Search

Low-energy spectra in the isotopic chain $^{250-262}$No are systematically investigated within the fully self-consistent Quasiparticle Random-Phase-Approximation (QRPA) using Skyrme forces SLy6, SkM* and SVbas. QRPA states of multipolarity $\lambda\mu$=20, 22, 30, 31, 32, 33, 43, 44 and 98 are considered. The main attention is paid to isotopes $^{252}$No and $^{254}$No, for which the most extensive experimental spectroscopic information is available. In these two nuclei, a reasonable description of $K^{\pi}=8^-, 2^-$and $3^+$ isomers is obtained with the force SLy6. The disputed $8^-$ isomer in $^{254}$No is assigned as neutron two-quasiparticle configuration $nn[734\uparrow,613\uparrow]$. At the energies 1.2 - 1.4 MeV, the 2qp K-isomers $4^-, 7^-$ in $^{252}$No and $4^-, 6^-, 7^-$ in $^{254}$No are predicted. In $^{254}$No, the $K^{\pi}=3^+$ isomer should be accompanied by the nearby $K^{\pi}=4^+$ counterpart. It is shown that, in the chain $^{250-262}$No, some features of $^{252}$No and $^{254}$No exhibit essential irregularities caused by a shell gap in the neutron single-particle spectrum and corresponding breakdown of the neutron pairing. In particular, low-energy pairing-vibrational $K^{\pi}=0^+$ states in $^{252,254}$No are predicted., Comment: 18 pages, 10 tables, 11 figures

A simple and clear method is proposed to calculate the averaged motion of the apsis line in the Moon orbit. The obtained result is $3^{\circ}1'12''$ for the starry period of the Moon revolution around the Earth or $40^{\circ}22'48''$ per year. The modern observed value of the latter quantity is $40^{\circ}41'$ per year. In "Principia" Newton derived $1^{\circ}31'28''$ for the Moon month and $20^{\circ}12''$ per year. That is approximately two times less than the observable values. Unlike the Newton approach we use a simple and obvious averaging of the Sun disturbing force for the starry period of the Moon revolution around the Earth. The applicability of the obtained formulae to satellites of other planets and to the planets themselves is grounded. Comparing Newton's calculation with our method we reveal the reason, rather convincing, that brings Newton to inadequate result., Comment: 13 pages, 1 figure

Dipole toroidal modes appear in many fields of physics. In nuclei, such a mode was predicted more than 50 years ago, but clear experimental evidence was lacking so far. Using a combination of high-resolution inelastic scattering experiments with photons, electrons and protons, we identify for the first time candidates for toroidal dipole excitations in the nucleus $^{58}$Ni and demonstrate that transverse electron scattering form factors represent a relevant experimental observable to prove their nature., Comment: 13 pages, 8 figures

The dipole electric ($E1$) and magnetic ($M1$) strengths in strongly deformed $^{156}$Gd are investigated within a fully self-consistent Quasiparticle Random Phase Approximation (QRPA) with Skyrme forces SVbas, SLy6 and SG2. We inspect, on the same theoretical footing, low-lying dipole states and the isovector giant dipole resonance in $E1$ channel and the orbital scissors resonance as well as the spin-flip giant resonance (SFGR) in $M1$ channel. Besides, $E1$ toroidal mode and low-energy spin-flip $M1$ excitations are considered. The deformation splitting and dipole-octupole coupling of electric excitations are analyzed. The origin of SFGR gross structure, impact of the residual interaction and interference of orbital and spin contributions to SFGR are discussed. The effect of the central exchange $\textbf{J}^2$-term from the Skyrme functional is demonstrated. The calculations show a satisfactory agreement with available experimental data, except for the recent NRF measurements of M. Tamkas et al for $M1$ strength at 4-6 MeV, where, in contradiction with our calculations and previous $(p,p')$ data, almost no $M1$ strength was observed., Comment: 13 pages, 6 figures, 8 tables

The dependence of the moment of inertia $\cal J$ on the pairing and axial quadrupole deformation $\beta$ in $^{24}$Mg and $^{20}$Ne was investigated. The study is based on quadrupole-constrained calculations with three cranking approaches for $\cal J$ (Inglis-Belyaev, Thouless-Valatin, adiabatic time-dependent Hartree-Fock) and a representative set of Skyrme forces (SVbas, SkM*, SLy6). At variance with macroscopic collective models, the calculations predict the specific regime $d{\cal J}/d\beta<0$ at $\beta \ge 0.5$ ($^{24}$Mg) and $\beta \ge 0.6$ ($^{20}$Ne), where the pairing breaks down. This regime is explained by two effects: full break up of the pairing and specific evolution of a {\it single} dominant particle-hole (1ph) configuration with $\beta$. The analysis of experimental data for the ground-state rotational bands in $^{24}$Mg and $^{20}$Ne shows that such regime is possible at low spins., Comment: 17 pages, 8 figures; refs. [15,16] were added as compared with the previous version

