An iterative adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method is developed within the framework of the Skyrme density functional theory. The ATDHFB equation is solved iteratively to avoid explicitly calculating the stability matrix. The contribution of the time-odd mean fields to the ATDHF(B) moment of inertia is incorporated self-consistently, and the results are verified by comparing them with the dynamical cranking predictions. The inertia mass tensor is calculated with the density-derivative term evaluated by numerical differentiation.

The excitation energy of the 1/2^{-} isomer in ^{99}In at N=50 is measured to be 671(37) keV and the mass uncertainty of the 9/2^{+} ground state is significantly reduced using the ISOLTRAP mass spectrometer at ISOLDE/CERN. The measurements exploit a major improvement in the resolution of the multireflection time-of-flight mass spectrometer. The results reveal an intriguing constancy of the 1/2^{-} isomer excitation energies in neutron-deficient indium that persists down to the N=50 shell closure, even when all neutrons are removed from the valence shell. This trend is used to test large-scale shell model, ab initio, and density functional theory calculations. The models have difficulties describing both the isomer excitation energies and ground-state electromagnetic moments along the indium chain.

The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are strongly interacting medium and heavy mass atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact many-body wave function is mapped onto a non-linear one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. In this way, additional correlations are subsumed in the system. However, the mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group-theory techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. Applications of the projection methods are presented for simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional (EDF) theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the EDF theories are highlighted in the present work.

The volum e and surface e ects in the nuclear localenergy density and the volum e and surface com ponents ofthe pairing interaction are discussed in the context ofthe m eaneld,Hartree-FockBogoliubov description ofatom icnuclei.Predictionsofpropertiesofexoticnucleicloseto theparticledrip linesare presented. PACS. 21.60.Jz Hartree-Fock and random -phaseapproxim ations{ 21.10.D r Binding energiesand m asses

We present the first application of a new approach, proposed in (2016J.Phys.G:Nucl.Part.Phys.4304LT01) to derive coupling constants of the Skyrme energy density functional (EDF) fromab initioHamiltonian. By perturbing theab initioHamiltonian with several functional generators defining the Skyrme EDF, we create a set of metadata that is then used to constrain the coupling constants of the functional. We use statistical analysis to obtain such anab initio-equivalent Skyrme EDF. We find that the resulting functional describes properties of atomic nuclei and infinite nuclear matter quite poorly. This may point to the necessity of building up theab initio-equivalent functionals from more sophisticated generators. However, we also indicate that the current precision of theab initiocalculations may be insufficient for deriving meaningful nuclear EDFs.

We present the first application of a new approach, proposed in [Journal of Physics G: Nuclear and Particle Physics, 43, 04LT01 (2016)] to derive coupling constants of the Skyrme energy density functional (EDF) from ab initio Hamiltonian. By perturbing the ab initio Hamiltonian with several functional generators defining the Skyrme EDF, we create a set of metadata that is then used to constrain the coupling constants of the functional. We use statistical analysis to obtain such an ab initio-equivalent Skyrme EDF. We find that the resulting functional describes properties of atomic nuclei and infinite nuclear matter quite poorly. This may point out to the necessity of building up the ab initio-equivalent functionals from more sophisticated generators. However, we also indicate that the current precision of the ab initio calculations may be insufficient for deriving meaningful nuclear EDFs.

We measure the hyperfine $C$-constant of the $3d4s^2 ~^2D_{5/2}$ atomic state in $^{45}$Sc: $C=-0.25(12)$\,kHz. High-precision atomic calculations of the hyperfine structure of the $3d4s^2 ~^2D_{5/2}$ state and second-order corrections are performed to infer the nuclear magnetic octupole moment $\Omega = 1.6(8) \mu_N b$. With a single valence proton outside of the doubly-magic calcium core, this element is ideally suited for an in-depth study of the many intriguing nuclear structure phenomena observed within the neighboring isotopes of calcium. We compare $\Omega$ to shell-model calculations, and find that they cannot reproduce the experimental value of $\Omega$ for $^{45}$Sc. We furthermore explore the use of Density Functional Theory for evaluating $\Omega$, and obtain values in line with the shell-model calculations. This work provides a crucial step in guiding future measurements of this fundamental quantity on radioactive scandium isotopes and will hopefully motivate a renewed experimental and theoretical interest.

