We give in this paper detailed formulae derived for the calculation of densities and form factors. These formulae are rather easy to obtain when both initial and final states are $0^+$ states but are far from being trivial when one of the states has a finite $J$-value. Illustrative applications to $^{24}$Mg and to the even-mass $^{58-68}$Ni have permitted to analyse the main features of our method, in particular the effect of deformation on densities and form factors. An illustration calculation of both elastic and inelastic scattering form factors is presented...., Comment: 18 pages with 18 figures and 1 table, accepted for publication in Physical Review C

The restoration of particle number within Energy Density Functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and non-projected densities. As an alternative that might be advantageous for mass models, nuclear dynamics and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an Energy Density Functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies., 11 pages, 3 figures

We perform an analysis of a binding energy difference called $\ensuremath{\delta}{V}_{\mathit{pn}}(N,Z)\ensuremath{\equiv}\ensuremath{-}\frac{1}{4}[E(Z,N)\ensuremath{-}E(Z,N\ensuremath{-}2)\ensuremath{-}E(Z\ensuremath{-}2,N)+E(Z\ensuremath{-}2,N\ensuremath{-}2)]$ in the framework of a realistic nuclear model. It has been suggested that $\ensuremath{\delta}{V}_{\mathit{pn}}$ values provide a sensitive probe of nuclear structure, and it has been put forward as a primary motivation for the measurement of specific nuclear masses. Using the angular momentum and particle-number projected generator coordinate method and the Skyrme interaction SLy4, we analyze the contribution brought to $\ensuremath{\delta}{V}_{\mathit{pn}}$ by static deformation and dynamic fluctuations around the mean-field ground state. Our method gives a good overall description of $\ensuremath{\delta}{V}_{\mathit{pn}}$ throughout the chart of nuclei with the exception of the anomaly related to the Wigner energy along the $N=Z$ line. The main conclusions of our analysis of $\ensuremath{\delta}{V}_{\mathit{pn}}$, which are at variance with its standard interpretation, are that (i) the structures seen in the systematics of $\ensuremath{\delta}{V}_{\mathit{pn}}$ throughout the chart of nuclei can be easily explained combining a smooth background related to the symmetry energy and correlation energies due to deformation and collective fluctuations, (ii) the characteristic pattern of $\ensuremath{\delta}{V}_{\mathit{pn}}$ having a much larger size for nuclei that add only particles or only holes to a doubly magic nucleus than for nuclei that add particles for one nucleon species and holes for the other is a trivial consequence of the asymmetric definition of $\ensuremath{\delta}{V}_{\mathit{pn}}$ and not due to a the different structure of these nuclei, (iii) $\ensuremath{\delta}{V}_{\mathit{pn}}$ does not provide a very reliable indicator for structural changes, (iv)$\ensuremath{\delta}{V}_{\mathit{pn}}$ does not provide a reliable measure of the proton-neutron interaction in the nuclear energy density functional (EDF) or of that between the last filled orbits or of the one summed over all orbits, and (v) $\ensuremath{\delta}{V}_{\mathit{pn}}$ does not provide a conclusive benchmark for nuclear EDF methods that is superior or complementary to other mass filters such as two-nucleon separation energies or $Q$ values.

Absolute electromagnetic transition probabilities in $^{196}\mathrm{Po}$ have been measured using the recoil distance Doppler-shift technique. The lifetimes of the three lowest yrast states in $^{196}\mathrm{Po}$ were extracted from singles \ensuremath{\gamma}-ray spectra by using the recoil-decay tagging method. In addition, configuration mixing calculations of angular momentum projected mean-field states have been carried out for $^{196}\mathrm{Po}$. The present study sheds light on the onset of collectivity and mixing of competing structures in neutron-deficient Po nuclei.

By means of HFB calculations with independent constraints on axial neutron and proton quadrupole moments Q{sub n} and Q{sub p}, we investigate the large amplitude isoscalar and isovector deformation properties of the neutron-rich isotope {sup 20}O. Using the particle-number and angular-momentum projected generator coordinate method, we analyze the collective dynamics in the {l_brace} , {r_brace} plane. The parametrization SLy4 of the Skyrme interaction is used for all calculations in connection with a density-dependent zero-range pairing interaction. Our results show that already for this moderately neutron-rich nucleus the transition moments are modified when independent neutron and proton collective dynamics are allowed.

For the first time, non-yrast structures of the neutron mid-shell nucleus $^{186}\mathrm{Pb}$ have been identified in an in-beam \ensuremath{\gamma}-ray spectroscopy measurement using the recoil-decay tagging technique. The yrast band has been tentatively extended up to ${I}^{\ensuremath{\pi}}=20{}^{+},$ revealing a similar backbend to that observed in the Pt and Hg isotones. Three new bands and several other transitions have been observed. Calculations carried out in the framework of the interacting boson model together with mean-field studies using the generator coordinate method provide arguments for the association of one of the new bands with an oblate shape. The present data also show evidence for octupole and \ensuremath{\gamma}-vibrational bands.