The low-energy $M1$ states in deformed $^{164}$Dy and spherical $^{58}$Ni are explored in the framework of fully self-consistent Quasiparticle Random-Phase Approximation (QRPA) with various Skyrme forces. The main attention is paid to orbital and spin $M1$ excitations. The obtained results are compared with the prediction of the low-energy {\it spin-scissors} $M1$ resonance suggested within Wigner Function Moments (WFM) approach. A possible relation of this resonance to low-energy spin-flip excitations is analyzed. In connection with recent WFM studies, we consider evolution of the low-energy spin-flip states in $^{164}$Dy with deformation (from the equilibrium value to the spherical limit). The effect of tensor forces is briefly discussed. It is shown that two groups of $1^+$ states observed at 2.4-4 MeV in $^{164}$Dy are rather explained by fragmentation of the orbital $M1$ strength than by the occurrence of the collective spin-scissors resonance. In general, our calculations do not confirm the existence of this resonance., Comment: 7 pages, 7 figures, submitted to Physics of Atomic Nuclei. arXiv admin note: text overlap with arXiv:2102.13580. As compared with the previous version, Ref. [1] was removed, Ref [33] was replaced, description of Fig. 3 was modified

At the physical level of rigour it is shown that there are no substantial theoretical arguments in favour of using either plasma mode permittivity or Drude model permittivity in the Lifshitz formula. The decision in this question rests with the comparison of theoretical calculations with the experiment. In the course of the study the derivation of the fluctuation-dissipation theorem is proposed where it is displayed clear at which reasoning stage and in what way the dissipation is taken into account. In particular it is shown how this theorem works in the case of the system with reversible dynamics, that is when dissipation is absent. Thereby it is proved that explicit assertion according to which this theorem is inapplicable to systems without dissipation is erroneous. The research is based on making use of the rigorous formalism of equilibrium two-time Green functions in statistical physics at finite temperature., Comment: 31 pages, 2 figures

Background: In highly deformed nuclei, there is a noticeable coupling of the Isoscalar Giant Monopole Resonance (ISGMR) and the $K = 0$ component of the Isoscalar Giant Quadrupole Resonance (ISGQR), which results in a double peak structure of the isoscalar monopole (IS0) strength (a narrow low-energy deformation-induced peak and a main broad ISGMR part). The energy of the narrow low-lying IS0 peak is sensitive to both the incompressibility modulus $K_\infty$ and the coupling between IS0 and isoscalar quadrupole (IS2) strength. Objective: This study aims to investigate the two-peaked structure of the ISGMR in the prolate $^{24}$Mg and oblate $^{28}$Si nuclei and identify among a variety of energy density functionals based on Skyrme parameterisations the one which best describes the experimental data. This will allow for conclusions regarding the nuclear incompressibility. Because of the strong IS0/IS2 coupling, the deformation splitting of the ISGQR will also be analysed. Methods: The ISGMR was excited in $^{24}$Mg and $^{28}$Si using $\alpha$-particle inelastic scattering measurements acquired with an $E_\alpha = 196$ MeV beam at scattering angles $\theta_{\text{Lab}} = 0^\circ$ and $4^\circ$. The K$600$ magnetic spectrometer at iThemba LABS was used to detect and momentum analyse the inelastically scattered $\alpha$ particles. An experimental energy resolution of $\approx 70$ keV (FWHM) was attained, revealing fine structure in the excitation-energy region of the ISGMR. The IS0 strength distributions in the nuclei studied were obtained with the Difference-of-Spectrum (DoS) technique. The theoretical comparison is based on the quasiparticle random-phase approximation (QRPA) with a representative set of Skyrme forces., Comment: 17 pages, 16 figures, regular article

A low-energy magnetic dipole $(M1)$ spin-scissors resonance (SSR) located just below the ordinary orbital scissors resonance (OSR) was recently predicted in deformed nuclei within the Wigner Function Moments (WFM) approach. We analyze this prediction using fully self-consistent Skyrme Quasiparticle Random Phase Approximation (QRPA) method. Skyrme forces SkM*, SVbas and SG2 are implemented to explore SSR and OSR in $^{160,162,164}$Dy and $^{232}$Th. Accuracy of the method is justified by a good description of M1 spin-flip giant resonance. The calculations show that isotopes $^{160,162,164}$Dy indeed have at 1.5-2.4 MeV (below OSR) $I^{\pi}K=1^+1$ states with a large $M1$ spin strength ($K$ is the projection of the total nuclear moment to the symmetry z-axis). These states are almost fully exhausted by $pp[411\uparrow, 411\downarrow]$ and $nn[521\uparrow, 521\downarrow]$ spin-flip configurations corresponding to $pp[2d_{3/2}, 2d_{5/2}]$ and $nn[2f_{5/2}, 2f_{7/2}]$ structures in the spherical limit. So the predicted SSR is actually reduced to low-orbital (l=2,3) spin-flip states. Following our analysis and in contradiction with WFM spin-scissors picture, deformation is not the principle origin of the low-energy spin $M1$ states but only a factor affecting their features. The spin and orbital strengths are generally mixed and exhibit the interference: weak destructive in SSR range and strong constructive in OSR range. In $^{232}$Th, the $M1$ spin strength is found very small. Two groups of $I^{\pi}=1^+$ states observed experimentally at 2.4-4 MeV in $^{160,162,164}$Dy and at 2-4 MeV in $^{232}$Th are mainly explained by fragmentation of the orbital strength. Distributions of nuclear currents in QRPA states partly correspond to the isovector orbital-scissors flow but not to spin-scissors one., Comment: 15 pages, 13 figures

