To synthesize superheavy element 119 is becoming a highly concerned issue as several experimental projects in major laboratories are being pursued. This work studied the survival probabilities of compound superheavy nuclei after multiple neutron emissions based on microscopic energy dependent fission barriers, demonstrating a significant role of triaxial deformation in decreasing the first fission barriers in the heaviest region. Together with the fusion cross sections by the dinuclear system model, the optimal energy and the residual cross section of 243Am(48Ca, 3n)288Mc are reproduced. Finally the cross sections and optimal beam energies of 54Cr+243Am and 50Ti+249Bk reactions are estimated, providing clues for the synthesis of new elements.

Received 14 March 2023DOI:https://doi.org/10.1103/PhysRevC.107.049901©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsElectromagnetic transitionsEnergy levels & level densitiesNuclear structure & decaysTransfer reactionsProperties150 ≤ A ≤ 189Nuclear Physics

Background: The symmetry-unrestricted Hartree-Fock-Bogoliubov (HFB) simulation is important for describing various quantum many-body systems. However, the HFB problem in Cartesian coordinate space is numerically challenging. Purpose: For describing ground states without imposing axial symmetry and looking ahead to future extension for dynamics with full time dependence, we present a numerically efficient implementation of the three-dimensional (3D) HFB code. Methods: We develop a 3D Skyrme HFB code based on the mixed-basis representation (HFBmix) which consists of two harmonic-oscillator (HO) bases in the x- and y-directions, and finite-difference (FD) basis in the z-direction in solving the nuclear 3D HFB problem. Results: The results show very well agreement among all the three codes (HFBmix, HO3D, and hfodd). Especially for the HF calculations, the differences in total energies are on the order of a few keV for the lightest O and Mg nuclei. The HFBmix is applied to spherical, prolate, and triaxial systems, and gives the same quadrupole moments for the deformed nuclei as those of the HO-based calculations. Feasibility of the HFBmix is demonstrated in the fission isomer and barrier calculations of 240Pu. Conclusions: The HFBmix is useful for solving the nuclear 3D HFB problem for its numerical efficiency. Future work will include the analysis of deformed drip-line systems and systematic potential-energy surface calculation for fission-path analysis as well as the time-dependent extension of the HFBmix code for dynamics calculations.

The survey of different configurations near Fermi surface of 138Nd results in 12 lowest configurations, at both positive- and negative-deformations. These are calculated to be the energetically lowest configurations. The results show that, for both EDFs, the rotational states based on positive-minimum, which is at gamma~35, are lower than the respective configurations with negative-deformation. The general trends of the spin-versus-omega curve, and the energy-versus-spin curve reproduce well those of the experimental data. Further, for the observed bands `T1-T8', the calculated results using SLy4L allows the configurations of the observed bands to be assigned. The calculations predict transitional quadrupole moments, which can be used to compare with future experimental data. The current cranked self-consistent mean-field calculations of the near-yrast high-spin rotational bands in 138Nd reproduce well the experimental data. The results suggest that the experimentally observed bands can be assigned to the calculated bands with various configurations at the positive-deformation. The predictions of the current calculations are complementary to that of the well-know macroscopic-microscopic calculations, both of which await future experiment to verify.

Products of the fusion-evaporation reaction Ca-48 + Am-243 were studied with the TASISpec set-up at the gas-filled separator TASCA at the GSI Helmholtzzentrum fur Schwerionenforschung, Darmstadt, Germany. Amongst the detected thirty correlated alpha-decay chains associated With the production of element Z = 115, two recoil-alpha-fission and five recoil-alpha-alpha-fission events were observed. The latter five chains are similar to four such events reported from experiments performed at the Dubna gas-filled separator, and three such events reported from an experiment at the Berkeley gas-filled separator. The four chains observed at the Dubna gas-filled separator were assigned to start from the 2n-evaporation channel (289)115 due to the fact that these recoil-alpha-alpha-fission events were observed only at low excitation energies. Contrary to this interpretation, we suggest that some of these recoil-alpha-alpha-fission decay chains, as well as some of the recoil-alpha-alpha-fission and recoil-alpha-fission decay chains reported from Berkeley and in this article, start from the 3n-evaporation channel (288)115. (C) 2016 Elsevier B.V. All rights reserved.