We take an additional step towards the optimization of the novel finite-range pseudopotential at constrained Hartree-Fock-Bogolyubov level and implement an optimization procedure within an axial code using harmonic oscillator basis. We perform the optimization using three different numbers of the harmonic oscillator shells. We apply the new parameterizations in the O-Kr part of the nuclear chart and isotopic chain of Sn, and we compare the results with experimental values and those given by a parameterization obtained using a spherical code.

An upgraded ion-guide system for the production of neutron-deficient isotopes with heavy-ion beams has been commissioned at the IGISOL facility with an Ar-36 beam on a Ni-nat target. It was used together with the JYFLTRAP double Penning trap to measure the masses of Zr-82, Nb-84, Mo-86, Tc-88, and Ru-89 ground states and the isomeric state Tc-88(m). Of these, Ru-89 and Tc-88(m) weremeasured for the first time. The precision of measurements of Zr-82, Nb-84, and Tc-88 was significantly improved. The literature value for Mo-86 was verified. The measured states in Tc-88 were compared to shell-model calculations and additional constraints on the spins and level scheme were obtained. The masses of Mo-82 and Ru-86 have been predicted using the measured masses of their mirror partners and theoretical mirror displacement energies, resulting in more tightly bound nuclei with smaller atomic mass uncertainties than reported in the literature.

We extend the nuclear Density Functional Theory (DFT) by including proton-neutron mixing and contact isospin-symmetry-breaking (ISB) terms up to next-to-leading order (NLO). Within this formalism, we perform systematic study of the nuclear mirror and triple displacement energies, or equivalently of the Isobaric Multiplet Mass Equation (IMME) coefficients. By comparing results with those obtained within the existing Green Function Monte Carlo (GFMC) calculations, we address the fundamental question of the physical origin of the ISB effects. This we achieve by analyzing separate contributions to IMME coefficients coming from the electromagnetic and nuclear ISB terms. We show that the ISB DFT and GFMC results agree reasonably well, and that they describe experimental data with a comparable quality. Since the separate electromagnetic and nuclear ISB contributions also agree, we conclude that the beyond-mean-field electromagnetic effects may not play a dominant role in describing the ISB effects in finite nuclei.

We describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at nite temperature, (iv) ssion toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between hfbtho and hfodd, (vi) parallel capabilities, signi cantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particlenumber corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at nite temperature and several other little signi cant errors of the previous published version were corrected. PACS numbers: 07.05.T, 21.60.-n, 21.60.Jz E-mail: schunck1@llnl.gov

The ground-state rotational band of the neutron-deficient californium (Z = 98) isotope 244Cf was identified for the first time and measured up to a tentative spin and parity of I I-pi = 20(+). The observation of the rotational band indicates that the nucleus is deformed. The kinematic and dynamic moments of inertia were deduced from the measured gamma-ray transition energies. The behavior of the dynamic moment of inertia revealed an up-bend due to a possible alignment of coupled nucleons in high-j orbitals starting at a rotational frequency of about (h) over bar (omega) = 0.20 MeV. The results were compared with the systematic behavior of the even-even N = 146 isotones as well as with available theoretical calculations that have been performed for nuclei in the region.

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=12 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, ann, app, and anp. Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.

We show that the symmetry-restored paired mean-field states (quasiparticle vacuua) properly account for isoscalar vs. isovector nuclear pairing properties. Full particle-number, spin, and isospin symmetries are restored in a simple SO(8) proton-neutron pairing model, and prospects to implement similar approach in a realistic setting are delineated. Our results show that provided all symmetries are restored, the pictures based on pair-condensate and quartet-condensate wave functions represent two equivalent ways of looking at the physics of the nuclear proton-neutron pairing.