Nuclei in the $sd$-shell demonstrate a remarkable interplay of cluster and mean-field phenomena. The $N=Z$ nuclei, such as $^{24}$Mg and $^{28}$Si, have been the focus of the theoretical study of both these phenomena in the past. The cluster and vortical mean-field phenomena can be probed by excitation of isoscalar monopole and dipole states in scattering of isoscalar particles such as deuterons or $\alpha$ particles. Inelastically scattered $\alpha$ particles were momentum-analysed in the K600 magnetic spectrometer at iThemba LABS, Cape Town, South Africa. The scattered particles were detected in two multi-wire drift chambers and two plastic scintillators placed at the focal plane of the K600. In the theoretical discussion, the QRPA and AMD+GCM were used. The QRPA calculations lead us to conclude that: i) the mean-field vorticity appears mainly in dipole states with $K=1$, ii) the dipole (monopole) states should have strong deformation-induced octupole (quadrupole) admixtures, and iii) that near the $\alpha$-particle threshold, there should exist a collective state (with $K=0$ for prolate nuclei and $K=1$ for oblate nuclei) with an impressive octupole strength. The results of the AMD+GCM calculations suggest that some observed states may have a mixed (mean-field + cluster) character or correspond to particular cluster configurations. A tentative correspondence between observed states and theoretical states from QRPA and AMD+GCM was established. The QRPA and AMD+GCM analysis shows that low-energy isoscalar dipole states combine cluster and mean-field properties. The QRPA calculations show that the low-energy vorticity is well localized in $^{24}$Mg, fragmented in $^{26}$Mg, and absent in $^{28}$Si., Comment: 11 figures, 18ish pages, accepted in Phys Rev C

Background: Inelastic proton scattering at energies of a few hundred MeV and very-forward angles including $0^\circ$ has been established as a tool to study electric-dipole strength distributions in nuclei. The present work reports a systematic investigation of the chain of stable even-mass Nd isotopes representing a transition from spherical to quadrupole-deformed nuclei. Purpose: Extraction of the equivalent photo-absorption cross sections and analysis of their fine structure in the energy region of the IsoVector Giant Dipole Resonance (IVGDR). Method: Proton inelastic scattering reactions of 200 MeV protons were measured at iThemba LABS in Cape Town, South Africa. The scattering products were momentum-analysed by the K600 magnetic spectrometer positioned at $\theta_{\mathrm{Lab}}=0^\circ$. Using dispersion-matching techniques, energy resolutions of $\Delta E \approx 40 - 50$ keV were obtained. After subtraction of background and contributions from other multipoles, the spectra were converted to photo-absorption cross sections using the equivalent virtual-photon method. Results: Wavelet-analysis techniques are used to extract characteristic energy scales of the fine structure of the IVGDR from the experimental data. Comparisons with the Quasiparticle-Phonon Model (QPM) and Skyrme Separable Random Phase Approximation (SSRPA) predictions provide insight into the role of different giant resonance damping mechanisms. Conclusions: Fine structure is observed even for the most deformed nuclei studied. Fragmentation of the one particle-one hole ($1p1h$) strength seems to be the main source of fine structure in both spherical and deformed nuclei. Some impact of the spreading due to coupling of the two particle-two hole ($2p2h$) states to the $1p1h$ doorway states is seen in the spherical/transitional nuclei, where calculations beyond the $1p1h$ level are available., Comment: 17 pages, 17 figures; Minor changes made such as those clarifying the descriptions of the analysis procedure, but the results are unchanged. The current version was accepted for publication by PRC on 7 December 2020