We calculate properties of the ground and excited states of nuclei in the nobelium region for proton and neutron numbers of 92≤Z≤104 and 144≤N≤156, respectively. We use three different energy-density-functional (EDF) approaches, based on covariant, Skyrme, and Gogny functionals, each with two different parameter sets. A comparative analysis of the results obtained for quasiparticle spectra, odd–even and two-particle mass staggering, and moments of inertia allows us to identify single-particle and shell effects that are characteristic to these different models and to illustrate possible systematic uncertainties related to using the EDF modelling.

For a shape-soft nucleus, the deformation change with increasing angular momentum of rotation can be significant. Total-Routhian-surface (TRS) calculations include the shape changes, but angular momentum is not conserved (neither is it a good quantum number, nor is it kept unchanged in the whole TRS mesh). In the projected shell model (PSM), the angular momentum appears as a good quantum number, but calculations have usually been performed with fixed deformation. In the present work, by performing angular-momentum projection on the mean-field potential-energy surface (PES), we can obtain an angular-momentum-conserved PES which gives deformation for a rotational state at a given spin. In order to investigate the shape-changing effect, we have chosen neutron-deficient Hg and Pb isotopes in which shape coexistence occurs. We interpret the irregular rotational behavior of the oblate bands at low spin as arising from deformation changes which are induced by collective rotation. At higher spin, the oblate rotational spectrum can also be influenced by the crossing between the K = 0 ground-state band and a low-K two-quasineutron band. Calculated g factors for the states of oblate bands are given for future experimental testing, and the intrinsic structures of high-K oblate states are investigated.

This paper reviews the systematic investigations and understanding for the shape transitions and coexistence with regard to triaxial deformations in A ～100 to 126 neutron-rich Rh (Z=45), Pd (Z=46), Ag (Z=47), Cd (Z=48) and Zr (Z=40), Nb (Z=41), Mo (Z=42), Tc (Z=43) isotopes with Z beyond and below Ru (Z = 44), respectively, in Ru the maximal triaxial deformation having been predicted and deduced. The recent measurements and studies of prompt triple-and four-fold,γ-γ-γand γ-γ-γ-γ, coincidence data from the spontaneous fission of 252Cf using Gammasphere have yielded considerable expansion and extension or first observation of the bands in Ru, Pd, Cd, and Nb isotopes, which provided important data for the studies of nuclear shapes in this region. Combined with previous investigations, recent systematic studies of the new data well reproduced by PES, TRS, PSM, CCCSM and SCTAC model calculations have traced shape changes along the isotonic and isotopic chains, re-spectively, and with changing excitations/spins as well, significantly expanding our knowledge of shape transitions/coexistence in nuclei. For the neutron-rich Ru and beyond, Rh, Pd, Ag and Cd isotopes, triaxial deformations γ=?28°, slightly smaller than the maximal value, were deduced in Rh (Z =45) isotopes, with chiral symmetry breaking proposed in 103?106Rh;onset of wobbling motions were identified in 112Ru and 114Pd (N=68), and probably also in 114Ru (N=70);evolution from chiral symmetry breaking in 110,112Ru with maximal triaxial deformations to disturbed chirality in 112,114,116Pd with less pronounced triaxial deformations was proposed; rich nuclear structure was proposed in soft Ag isotopes with possible chiral doubling structure suggested in 104,105Ag, and softness towards triaxial deformation proposed in heavier 115,117Ag;quasi-particle couplings, quasi-rotations and soft triaxiality were suggested in Cd (Z=48) isotopes with small deformations;onset of collectivity was recently suggested in 122,124,126 Cd in the vicinity of Z=50 and N = 82 closed shells by studies of Coulomb excitations; shape evolutions from maximal triaxial deformations in Ru (γ=?30°, with triaxial minimum energy gain of 0.67 MeV), through Rh with large triaxial deformations (γ=?28°), to less pronounced triaxiality in Pd (with triaxial minimum energy gain of 0.32 MeV), then soft triaxiality in Ag, and finally to slightly deformed Cd isotopes but with emergence of collectivity and soft triaxiality were proposed. The systematic studies of the band crossings in Pd revealed up-rising γ drivings of the first band crossings caused by (νh11/2)2 and down-sloping γdrivings of the second band crossings by (πg9/2)2, explained the onset of wobbling motions in 114Pd, and showed a long-sought picture of shape evolution and coexistence in the Pd isotopic chain which is more complete but complex than earlier predictions. Based on the systematic studies in the mass region, maximal triaxial deformation is found to be reached in 112Ru and less-pronounced triaxiality centered at 114Pd, both for N=68, four neutrons more than predicted in earlier theoretical calculations. In the neutron-rich Zr (Z=40), Nb (Z=41), Mo (Z=42) and Tc (Z=43) isotopes with Z just below Ru, large quadrupole deformations of axially symmetric shapes were deduced in Y and Zr isotopes, with emergence of the γ degree of freedom having been suggested for heavier Zr isotopes; medium triaxial deformations were deduced for the ground states of heavier (A>104) Nb isotopes, and, with increasing excitations and spins, evolution from medium triaxial deformations with strong quadrupole deformations at ground states to nearly axially-symmetric shapes were deduced;light Nb isotopes (A 6 103) have near axially-symmetric shapes with strong quadrupole deformations;combining with the identification of onset of strong quadrupole deformation at 100Nb in the Nb isotopic chain, an increase of soft triaxiality with increasing neutron number was proposed in 100?106Nb. Shape coexistence with regard to soft triaxiality is also proposed in Nb isotopes;large triaxial deformations,γvibrations and chiral doublets were proposed in Mo isotopes; chiral doubling and large triaxial deformations (γ ～ ?26°) slightly smaller than the maximal triaxiality were suggested in Tc isotopes. The neutron-rich nuclei with Z ranging from 41 through 48 and A ～100 to 126, especially the Pd and Nb isotopes are thus found to be transitional nuclei with regard to triaxiality.