Letter of Intent to the ISOLDE and Neutron Time-of-Flight Committee An inelastic excitation study of multiple shape coexistence in Zr 10 Jan 2018 B.S. Nara Singh, R. Wadsworth, L. Barber, D.M. Cullen, S. Freeman, M. Giles, D. Sharp, A. Andreyev, C.J. Barton, M.A. Bentley, J. Dobaczewski, D.G. Jenkins, A. Pastore, A. Blazhev, T. Braunroth, A. Dewald, Ch. Fransen, R.-B. Gerst, J. Jolie, V. Karayonchev, J. Litzinger, K. Moschner, C. Müller-Gatermann, P. Reiter, N. Warr, M. Huyse, R. Raabe, P. Van Duppen, J. Ljungvall, T. Grahn, P. Greenlees, R. Julin, J. Pakarinen, P. Rahkila, T. Kroell, N. Pietralla, J. N. Orce, P. Butler, D.T. Joss, R.D. Page, L.J. Harkness-Brennan, D.S. Judson, P. Papadakis, M.J.G. Borge, E. Nacher, O. Tengblad, E. Clement, G. Rainovski, K. Gladnishki, M. Djongolov, A. Goergen, S. Siem, A. Algora, J. F. Smith, M. Scheck, P.J. Woods, S. Leoni, G. Jnaneswari, S.K. Mandal, D. T. Doherty, K. Hadynska-Klek, G.de Angelis, D.R.Napoli, J.J.Valiente Dobon, F.Recchia, S.M.Lenzi, D.Mengoni, P.J. Napiorkowski, K. Wrzosek-Lipska, J. Ballof, L.P. Gaffney, S. Rothe, T. Stora, F. Wenander, A. Poves, Toma ́s R. Rodri ́guez, P.C. Srivatsava and the Miniball/HIE-ISOLDE Collaboration The University of Manchester, Manchester, UK, University of York, York, UK, University of Cologne, Cologne, Germany, K.U. Leuven, Leuven, Belgium, CSNSM Orsay, France, JYFL, Jyvaskyla, Finland, TU Darmstadt, Darmstadt, Germany, University of Western Cape, South Africa, University of Liverpool, Liverpool, UK, IEM-CSIC Madrid, Spain, GANIL, Caen, France, University of Sofia, Sofia, Bulgaria, University of Oslo, Oslo, Norway, IFIC-Univ. Valencia, Spain, University of West of Scotland, Paisley, UK, University of Edinburgh, Edinburgh, UK, INFN and University of Milano, Milano, Italy, University of Delhi, Delhi, India, University of Surrey, Guildford, UK, INFN Legnaro National Labs, Legnaro, Italy, INFN and University of Padova, Padova, Italy, University of Warsaw, Poland, ISOLDE-CERN, Switzerland, Universidad Auto ́noma de Madrid, Madrid, Spain, IIT Roorkee, India Spokespersons: B.S. Nara Singh (sreenivasa.bondili@manchester.co.uk) and R. Wadsworth (bob.wadsworth@york.ac.uk) Contact: L. P. Gaffney Abstract In line with the LoI I-102 [1], we propose to study a rare multiple shape co-existence phenomenon in the self-conjugate Zr nucleus, taking advantage of boost in beam energies at HIE-ISOLDE to perform multistep inelastic excitations. The influence of proton-neutron interaction on the low-lying level structure in this nucleus will also be addressed. At present, no beam of the refractory Zr element is available. Therefore, a development of Zr beam is proposed, using a procedure that is similar to the development of Hf beams.

We present results of the Hartree-Fock-Bogolyubov calculations performed using nuclear energy density functionals based on regularized functional generators at next-to-leading and next-to-next-to-leading order. We discuss properties of binding energies and pairing gaps determined in semi-magic spherical nuclei. The results are compared with benchmark calculations performed for the functional generator SLyMR0 and functional UNEDF0.

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.