Individual low-energy E1 toroidal and compressional states (TS and CS) produced by the convective nuclear current ${\bf j}_{\rm c}$ were recently predicted for $^{24}$Mg in the framework of quasiparticle random-phase-approximation (QRPA) with Skyrme forces. In the present QRPA study with Skyrme parametrization SLy6, we explore in more detail properties of these states (toroidal and compressional responses, current distributions, and transitions probabilities $B(E1K, 0^+0 \to 1^-K),\; B(E3K, 0^+0 \to 3^-K)$, $B(M2K, 0^+0 \to 2^-K)$ with $K=$0 and 1) and analyze the possibility to discriminate and identify TS in inelastic electron scattering to back angles. The interplay of the convective ${\bf j}_{\rm c}$ and magnetization ${\bf j}_{\rm m}$ nuclear currents is thoroughly scrutinized. A two-step scheme for identification of TS in $(e,e')$ reaction is proposed. The key element of the scheme is the strong interference of the orbital and spin contributions, resulting in specific features of E1 and M2 transversal form factors., Comment: 10 pages, 9 figures. The previous version of the paper was crucially revised and enlarged in both i) description on main features and ii) proposals for (e,e') reaction. Submitted to Phys. Rev. C

We analyze the relation between isoscalar toroidal modes and so-called pygmy dipole resonance (PDR) which both appear in the same region of low-energy dipole excitations. To this end, we use a theoretical description within the fully self-consistent Skyrme quasiparticle random-phase approximation (QRPA). Test cases are spherical nuclei $^{40,48}$Ca, $^{58,72}$Ni, $^{90,100}$Zr, and $^{100,120,132}$Sn which cover four different elements and for each element at least two isotopes with different neutron excess, one small and another large. The structure of the modes is investigated in terms of strength functions, transition densities (TD) and transition currents (TC). For all considered nuclei, we see that, independently on whether PDR strength exists or not, the flow pattern in the lower part of the "PDR energy region" is basically the isoscalar vortical toroidal motion with a minor irrotational fraction. A one-to-one correspondence between calculated TD and TC can be established. The toroidal flow appears already in the uncoupled two-quasiparticle (2qp) excitations and becomes definitively strong for the QRPA modes. Altogether, we find that low-lying dipole strength often denoted as isoscalar PDR is actually an oversimplified imitation of the basically toroidal motion in nuclei with a sufficient neutron excess., Comment: 12 pages, 14 figures

We suggest a generalized method for elimination of spurious admixtures (SA) from intrinsic nuclear excitations described within the Quasiparticle-Random-Phase-Approximation (QRPA). Various kinds of SA-corrections are treated at the same theoretical ground. The known corrections are well reproduced. As relevant cases, we consider subtraction of SA related with i) violation of the translational invariance (isovector E1 and isoscalar toroidal and compression E1 modes), ii) pairing-induced non-conservation of the particle number (E2(K=0) and E0 modes), and iii) rotational invariance (E2(K=1) and M1(K=1) modes). The SA subtraction can be done at the level of QRPA states, electromagnetic responses, and even transition operators. The additional deformation-induced corrections are proposed. The accuracy of the method is demonstrated by Skyrme QRPA calculations for axially-deformed $^{154}$Sm., Comment: 13 pages, 7 figures, to be published in Phys. Rev. C

The existence of individual low-energy E1 toroidal and compression states (TS and CS) in $^{24}$Mg was predicted recently in the framework of quasiparticle random-phase-approximation (QRPA) model with Skyrme forces. It was shown that the strong axial deformation of $^{24}$Mg is crucial to downshift the toroidal strength to the low-energy region and thus make the TS the lowest E1(K=1) dipole state. In this study, we explain this result by simple mean-field arguments. Comparing TS in two strongly axial nuclei, $^{24}$Mg and $^{20}$Ne, we show that the lowest TS is not not a universal phenomenon but rather a peculiarity of $^{24}$Mg. The spectroscopy of TS and CS is analyzed and some additional interpretation of these states is suggested., Comment: 6 pages, 8 figures, 2 tables. Submitted to proceedings of International Conference on Nuclear Structure and Related Topics - NSRT18 (Bulgaria, Bourgas, June 3-9, 2018). The paper was resubmitted to enlarge the reference list

The low-energy dipole excitations in $^{24}$Mg are investigated within the Skyrme quasiparticle random-phase-approximation (QRPA) for axial nuclei. The calculations with the force SLy6 reveal a remarkable feature: the lowest $I^{\pi}K=1^-1$ excitation (E = 7.92 MeV) in $^{24}$Mg is a vortical toroidal state (TS) representing a specific vortex-antivortex realization of well-known spherical Hill's vortex in a strongly deformed axial confinement. This is a striking example of an {\it individual} TS which can be much easier discriminated in experiment than the toroidal dipole resonance embracing many states. The TS acquires the lowest energy due to the huge prolate axial deformation in $^{24}$Mg. The result persists for different Skyrme parameterizations (SLy6, SVbas, SkM*). We analyze spectroscopic properties of the TS and its relation with the cluster structure of $^{24}$Mg. Similar TS could exist in other highly prolate light nuclei. They could serve as promising tests for various reactions to probe a vortical (toroidal) nuclear flow., Comment: 6 pages, 5 figures, Supplemental Material, to be published in Phys. Rev. Lett