Background: Recently, transition quadrupole moments in rotational bands of even-mass neutron-rich isotopes of molybdenum and ruthenium nuclei have been measured. The new data have provided a challenge for theoretical descriptions invoking stable triaxial deformations. Purpose: To understand experimental data on rotational bands in the neutron-rich Mo-Ru region, we carried out theoretical analysis of moments of inertia, shapes, and transition quadrupole moments of neutron-rich even-even nuclei around $^{110}$Ru using self-consistent mean-field and shell model techniques. Methods: To describe yrast structures in Mo and Ru isotopes, we use nuclear Density Functional Theory (DFT) with the optimized energy density functional UNEDF0. We also apply Triaxial Projected Shell Model (TPSM) to describe yrast and positive-parity, near-yrast band structures. Results: Our self-consistent DFT calculations predict triaxial ground-state deformations in $^{106,108}$Mo and $^{108.110,112}$Ru and reproduce the observed low-frequency behavior of moments of inertia. As the rotational frequency increases, a negative-$\gamma$ structure, associated with the aligned $\nu(h_{11/2})^2$ pair, becomes energetically favored. The computed transition quadrupole moments vary with angular momentum, which reflects deformation changes with rotation; those variations are consistent with experiment. The TPSM calculations explain the observed band structures assuming stable triaxial shapes. Conclusions: The structure of neutron-rich even-even nuclei around $^{110}$Ru is consistent with triaxial shape deformations. Our DFT and TPSM frameworks provide a consistent and complementary description of experimental data.

U. Forsberg, D. Rudolph, L.-L. Andersson, A. Di Nitto, Ch.E. Düllmann, J.M. Gates, P. Golubev, K.E. Gregorich, C.J. Gross, R.-D. Herzberg, F.P. Heßberger, J. Khuyagbaatar, J.V. Kratz, K. Rykaczewski, L.G. Sarmiento, M. Schädel, A. Yakushev, S. Åberg, D. Ackermann, M. Block, H. Brand, B.G. Carlsson, D. Cox, X. Derkx, J. Dobaczewski, K. Eberhardt, J. Even, C. Fahlander, J. Gerl, E. Jäger, B. Kindler, J. Krier, I. Kojouharov, N. Kurz, B. Lommel, A. Mistry, C. Mokry, W. Nazarewicz, H. Nitsche, J.P. Omtvedt, P. Papadakis, I. Ragnarsson, J. Runke, H. Schaffner, B. Schausten, Yue Shi, P. Thörle-Pospiech, T. Torres, T. Traut, N. Trautmann, A. Türler, A. Ward, D.E. Ward, N. Wiehl, 1 Lund University, 22100 Lund, Sweden 2 Helmholtz Institute Mainz, 55099 Mainz, Germany 3 Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany 4 GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany 5 Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 6 Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 7 University of Liverpool, Liverpool L69 7ZE, United Kingdom 8 Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan 9 University of Warsaw, 00681 Warsaw, Poland 10 University of Tennessee, Knoxville, Tennessee 37996, USA 11 University of Oslo, 0315 Oslo, Norway and 12 Paul Scherrer Institute and University of Bern, 5232 Villigen, Switzerland (Dated: February 11, 2015)

Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory.Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions.Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed.Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver MADNESS-HFB is bench-marked against a two-dimensional coordinate-space solver HFB-AX that is based on the B-spline technique and a three-dimensional solver HFODD that is based on the harmonic-oscillator basis expansion. Several examples are considered, including the self-consistent HFB problem for spin-polarized trapped cold fermions and the Skyrme-Hartree-Fock (+BCS) problem for triaxial deformed nuclei.Conclusions: The new MADNESS-HFB framework has many attractive features when applied to nuclear and atomic problems involving many-particle superfluid systems. Of particular interest are weakly bound nuclear configurations close to particle drip lines, strongly elongated and dinuclear configurations such as those present in fission and heavy-ion fusion, and exotic pasta phases that appear in neutron star crust.

Background: Nuclei in the Z approximate to 100 mass region represent the heaviest systems where detailed spectroscopic information is experimentally available. Although microscopic-macroscopic and self-consistent models have achieved great success in describing the data in this mass region, a fully satisfying precise theoretical description is still missing.Purpose: By using fine-tuned parametrizations of the energy density functionals, the present work aims at an improved description of the single-particle properties and rotational bands in the nobelium region. Such locally optimized parametrizations may have better properties when extrapolating towards the superheavy region.Methods: Skyrme Hartree-Fock-Bogolyubov and Lipkin-Nogami methods were used to calculate the quasi-particle energies and rotational bands of nuclei in the nobelium region. Starting from the most recent Skyrme parametrization, UNEDF1, the spin-orbit coupling constants and pairing strengths have been tuned, so as to achieve a better agreement with the excitation spectra and odd-even mass differences in Cf-251 and Bk-249.Results: The quasiparticle properties of 251Cf and 249Bk were very well reproduced. At the same time, crucial deformed neutron and proton shell gaps open up at N = 152 and Z = 100, respectively. Rotational bands in Fm, No, and Rf isotopes, where experimental data are available, were also fairly well described. To help future improvements towards a more precise description, small deficiencies of the approach were carefully identified.Conclusions: In the Z approximate to 100 mass region, larger spin-orbit strengths than those from global adjustments lead to improved agreement with data. Puzzling effects of particle-number restoration on the calculated moment of inertia, at odds with the experimental behavior, require further scrutiny.

A recent high-resolution alpha, X-ray, and gamma-ray coincidence-spectroscopy experiment offered the first glimpse of excitation schemes of isotopes along alpha-decay chains of Z = 115. To understand these observations and to make predictions about shell structure of superheavy nuclei below (288)115, we employ two complementary mean-field models: the self-consistent Skyrme energy density functional approach and the macroscopic-microscopic Nilsson model. We discuss the spectroscopic information carried by the new data. In particular, candidates for the experimentally observed E1 transitions in (276)Mt are proposed. We find that the presence and nature of low-energy E1 transitions in well-deformed nuclei around Z = 110, N = 168 strongly depends on the strength of the spin-orbit coupling; hence, it provides an excellent constraint on theoretical models of superheavy nuclei. To clarify competing theoretical scenarios, an experimental search for E1 transitions in odd-A systems (275,277)Mt, (275)Hs, and (277)Ds is strongly recommended.

Background: For cranked mean-field calculations with arbitrarily oriented rotational frequency vector. in the intrinsic frame, one has to employ constraints on average values of the quadrupole-moment tensor, so as to keep the nucleus in the principal-axis reference frame. Kerman and Onishi [Nucl. Phys. A 361, 179 (1981)] have shown that the Lagrange multipliers that correspond to the required constraints are proportional to omega x J, where J is the average angular momentum vector. Purpose: We study the validity and consequences of the Kerman-Onishi conditions in the context of self-consistent tilted-axis-cranking (TAC) mean-field calculations. Methods: We perform self-consistent two-dimensional-cranking calculations (with and without pairing) utilizing the symmetry-unrestricted solver HFODD. At each tilting angle, we compare the calculated values of quadrupole-moment-tensor Lagrange multipliers and. x J. Results: We show that in self-consistent calculations, the Kerman-Onishi conditions are obeyed with high precision. Small deviations seen in the calculations with pairing can be attributed to the truncation of the quasiparticle spectrum. We also provide results of systematic TAC calculations for triaxial strongly deformed bands in Yb-160. Conclusions: For nonstationary TAC solutions, Kerman-Onishi conditions link the nonzero values of the angle between rotational-frequency and angular-momentum vectors to the constraints on off-diagonal components of the quadrupole-moment tensor. To stabilize the convergence of self-consistent iterations, such constraints have to be taken into account. Only then one can determine the Routhian surfaces as functions of the tilting angles.

