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The rotational properties of the transfermium nuclei are investigated in the full deformation space by implementing a shell-model-like approach in the cranking covariant density functional theory on a three-dimensional lattice, where the pairing correlations, deformations, and moments of inertia are treated in a microscopic and self-consistent way. The kinematic and dynamic moments of inertia of the rotational bands observed in the transfermium nuclei $^{252}$No, $^{254}$No, $^{254}$Rf, and $^{256}$Rf are well reproduced without any adjustable parameters using a well-determined universal density functional. It is found for the first time that the emergence of the octupole deformation should be responsible for the significantly different rotational behavior observed in $^{252}$No and $^{254}$No. The present results provide a microscopic solution to the long-standing puzzle on the rotational behavior in No isotopes, and highlight the risk of investigating only the hexacontetrapole ($\beta_{60}$) deformation effects in rotating transfermium nuclei without considering the octupole deformation.

The neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay and the double Gamow-Teller (DGT) transition are investigated with the state-of-the-art Relativistic Configuration-interaction Density functional theory. A strong linear correlation between the nuclear matrix elements (NMEs) of the $0\nu\beta\beta$ decay and the DGT transition is demonstrated. This linear correlation is found to originate from the similarity of the leading-order term of the $0\nu\beta\beta$-decay operator and the DGT-transition one, as revealed by expanding the $0\nu\beta\beta$-decay operator in terms of the spherical harmonics. The present results provide a strong support to constrain the $0\nu\beta\beta$-decay NMEs through the double charge-exchange reactions., Comment: 13 pages, 5 figures

The recently observed abnormal bifurcation of the double binding energy differences $\delta V_{pn}$ between the odd-odd and even-even nuclei along the $N=Z$ line from Ni to Rb has challenged the nuclear theories. To solve this problem, a shell-model-like approach based on the relativistic density functional theory is established, by treating simultaneously the neutron-neutron, proton-neutron, and proton-proton pairing correlations both microscopically and self-consistently. Without any \textit{ad hoc} parameters, the calculated results well reproduce the observations, and the mechanism for this abnormal bifurcation is found to be due to the enhanced proton-neutron pairing correlations in the odd-odd $N=Z$ nuclei, compared with the even-even ones. The present results provide an excellent interpretation for the abnormal $\delta V_{pn}$ bifurcation, and provide a clear signal for the existence of the proton-neutron pairing correlations for nuclei close to the $N=Z$ line., Comment: 6 pages, 4 figures

The level structure of the transitional nucleus $\mathrm{^{217}Ra}$ has been extended with the addition of around 20 new transitions. The discrepancies between the placements of several transitions reported in the earlier studies are resolved. The newly-established negative-parity sequence at low excitation energies hints at the expected parity-doublet structures in this nucleus. The properties of the observed simplex bands are compared with that of similar bands in neighboring nuclei. Since the presence of parity-doublet structures reflect octupole correlations, theoretical calculations using reflection-asymmetric triaxial particle rotor model (RAT-PRM) have been performed. A comparison of the observed features of the simplex bands with the predictions of the RAT-PRM calculations suggests that $\mathrm{^{217}Ra}$ exhibits an intermediate the behavior between the extremes of spherical and octupole-deformed nuclei. The termination of the simplex bands at intermediate energies and the structures lying above reflect the dominance of the single-particle excitations at higher excitation energies., Comment: 15 pages, 16 figures

The relativistic configuration-interaction density functional theory is developed for even-even and odd-odd nuclei and is used to predict the nuclear matrix element of the neutrinoless $\beta\beta$ ($0\nu\beta\beta$) decay in $^{76}$Ge, amongst the most promising $\beta\beta$-decay candidates. The spectroscopic properties of the $\beta\beta$-decay partners $^{76}$Ge and $^{76}$Se, and the nuclear matrix element governing the two-neutrino $\beta\beta$ ($2\nu\beta\beta$) decay in $^{76}$Ge are well reproduced, providing solid benchmarks for the theoretical calculations. The inclusion of the triaxial degree of freedom slightly enhances the nuclear matrix element of the $2\nu\beta\beta$ decay while raises that of the $0\nu\beta\beta$ decay significantly by a factor around two. The present results highlight the importance of nuclear triaxial deformation for a better prediction of the $0\nu\beta\beta$-decay nuclear matrix element., Comment: 14 pages, 4 figures