The phenomenon of fine structure of the Isoscalar Giant Quadrupole Resonance (ISGQR) has been studied with high energy-resolution proton inelastic scattering at iThemba LABS in the chain of stable even-mass Nd isotopes covering the transition from spherical to deformed ground states. A wavelet analysis of the background-subtracted spectra in the deformed 146,148,150Nd isotopes reveals characteristic scales in correspondence with scales obtained from a Skyrme RPA calculation using the SVmas10 parameterization. A semblance analysis shows that these scales arise from the energy shift between the main fragments of the K = 0, 1 and K = 2 components., Comment: 7 pages, 6 figures

We investigate effects of pairing and of quadrupole deformation on two sorts of nuclear excitations,$\gamma$-vibrational $K^{\pi}=2^+$ states and dipole resonances (isovector dipole, pygmy, compression, toroidal). The analysis is performed within the quasiparticle random-phase approximation (QRPA) based on the Skyrme energy functional using the Skyrme parametrization SLy6. Particular attention is paid to i) the role of the particle-particle (pp) channel in the residual interaction of QRPA, ii) comparison of volume pairing (VP) and surface pairing (SP), iii) peculiarities of deformation splitting in the various resonances. We find that the impact of the pp-channel on the considered excitations is negligible. This conclusion applies also to any other excitation except for the $K^{\pi}=0^+$ states. Furthermore, the difference between VP and SP is found small (with exception of peak height in the toroidal mode). In the low-energy isovector dipole (pygmy) and isoscalar toroidal modes, the branch $K^{\pi}=1^-$ is shown to dominate over $K^{\pi}=0^-$ one in the range of excitation energy $E <$ 8--10 MeV. The effect becomes impressive for the toroidal resonance whose low-energy part is concentrated in a high peak of almost pure $K^{\pi}=1^-$ nature. This peculiarity may be used as a fingerprint of the toroidal mode in future experiments. The interplay between pygmy, toroidal and compression resonances is discussed, the interpretation of the observed isoscalar giant dipole resonance is partly revised., Comment: 12 pages, 12 figures

Proton inelastic scattering experiments at energy E_p = 200 MeV and a spectrometer scattering angle of 0 degree were performed on 144,146,148,150Nd and 152Sm exciting the IsoVector Giant Dipole Resonance (IVGDR). Comparison with results from photo-absorption experiments reveals a shift of resonance maxima towards higher energies for vibrational and transitional nuclei. The extracted photo-absorption cross sections in the most deformed nuclei, 150Nd and 152Sm, exhibit a pronounced asymmetry rather than a distinct double-hump structure expected as a signature of K-splitting. This behaviour can be related to the proximity of these nuclei to the critical point of the phase shape transition from vibrators to rotors with a soft quadrupole deformation potential. Self-consistent random-phase approximation (RPA) calculations using the SLy6 Skyrme force provide a relevant description of the IVGDR shapes deduced from the present data, Comment: 8 pages, 4 figures

The deformation-induced splitting of isoscalar giant monopole resonance (ISGMR) is systematically analyzed in a wide range of masses covering medium, rare-earth, actinide, and superheavy axial deformed nuclei. The study is performed within the fully self-consistent quasiparticle random-phase-approximation (QRPA) method based on the Skyrme functional. Two Skyrme forces, one with a large (SV-bas) and one with a small (SkP) nuclear incompressibility, are considered. The calculations confirm earlier results that, due to the deformation-induced E0-E2 coupling, the isoscalar E0 resonance attains a double-peak structure and significant energy upshift. Our results are compared with available analytic estimations. Unlike earlier studies, we get a smaller energy difference between the lower and upper peaks and thus a stronger E0-E2 coupling. This in turn results in more pumping of E0 strength into the lower peak and more pronounced splitting of ISGMR. We also discuss widths of the peaks and their negligible correlation with deformation., Comment: 11 pages, 10 figures

In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive equations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium., Comment: 30 pages, no figures, revtex-4.1, added Ref. [4] and the second paragraph in Introduction; the version published in J. Math. Phys. v. 57, 092902 (2016)

We review a recent progress in investigation of the isoscalar toroidal dipole resonance (TDR). A possible relation of the TDR and low-energy dipole strength (also called a pygmy resonance) is analyzed. It is shown that the dipole strength in the pygmy region can by understood as a local manifestation of the collective vortical toroidal motion at the nuclear surface. Application of the TDR as a measure of the nuclear dipole vorticity is discussed. Finally, an anomalous splitting of the TDR in deformed nuclei is scrutinized., Comment: 8 pages, 5 figures, submitted to "Physics of Atomic Nuclei"