The neutron-rich nucleus Rh-112 has been reinvestigated by examining the prompt. rays emitted in the spontaneous fission of Cf-252 with the Gammasphere detector array. A new side band was built in 112Rh. Total Routhian surface calculations have been performed and confirm the role of triaxiality in the negative-parity structure of Rh-112.

The total-Routhian-surface (TRS) calculation provides a powerful theoretical tool to describe the collective rotations of nuclei. It gives a straightforward way to determine nuclear deformation which can change with increasing rotational frequency. In most cases, however, TRS calculations with a conventional pairing approach (e. g., Bardeen-Cooper-Schrieffer pairing) encounter a nonconvergence problem when applied to sidebands which are built on broken-pair excited intrinsic configurations. To overcome this problem, we have developed the TRS calculations with a particle-number-conserving pairing method in which the pairing correlation is treated with the merit of the shell model. In this paper, we present the first results of the calculations, focusing on the sidebands of the W-178 nucleus, investigating deformation changes and incurred effects on the rotational behaviors of sidebands. DOI: 10.1103/PhysRevC.87.044319

Since the cranking shell model was established, it has been well developed with several key landmarks. The model has been one of the most successful models which describe the collective rotation of nuclei. Two key developments are: (1) the inclusion of pairing interaction; (2) total-Routhian-surface (TRS) calculations. Such calculations can give nuclear structure information about shape evolution with increasing rotational frequency and rotational alignments of paired nucleons. We have made significant developments based on the cranking shell model: (1) developed pairing-deformationfrequency self-consistent TRS calculations; (2) developed configuration-constrained potential-energy-surface (PES) calculations which can calculate for any excited configurations in a self-consistent way; (3) developed configuration-constrained total-Routhian-surface (TRS) calculations, achieving the self-consistent calculations of rotational motions of any excited configurations.

We have performed self-consistent Skyrme Hartree-Fock-Bogolyubov calculations for nuclei close to No-254. Self-consistent deformations, including beta(2,4,6,8) as functions of the rotational frequency, were determined for even-even nuclei Fm-246,Fm-248,Fm-250, No-252,No-254, and (256)Rf. The quasiparticle spectra for N = 151 isotones and Z = 99 isotopes were calculated and compared with experimental data and the results of Woods-Saxon calculations. We found that our calculations give high-order deformations similar to those obtained for the Woods-Saxon potential, and that the experimental quasiparticle energies are reasonably well reproduced.

New level schemes of 112,114,115,116,117,118Pd are established by means of γ–γ–γ, γ–γ–γ–γ and γ–γ(θ) measurements of prompt fission γ rays from 252Cf using the Gammasphere multi-detector array. Spins/parities were assigned to levels based on γ–γ angular correlation measurements, level systematics and decay patterns. In the even-N isotopes 112,114,116Pd, two sets of odd-parity bands were identified and extended with spins measured in each band. The odd-parity bands with large level staggerings were interpreted as disturbed chirality with less pronounced triaxial deformations in the Pd isotopes than observed in the chiral symmetry breaking 110,112Ru with maximum triaxiality. Onset of wobbling motion was identified from the sign of the signature splitting in the γ band of even–even 114Pd, and probably also in 116Pd, as first seen in the N=68 isotone 112Ru. Maximal triaxiality in Ru and Pd isotopes is found to be reached for N=68, 112Ru and 114Pd, 4 neutrons more than predicted in the theoretical calculations. The new data and TRS calculations allowed a systematic study of the band crossings in the even-N 112,114,116Pd and odd-N 115,117Pd isotopes. Now we find a new overall, more complex shape evolution than previously proposed from triaxial prolate in 110Pd via triaxial oblate in 112Pd to nearly oblate in 114,116Pd with a large change of the triaxial deformation parameter γ toward nearly oblate in the (πg9/2)2 alignment in 114,115,116,117,118Pd, and triaxial-prolate–triaxial-oblate shape coexisting bands in 115Pd.