The effects of four-quasiparticle configurations and time-odd interactions are investigated in the framework of configuration interaction projected density functional theory by taking the yrast states of 60Fe as examples. Based on the universal PC-PK1 density functional, the energies of the yrast states with spin up to 20\hbar and the available B(E2) transition probabilities are well reproduced. The yrast states are predicted to be of four-quasiparticle structure above spin I = 16\hbar. The inclusion of the time-odd interactions increases the kinetic moments of inertia and delays the appearance of the first band crossing, and, thus, improves the description of the data., Comment: 14 pages,5 figures

The nuclear landscape has been investigated within the triaxial relativistic Hartree-Bogoliubov theory with the PC-PK1 density functional, and the beyond-mean-field dynamical correlation energies are taken into account by a microscopically mapped five-dimensional collective Hamiltonian without additional free parameters. The effects of triaxial deformation and dynamical correlations on the nuclear landscape are analyzed. The present results provide the best description of the experimental binding energies, in particular for medium and heavy mass regions, in comparison with the results obtained previously with other state-of-the-art covariant density functionals. The inclusion of the dynamical correlation energies plays an important role in the PC-PK1 results. It is emphasized that the nuclear landscape is considerably extended by the PC-PK1 functional in comparison with the previous results with other density functionals, which may be due to the different isovector properties in the density functionals., Comment: 10 pages, 3 figures. See http://nuclearmap.jcnp.org/index.html for the data of calculated ground-state properties and potential energy surfaces

The nuclear matrix elements of neutrinoless double-$\beta$ decay for nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation and quasiparticle configuration mixing. The low-lying spectra and the $B(E2:0^+\rightarrow2^+)$ values are reproduced well. The effects of the quasiparticles configuration mixing, the triaxial deformation, and the closure approximation on the nuclear matrix elements are studied in detail. For nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, the nuclear matrix elements are respectively reduced by the quasiparticle configuration mixing by 6%, 7%, 2%, 3%, and 4%, and enhanced by the odd-odd intermediate states by 7%, 4%, 11%, 20%, and 14%. Varying the triaxial deformation $\gamma$ from $0^\circ$ to $60^\circ$ for the mother and daughter nuclei, the nuclear matrix elements change by 41%, 17%, 68%, 14%, and 511% respectively for $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, which indicates the importance of treating the triaxial deformation consistently in calculating the nuclear matrix elements., Comment: 17 pages, 5 figures

Two newly observed bands built on a two-quasiparticle configuration in 130Ba have been investigated for the first time with the microscopic projected shell model. The experimental energy spectra and the available electromagnetic transition probabilities are well reproduced. The wobbling character of the higher band is revealed by the angular momentum projected wavefunctions via the K plot and the azimuthal plot. This provides the first strong microscopic evidence for wobbling motion based on a two-quasiparticle configuration in even-even nuclei., Comment: 12 pages, 4 figures

The nuclear chiral conundrum with crossing twin bands is investigated with three-dimensional tilted axis cranking covariant density functional theory in a fully self-consistent and microscopic way. The energy spectra and electromagnetic transition strengths for bands 1 and 2 in Ag-106 are well reproduced with two distinct configurations with two and four quasiparticles, respectively. For the four-quasiparticle configuration, a chiral vibrational band on top of band 2 is expected due to the soft Routhian curves. Therefore, it provides a microscopic and solid solution for the chiral conundrum in Ag-106. It also paves the way for understanding similar chiral structure in other nuclei in the future.., Comment: 6 pages, 4 figures

A triaxial projected shell model including configurations with more than four quasiparticles in the configuration space is developed, and applied to investigate the recently reported five chiral doublets candidates in a single even-even nucleus $^{136}$Nd. The energy spectra and transition probability ratios $B(M1)/B(E2)$ are reproduced satisfactorily. The configuration mixing along the rotational bands is studied by analyzing the intrinsic composition of the eigenfunctions. The chiral geometry of these nearly degenerate bands is examined by the \textit{K plot} and the \textit{azimuthal plot}, and the evolution from the chiral vibration to the static chirality with spin is clearly demonstrated for four pairs of partner bands. From the features in the \textit{azimuthal plot}, it is difficult to interpret the other candidate as chiral partners., Comment: 4 figures