We discuss shape coexistence in the neutron-deficient Kr72-Kr78 isotopes in the framework of configuration mixing calculations of particle-number and angular-momentum projected axial mean-field states obtained from self-consistent calculations with the Skyrme interaction SLy6 and a density-dependent pairing interaction. While our calculation reproduces qualitatively and quantitatively many of the global features of these nuclei, such as coexistence of prolate and oblate shapes, their strong mixing at low angular momentum, and the deformation of collective bands, the ordering of our calculated low-lying levels is at variance with experiment. We analyse the role of the single-particle spectrum of the underlying mean-field for the spectrum of collective excitations., accepted for publication in Phys. Rev. C

Beyond mean-field methods based on restoration of symmetries and configuration mixing by the generator coordinate method (GCM) enable to calculate on the same footing correlations in the ground state and the properties of excited states. Excitation energies are often largely overestimated, especially in nuclei close to magicity, even when transition probabilities are well-described. We analyse here the origin of this failure. The first part of the paper compares realistic projected GCM and QRPA calculations for selected Sn isotopes performed with the same effective Skyrme interaction. Although it is difficult to perform RPA and GCM calculations under exactly the same conditions, this comparison shows that the projected GCM overestimates the RPA results. In the second part of this paper, we compare GCM and RPA in the framework of the exactly solvable Lipkin-Meshkov-Glick model. We show that the discretized GCM works quite well and permits to obtain nearly exact results with a small number of discretization points. This analysis indicates also that to break more symmetries of the nuclear Hamiltonian in the construction of the GCM basis is probably the best way to improve the description of excited states by the GCM., Comment: 10 pages revtex4, 6 eps figures, submitted to Phys. Rev. C

The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the non-relativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of A^{-1/3} (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons, of the order of 10^6. The Coulomb interaction has been ignored to be able to approach nuclei of arbitrary sizes and to avoid radial instabilities characteristic of systems with very large atomic numbers. The main contribution to the fluctuating part of the binding energy has been removed using the Green's function method to calculate the shell correction. The limitations of applying the leptodermous expansion to actual nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects., Comment: 13 pages revtex4, 7 eps figures, submitted to Phys. Rev. C

The influence of exact angular-momentum projection and configuration mixing on properties of a heavy, well-deformed nucleus is discussed for the example of $^{240}\mathrm{Pu}$. Starting from a self-consistent model using Skyrme interactions, we analyze the resulting modifications of the deformation energy, the fission barrier height, the excitation energy of the superdeformed minimum associated with the fission isomer, the structure of the lowest rotational bands with normal deformation and superdeformation, and the corresponding quadrupole moments and transition moments. We present results obtained with the Skyrme interactions SLy4 and SLy6, which have slightly different surface tensions.

We investigate truncation schemes to reduce the computational cost of calculating correlations by the generator coordinate method based on mean-field wave functions. As our test nuclei, we take examples for which accurate calculations are available. These include a strongly deformed nucleus, 156Sm, a nucleus with strong pairing, 120Sn, the krypton isotope chain which contains examples of soft deformations, and the lead isotope chain which includes the doubly magic 208Pb. We find that the Gaussian overlap approximation for angular momentum projection is effective and reduces the computational cost by an order of magnitude. Cost savings in the deformation degrees of freedom are harder to realize. A straightforward Gaussian overlap approximation can be applied rather reliably to angular-momentum projected states based on configuration sets having the same sign deformation (prolate or oblate), but matrix elements between prolate and oblate deformations must be treated with more care. We propose a two-dimensional GOA using a triangulation procedure to treat the general case with both kinds of deformation. With the computational gains from these approximations, it should be feasible to carry out a systematic calculation of correlation energies for the nuclear mass table., Comment: 11 pages revtex, 9 eps figures

We investigate the systematics of fission barriers in superheavy elements in the range Z = 108-120 and N = 166-182. Results from two self-consistent models for nuclear structure, the relativistic mean-field (RMF) model as well as the non-relativistic Skyrme-Hartree-Fock approach are compared and discussed. We restrict ourselves to axially symmetric shapes, which provides an upper bound on static fission barriers. We benchmark the predictive power of the models examining the barriers and fission isomers of selected heavy actinide nuclei for which data are available. For both actinides and superheavy nuclei, the RMF model systematically predicts lower barriers than most Skyrme interactions. In particular the fission isomers are predicted too low by the RMF, which casts some doubt on recent predictions about superdeformed ground states of some superheavy nuclei. For the superheavy nuclei under investigation, fission barriers drop to small values around Z = 110, N = 180 and increase again for heavier systems. For most of the forces, there is no fission isomer for superheavy nuclei, as superdeformed states are in most cases found to be unstable with respect to octupole distortions., 17 pages REVTEX, 12 embedded eps figures. corrected abstract

We investigate the coexistence of spherical, deformed, and superdeformed states at low spin in $^{32}\mathrm{S}$, $^{36}\mathrm{Ar}$, $^{38}\mathrm{Ar}$, and $^{40}\mathrm{Ca}$. The microscopic states are constructed by configuration mixing of BCS states projected on good particle number and angular momentum. The BCS states are themselves obtained from Hartree-Fock BCS calculations using the Skyrme interaction SLy6 for the particle-hole channel and a density-dependent contact force in the pairing channel. The same interaction is used within the generator coordinate method to determine the configuration mixing and calculate the properties of even-spin states with positive parity. Our calculations underestimate moments of inertia. Nevertheless, for the four nuclei, the global structural properties of the states of normal deformation as well as the recently discovered superdeformed bands up to spin 6 are correctly reproduced with regard to both the energies and the transition rates.

A comparison of calculated and experimental ${Q}_{\ensuremath{\alpha}}$ values of superheavy even-even nuclei and a few selected odd-$N$ nuclei is presented in the framework of the relativistic mean-field model with the parametrization NL-Z2. Blocking effects are found to be important for a proper description of ${Q}_{\ensuremath{\alpha}}$ of odd mass nuclei. The model gives a good overall description of the available experimental data. The mass and charge assignment of the recently measured decay chains from Dubna and Berkeley is in agreement with the predictions of the model. The analysis of the new data does not allow a final conclusion about the location of the expected island of spherical doubly magic superheavy nuclei.