The low-lying $M1$-strength of the open-shell nucleus $^{50}$Cr has been studied with the method of nuclear resonance fluorescence up to 9.7 MeV, using bremsstrahlung at the superconducting Darmstadt linear electron accelerator S-DALINAC and Compton backscattered photons at the High Intensity $\gamma$-ray Source (HI$\gamma$S) facility between 6 and 9.7 MeV of the initial photon energy. Fifteen $1^{+}$ states have been observed between 3.6 and 9.7 MeV. Following our analysis, the lowest $1^{+}$ state at 3.6 MeV can be considered as an isovector orbital mode with some spin admixture. The obtained results generally match the estimations and trends typical for the scissors-like mode. Detailed calculations within the Skyrme Quasiparticle Random-Phase-Approximation method and the Large-Scale Shell Model justify our conclusions. The calculated distributions of the orbital current for the lowest $1^{+}$-state suggest the schematic view of Lipparini and Stringari (isovector rotation-like oscillations inside the rigid surface) rather than the scissors-like picture of Lo Iudice and Palumbo. The spin M1 resonance is shown to be mainly generated by spin-flip transitions between the orbitals of the $fp$-shell., Comment: Accepted in PRC as a regular article

The strong deformation splitting of the isoscalar giant monopole resonance (ISGMR), recently observed in ($\alpha,\alpha'$) reaction in prolate $^{24}$Mg, is analyzed in the framework of the Skyrme quasiparticle random-phase-approximation (QRPA) approach with the Skyrme forces SkM*, SVbas and SkP$^{\delta}$. The calculations with these forces give close results and confirm that the low-energy E0-peak is caused by the deformation-induced coupling of ISGMR with the K=0 branch of the isoscalar giant quadrupole resonance., Comment: 3 pages, 1 figure, to be published in EPJ Web of Conferences (Proceedings of the International Conference NSRT15, Dubna, Russia, 2015)

Random Phase Approximation (RPA) is the basic method for calculation of excited states of nuclei over the Hartree-Fock ground state, suitable also for energy density functionals (EDF or DFT). We developed a convenient formalism for expressing densities and currents in a form of reduced matrix elements, which allows fast calculation of spectra for spherical nuclei. All terms of Skyrme functional were taken into account, so it is possible to calculate electric, magnetic and vortical/toroidal/compression transitions and strength functions of any multipolarity. Time-odd (spin) terms in Skyrme functional become important for magnetic M1 and isovector toroidal E1 transitions. It was also found that transition currents in pygmy region (low-lying part of E1 resonance) exhibit isoscalar toroidal flow, so the previously assumed picture of neutron-skin vibration is not the only mechanism present in pygmy transitions. RPA calculations with heavy axially-symmetric nuclei now become feasible on ordinary PC. Detailed formulae for axial Skyrme RPA are given. Some numerical results are shown in comparison with the approximate approach of separable RPA, previously developed in our group for fast calculation of strength functions., Comment: 10 pages, 6 figures, published version, see http://www.fu.sav.sk/fileadmin/user_upload/oddelenia/ojf/nph/events/ISTROS/2015/ISTROS_2015_Proceedings.pdf

The lowest quadrupole $\gamma$-vibrational $K^{\pi}=2^+$ states in axially deformed rare-earth (Nd, Sm, Gd, Dy, Er, Yb, Hf, W) and actinide (U) nuclei are systematically investigated within the separable random-phase-approximation (SRPA) based on the Skyrme functional. The energies $E_{\gamma}$ and reduced transition probabilities $B(E2)$ of $2^+_{\gamma}$-states are calculated with the Skyrme forces SV-bas and SkM$^*$. The energies of two-quasiparticle configurations forming the SRPA basis are corrected by using the pairing blocking effect. This results in a systematic downshift of $E_{\gamma}$ by 0.3-0.5 MeV and thus in a better agreement with the experiment, especially in Sm, Gd, Dy, Hf, and W regions. For other isotopic chains, a noticeable overestimation of $E_{\gamma}$ and too weak collectivity of $2^+_{\gamma}$-states still persist. It is shown that domains of nuclei with a low and high $2^+_{\gamma}$ -collectivity are related with the structure of the lowest 2-quasiparticle states and conservation of the Nilsson selection rules. The description of $2^+_{\gamma}$ states with SV-bas and SkM$^*$ is similar in light rare-earth nuclei but deviates in heavier nuclei. However SV-bas much better reproduces the quadrupole deformation and energy of the isoscalar giant quadrupole resonance. The accuracy of SRPA is justified by comparison with exact RPA. The calculations suggest that a further development of the self-consistent calculation schemes is needed for a systematic satisfactory description of the $2^+_{\gamma}$ states., Comment: 16 pages, 10 figures, 2 tables