We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian product structures on the base. As an application, we estimate the coindex of the Einstein metrics constructed in \cite{WZ90} and \cite{Wan92}. Finally, we investigate more closely the linear stability of Einstein metrics from circle bundle constructions and obtain a rigidity result for linearly stable Einstein metrics of this type., Comment: 23 pages

The excitation function for the 7 alpha de-excitation of $^{28}$Si nuclei excited to high excitation energies in the collisions of 35 MeV/nucleon $^{28}$Si with $^{12}$C reveals resonance structures that may indicate the population of high spin toroidal isomers such as those predicted by a number of recent theoretical calculations. This interpretation is supported by extended theoretical analyses., Comment: 11 pages, 5 figures

The possibility that a fraction of the dark matter is comprised of massive compact halo objects (MACHOs) remains unclear, especially in the 20-100 $M_{\odot}$ window. MACHOs could make up binaries, whose mergers may be detected by LIGO as gravitational wave events. On the other hand, the cosmological origin of fast radio burst (FRBs) has been confirmed. We investigate the possibility of detecting fast radio bursts (FRBs) gravitational lensed by MACHO binaries to constrain their properties. Since lensing events could generate more than one images, lensing by binaries could cause multiple-peak FRBs. The angular separation between these images is roughly $10^{-3}$ mas, which is too small to be resolved. The typical time interval between different images is roughly 1 millisecond (ms). The flux ratio between different images is roughly from 10 to $10^3$. With the expected detection rate of $10^4$ FRBs per year by the upcoming experiments, we could expect five multi-peak FRBs observed per year with time interval larger than 1 ms and flux ratio less than $10^3$ if the fraction of dark matter in MACHOs is $f\sim0.01$. A null search multiple-peak FRBs for time interval larger than 1 ms and flux ratio less than $10^3$ with $10^4$ FRBs would constrain the fraction $f$ of dark matter in MACHOs to $f<0.001$., Comment: 6 pages, 3 figures, 3 tables, accepted for publication in A&A, final version after language editing

We generalize the ancient solutions of the Ricci flow on certain principal ${\rm SO}(3)$ bundles over compact quaternionic K\"ahler manifolds constructed by Bakas, Kong, and Ni to certain $RP^3$ fibre bundles over a product of two compact quaternionic K\"ahler manifolds. The ancient solutions are of Type I, $\kappa$-noncollapsed, and have positive Ricci curvature. Analogous solutions on even-dimensional non-K\"ahlerian bundle spaces are also constructed., Comment: 33 pages

Double-perovskite oxides that contain both 3d and 5d transition metal elements have attracted growing interest as they provide a model system to study the interplay of strong electron interaction and large spin-orbit coupling (SOC). Here, we report on experimental and theoretical studies of the magnetic and electronic properties of double-perovskites (La$_{1-x}$Sr$_x$)$_2$CuIrO$_6$ ($x$ = 0.0, 0.1, 0.2, and 0.3). The undoped La$_2$CuIrO$_6$ undergoes a magnetic phase transition from paramagnetism to antiferromagnetism at T$_N$ $\sim$ 74 K and exhibits a weak ferromagnetic behavior below $T_C$ $\sim$ 52 K. Two-dimensional magnetism that was observed in many other Cu-based double-perovskites is absent in our samples, which may be due to the existence of weak Cu-Ir exchange interaction. First-principle density-functional theory (DFT) calculations show canted antiferromagnetic (AFM) order in both Cu$^{2+}$ and Ir$^{4+}$ sublattices, which gives rise to weak ferromagnetism. Electronic structure calculations suggest that La$_2$CuIrO$_6$ is an SOC-driven Mott insulator with an energy gap of $\sim$ 0.3 eV. Sr-doping decreases the magnetic ordering temperatures ($T_N$ and $T_C$) and suppresses the electrical resistivity. The high temperatures resistivity can be fitted using a variable-range-hopping model, consistent with the existence of disorders in these double-pervoskite compounds., Comment: Submitted; updated and added references in v2