We compare the known in literature, explicitly covariant 4-dimensional formula for the symmetric energy-momentum tensor of electromagnetic field in a medium and the energy-momentum tensor derived by Abraham in the 3-dimensional vector form. It is shown that these two objects coincide only on the physical configuration space $\overline\Gamma$, formed by the field vectors and the velocity of the medium, which satisfy the Minkowski constitutive relations. It should be emphasized that the 3-dimensional vector formulae for the components of the energy-momentum tensor were obtained by Abraham only on $\overline\Gamma$, and the task of their extension to the whole unconditional configuration space $\Gamma$ was not posed. In order to accomplish the comparison noted above we derive the covariant formula anew by another method, namely, by generalizing the Abraham reasoning. The comparison conducted enables one to treat the explicitly covariant formula as a unique consistent extension of the Abraham formulae to the whole configuration space $\Gamma$. Thus the question concerning the relativistic covariance of the original 3-dimensional Abraham formulae defined on $\overline\Gamma$ is solved positively. We discuss in detail the relativistic covariance of the 3-dimensional vector formulae for individual components of the 4-dimensional tensors in electrodynamics which is manifested in the form-invariance of these formulae under Lorentz transformations., Comment: 25 pages, no figures, no tables; v3: minor changes, the version published in J. Math. Phys. v. 57, 032901 (2016)

Attenuation of short, strongly nonlinear stress pulses in chains of spheres and cylinders was investigated experimentally and numerically for two ratios of their masses keeping their contacts identical. The chain with mass ratio 0.98 supports solitary waves and another one (with mass ratio 0.55) supports nonstationary pulses which preserve their identity only on relatively short distances, but attenuate on longer distances because of radiation of small amplitude tails generated by oscillating small mass particles. Pulse attenuation in experiments in the chain with mass ratio 0.55 was faster at the same number of the particles from the entrance than in the chain with mass ratio 0.98. It is in quantitative agreement with results of numerical calculations with effective damping coefficient 6 kg/s. This level of damping was critical for eliminating the gap openings between particles in the system with mass ratio 0.55 present at lower or no damping. However with increase of dissipation numerical results show that the chain with mass ratio 0.98 provides faster attenuation than chain with mass ratio 0.55 due to the fact that the former system supports the narrower pulse with the larger difference between velocities of neighboring particles. The investigated chains demonstrated different wave structure at zero dissipation and at intermediate damping coefficients and the similar behavior at large damping., Comment: 49 pages, 19 figures, 39 references

The isoscalar giant monopole resonance (GMR) in spherical nuclei $^{100-132}$Sn, $^{144}$Sm, and $^{208}$Pb is investigated within the Skyrme random-phase-approximation (RPA) for a variety of Skyrme forces and different pairing options. The calculated GMR strength functions are directly compared to the available experimental distributions. It is shown that, in accordance to results of other groups, description of GMR in Sn and heavier Sm/Pb nuclei needs different values of the nuclear incompressibilty, $K \approx$ 200 or 230 MeV, respectively. Thus none from the used Skyrme forces is able to describe GMR in these nuclei simultaneously. The GMR peak energy in open-shell $^{120}$Sn is found to depend on the isoscalar effective mass, which might be partly used for a solution of the above problem. Some important aspects of the problem (discrepancies of available experimental data, proper treatment of the volume and surface compression in finite nuclei, etc) are briefly discussed., Comment: 6 pages, 3 figures, submitted to Phys. Scr. (Proceed. of XXI Nuclear Physics Workshop, 23-28.09.2014, Kazimierz Dolny, Poland)

A possible relation of the low-lying E1 (pygmy resonance) and toroidal strengths is analyzed by using Skyrme-RPA results for the strength functions, transition densities and current fields in $^{208}$Pb. It is shown that the irrotational pygmy motion can appear as a local manifestation of the collective vortical toroidal dipole resonance (TDR) at the nuclear surface. The RPA results are compared to unperturbed (1ph) ones., Comment: 3 pages, 5 figures, to be submitted to EPJ Web of Conferences [Proceedings of 15th International Symposium on Capture Gamma-Ray Spectroscopy and Related Topics (CGS15), Dresden, Germany, August 24-29, 2014]

Two aspects of the transport of the repulsive Bose-Einstein condensate (BEC) in a double-well trap are inspected: impact of the interatomic interaction and analogy to the Josephson effect. The analysis employs a numerical solution of 3D time-dependent Gross-Pitaevskii equation for a total order parameter covering all the trap. The population transfer is driven by a time-dependent shift of a barrier separating the left and right wells. Sharp and soft profiles of the barrier velocity are tested. Evolution of the relevant characteristics, involving phase differences and currents, is inspected. It is shown that the repulsive interaction substantially supports the transfer making it possible i) in a wide velocity interval and ii) three orders of magnitude faster than in the ideal BEC. The transport can be approximately treated as the d.c. Josephson effect. A dual origin of the critical barrier velocity (break of adiabatic following and d.c.-a.c. transition) is discussed. Following the calculations, robustness of the transport (d.c.) crucially depends on the interaction and barrier velocity profile. Only soft profiles which minimize undesirable dipole oscillations are acceptable., Comment: 10 pages, 8 figures, accepted by Laser Physis. arXiv admin note: text overlap with arXiv:1312.2750 The replaced version has a few corrections and additional references

The isoscalar giant monopole resonance (GMR) in Samarium isotopes (from spherical $^{144}$Sm to deformed $^{148-154}$Sm) is investigated within the Skyrme random-phase-approximation (RPA) for a variety of Skyrme forces. The exact RPA and its separable version (SRPA) are used for spherical and deformed nuclei, respectively. The quadrupole deformation is shown to yield two effects: the GMR broadens and attains a two-peak structure due to the coupling with the quadrupole giant resonance., Comment: 6 pages, 4 figures, proceedings of 11th Intern. Spring Seminar on Nuclear Physics (Ischia, Italy, May 12-16, 2014)

The general formula is derived for the vacuum friction force between two parallel perfectly flat planes bounding two material media separated by a vacuum gap and moving relative to each other with a constant velocity $\mathbf{v}$. The material media are described in the framework of macroscopic electrodynamics whereas the nonzero temperature and dissipation are taken into account by making use of the Kubo formulae from non-equilibrium statistical thermodynamics. The formula obtained provides a rigorous basis for calculation of the vacuum friction force within the quantum field theory methods in the condensed matter physics. The revealed $v$-dependence of the vacuum friction force proves to be the following: for zero temperature ($T=0$) it is proportional to $(v/c)^3$ and for $T>0$ this force is linear in $(v/c)$., Comment: 8 pages, no figures, no tables, REVTeX4-1, The paper is considerably extended, new results are obtained, presentation is improved

Two basic concepts of nuclear vorticity, hydrodynamical (HD) and Rawenthall-Wambach (RW), are critically inspected. As a test case, we consider the interplay of irrotational and vortical motion in isoscalar electric dipole E1(T=0) modes in $^{208}$Pb, namely the toroidal and compression modes. The modes are described in a self-consistent random-phase-approximation (RPA) with the Skyrme force SLy6. They are examined in terms of strength functions, transition densities, current fields, and formfactors. It is shown that the RW conception (suggesting the upper component of the nuclear current as the vorticity indicator) is not robust. The HD vorticity is not easily applicable either because the definition of a velocity field is too involved in nuclear systems. Instead, the vorticity is better characterized by the toroidal strength which closely corresponds to HD treatment and is approximately decoupled from the continuity equation., Comment: 12 pages, 9 figures

An inverse population transfer of the repulsive Bose-Einstein condensate (BEC) in a weakly bound double-well trap is explored within the 3D time-dependent Gross-Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, etc) and closely follows the conditions of Heidelberg experiments, thus providing a realistic description of BEC dynamics. The transfer is driven by a time-dependent shift of a barrier separating the left and right wells. It is shown that completeness and robustness of the process considerably depend on the amplitude and time profile of the shift velocity. Soft profiles provide the most robust inversion. The repulsive interaction substantially supports the transfer making it possible i) in a wide velocity interval and ii) three orders of magnitude faster than in the ideal BEC., Comment: 6 pages, 5 figures

The effect of nuclear deformation on the isoscalar toroidal and compression dipole modes in prolate $^{170}$Yb is studied in the framework of the random-phase-approximation method with a representative set of Skyrme forces (SV-bas, SLy6, SkM$^*$ and SkI3). It is shown that the deformation crucially redistributes the strength of both modes. The compression mode has the same sequence of $\mu$=0 and 1 branches as the isovector giant dipole resonance where for prolate nuclei the $\mu=0$ mode is lower in energy ($\mu$ being the projection of the axial momentum of the mode). Instead, the toroidal mode exhibits an anomalous (opposite) sequence where the $\mu$=1 branch precedes the $\mu$=0 one., Comment: 5 pages, 6 figures, submitted to Phys. Scripta

A comparative analysis of toroidal, compressional and vortical dipole strengths in the spherical $^{144}$Sm and the deformed $^{154}$Sm is performed within the random-phase-approximation using a set of different Skyrme forces. Isoscalar (T=0), isovector (T=1), and electromagnetic excitation channels are considered. The role of the nuclear convection $j_{\text{con}}$ and magnetization $j_{\text{mag}}$ currents is inspected. It is shown that the deformation leads to an appreciable redistribution of the strengths and causes a spectacular deformation splitting (exceeding 5 MeV) of the isoscalar compressional mode. In $^{154}$Sm, the $\mu$=0 and $\mu$=1 branches of the mode form well separated resonances. When stepping from $^{144}$Sm to $^{154}$Sm, we observe an increase of the toroidal, compression and vortical contributions in the low-energy region (often called pygmy resonance). The strength in this region seems to be an overlap of various excitation modes. The energy centroids of the strengths depend significantly on the isoscalar effective mass $m_0$. Skyrme forces with a large $m_0$ (typically $m_0/m \approx 0.8 - 1$) seem to be more suitable for description of experimental data for the isoscalar giant dipole resonance., Comment: 13 pages, 10 figures, submitted to EJPA