We generalize the circle bundle examples of ancient solutions of the Ricci flow discovered by Bakas, Kong, and Ni to a class of principal torus bundles over an arbitrary finite product of Fano K\"ahler-Einstein manifolds studied by Wang and Ziller in the context of Einstein geometry. As a result, continuous families of $\kappa$-collapsed and $\kappa$-noncollapsed ancient solutions of type I are obtained on circle bundles for all odd dimensions $\geq 7$. In dimension $7$ such examples moreover exist on pairs of homeomorphic but not diffeomorphic manifolds. Continuous families of $\kappa$-collapsed ancient solutions of type I are also obtained on torus bundles for all dimensions $\geq 8$., Comment: 40 pages, no figure

Recent ab intio studies of the magnetic properties of all 3d transition metal(TM) freestanding atomic chains predicted that these nanowires could have a giant magnetic anisotropy energy (MAE) and might support a spin-spiral structure, thereby suggesting that these nanowires would have technological applicationsin, e.g., high density magnetic data storages. In order to investigate how the substrates may affect the magnetic properties of the nanowires, here we systematically study the V, Cr and Mn linear atomic chains on the Cu(001) surface based on the density functional theory with the generalized gradient approximation. We find that V, Cr, and Mn linear chains on the Cu(001) surface still have a stable or metastable ferromagnetic state. However, the ferromagnetic state is unstable against formation of a noncollinear spin-spiral structure in the Mn linear chains and also the V linear chain on the atop sites on the Cu(001) surface, due to the frustrated magnetic interactions in these systems. Nonetheless, the presence of the Cu(001) substrate does destabilize the spin-spiral state already present in the freestanding V linear chain and stabilizes the ferromagnetic state in the V linear chain on the hollow sites on Cu(001). When spin-orbit coupling (SOC) is included, the spin magnetic moments remain almost unchanged, due to the weakness of SOC in 3d TM chains. Furthermore, both the orbital magnetic moments and MAEs for the V, Cr and Mn are small, in comparison with both the corresponding freestanding nanowires and also the Fe, Co and Ni linear chains on the Cu (001) surface., Comment: Accepted for publication in J. Phys. D: Applied Physics

This physics book provides detailed discussions on important topics in $\tau$-charm physics that will be explored during the next few years at \bes3 . Both theoretical and experimental issues are covered, including extensive reviews of recent theoretical developments and experimental techniques. Among the subjects covered are: innovations in Partial Wave Analysis (PWA), theoretical and experimental techniques for Dalitz-plot analyses, analysis tools to extract absolute branching fractions and measurements of decay constants, form factors, and CP-violation and \DzDzb-oscillation parameters. Programs of QCD studies and near-threshold tau-lepton physics measurements are also discussed., Comment: Edited by Kuang-Ta Chao and Yi-Fang Wang

We have theoretically designed three families of the half-metallic (HM) antiferromagnets (AFM), namely, La$A$VOsO$_6$, La$A$MoTcO$_6$ and La$A$MoReO$_6$ ($A$ = Ca, Sr, Ba), based on a systematic {\it ab initio} study of the ordered double perovskites La$ABB'$O$_6$ with the possible $B$ and $B'$ pairs from all the 3$d$, 4$d$ and 5$d$ transtion metal elements being considered. Electronic structure calculations based on first-principles density-functional theory with generalized gradient approximation (GGA) for more than sixty double perovskites LaCa$BB'$O$_6$ have been performed using the all-electron full-potential linearized augmented-plane-wave method. The found HM-AFM state in these materials survives the full {\it ab initio} lattice constant and atomic position optimizations which were carried out using frozen-core full potential projector augmented wave method. It is found that the HM-AFM properties predicted previously in some of the double perovskites would disappear after the full structural optimizations. The AFM is attributed to both the superexchange mechanism and the generalized double exchange mechanism via the $B$ ($t_{2g}$) - O (2$p_{\pi}$) - $B'$ ($t_{2g}$) coupling and the latter is also believed to be the origin of the HM. Finally, in our search for the HM-AFMs, we find La$A$CrTcO$_6$ and La$A$CrReO$_6$ to be AFM insulators of an unconventional type in the sense that the two antiferromagnetic coupled ions consist of two different elements and that the two spin-resolved densities of states are no longer the same., Comment: To appear in Phys. Rev. B