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The 9.2 keV nuclear transition in 227Th was studied in the β − -decay of 227Ac by means of the internal conversion electron spectroscopy to clarify the spin-parity assignment of the ground state and the two lowest excited states of 227Th. The transition multipolarity was proved to be of mixed character M1 + E2 and the spectroscopic admixture parameter δ 2 ( E 2 / M 1 ) = 0.695 ± 0.248 ( | δ ( E 2 / M 1 ) | = 0.834 ± 0.149 ) was determined. Nonzero value of δ ( E 2 / M 1 ) questioned the present theoretical interpretation of low-lying levels of 227Th. Calculations performed prefer the 1 / 2 + , 3 / 2 + , and 3 / 2 + sequence instead of the adopted 1 / 2 + , 5 / 2 + and 3 / 2 + one for the 0.0, 9.2, and 24.3 keV levels, respectively.

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

Background: Nuclei in the $sd$ shell demonstrate a remarkable interplay of cluster and mean-field phenomena. The $N=Z$ nuclei, such as $^{24}\mathrm{Mg}$ and $^{28}\mathrm{Si}$, have been the focus of the theoretical study of both phenomena in the past. A variety of different cluster structures in these nuclei are predicted, characterized by isoscalar dipole and monopole transitions. For example, low-energy isoscalar vortical dipole states were predicted in $^{24}\mathrm{Mg}$. 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 $\ensuremath{\alpha}$ particles.Purpose: We investigate, both experimentally and theoretically, the isoscalar dipole $IS1$ and monopole $IS0$ strengths in three essentially different light nuclei with different properties: stiff prolate $^{24}\mathrm{Mg}$, soft prolate $^{26}\mathrm{Mg}$, and soft oblate $^{28}\mathrm{Si}$. We analyze possible manifestations of clustering and vorticity in these nuclei.Methods: Inelastically scattered $\ensuremath{\alpha}$ particles were momentum analyzed in the K600 magnetic spectrometer at iThemba LABS, Cape Town, South Africa. The scattered particles were detected in two multiwire drift chambers and two plastic scintillators placed at the focal plane of the K600. In the theoretical discussion, the Skyrme quasiparticle random-phase approximation (QRPA) and antisymmetrized molecular dynamics $+$ generator coordinate method ($\mathrm{AMD}+\mathrm{GCM}$) were used.Results: A number of isoscalar monopole and dipole transitions were observed in the nuclei studied. Using this information, suggested structural assignments have been made for the various excited states. $IS1$ and $IS0$ strengths obtained within QRPA and $\mathrm{AMD}+\mathrm{GCM}$ are compared with the experimental data. 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) near the $\ensuremath{\alpha}$-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 $\mathrm{AMD}+\mathrm{GCM}$ calculations suggest that some observed states may have a mixed (mean-field $+$ cluster) character or correspond to particular cluster configurations.Conclusion: A tentative correspondence between observed states and theoretical states from QRPA and $\mathrm{AMD}+\mathrm{GCM}$ was established. The QRPA and $\mathrm{AMD}+\mathrm{GCM}$ 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 $^{24}\mathrm{Mg}$, fragmented in $^{26}\mathrm{Mg}$, and absent in $^{28}\mathrm{Si}$.

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.

The recent RCNP (α,α′) data on the Isoscalar Giant Monopole Resonance (ISGMR) and Isoscalar Giant Quadrupole Resonance (ISGQR) in $^{92,94,96,98,100}$Mo are analyzed within a fully self-consistent Quasiparticle Random Phase Approximation (QRPA) approach with Skyrme interactions, in which pairing correlations and possible axial deformations are taken into account. The Skyrme sets SkM*, SLy6, SVbas and SkPδ, that explore a diversity of nuclear matter properties, are used. We discuss the connection between the line shape of the monopole strength ISGMR and the deformation-induced coupling between the ISGMR and the K=0 branch of the ISGQR. The ISGMR is best described by the force SkPδ, having a low incompressibility K∞=202MeV. The ISGQR data are better reproduced by SVbas, that has large isoscalar effective mass m⁎/m=0.9. The need of a functional that can describe simultaneously the ISGMR and ISGQR data is stressed, with the requirement of suitable values of K∞ and m⁎/m. Possible extensions of the QRPA to deal with soft systems are also envisaged.

Individual low-energy $E1$ toroidal and compressional states (TS and CS) produced by the convective nuclear current ${\mathbf{j}}_{c}$ were recently predicted for $^{24}\mathrm{Mg}$ 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 $B(E1K,{0}^{+}0\ensuremath{\rightarrow}{1}^{\ensuremath{-}}K),\phantom{\rule{0.28em}{0ex}}B(E3K,{0}^{+}0\ensuremath{\rightarrow}{3}^{\ensuremath{-}}K)$, and $B(M2K,{0}^{+}0\ensuremath{\rightarrow}{2}^{\ensuremath{-}}K)$ 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 ${\mathbf{j}}_{c}$ and magnetization ${\mathbf{j}}_{m}$ nuclear currents is thoroughly scrutinized. A two-step scheme for identification of TS in $(e,{e}^{\ensuremath{'}})$ 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.

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 nonconservation 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 for $E1$ excitations are proposed and shown to be essential for the compression isoscalar mode. The accuracy of the method is demonstrated by Skyrme QRPA calculations for axially deformed $^{154}\mathrm{Sm}$.

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

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., 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 for axial nuclei. The calculations with the force SLy6 reveal a remarkable feature: the lowest I^{π}K=1^{-}1 excitation (E=7.92 MeV) in ^{24}Mg is a vortical toroidal state (TS) representing a specific vortex-antivortex realization of the well-known spherical Hill's vortex in a strongly deformed axial confinement. This is a striking example of an individual TS which can be much more easily 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 parametrizations (SLy6, SVbas, SkM*). We analyze spectroscopic properties of the TS and its relation with the cluster structure of ^{24}Mg. Similar TSs could exist in other highly prolate light nuclei. They could serve as promising tests for various reactions to probe a vortical (toroidal) nuclear flow.

The low-energy dipole excitations in ^{24}Mg are investigated within the Skyrme quasiparticle random phase approximation for axial nuclei. The calculations with the force SLy6 reveal a remarkable feature: the lowest I^{π}K=1^{-}1 excitation (E=7.92 MeV) in ^{24}Mg is a vortical toroidal state (TS) representing a specific vortex-antivortex realization of the well-known spherical Hill's vortex in a strongly deformed axial confinement. This is a striking example of an individual TS which can be much more easily 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 parametrizations (SLy6, SVbas, SkM*). We analyze spectroscopic properties of the TS and its relation with the cluster structure of ^{24}Mg. Similar TSs could exist in other highly prolate light nuclei. They could serve as promising tests for various reactions to probe a vortical (toroidal) nuclear flow.

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, Comment: 12 pages, 12 figures

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., 7 pages, 6 figures

We propose a method for solving the nuclear eigenvalue problem using a Hamiltonian of general form in a space spanned by multiphonon states built out of particle-hole TammDancoff phonons. The method consists in deriving for a given n-phonon subspace a set of equations of motion of simple structure, where all quantities are expressed in terms of energies and one-body density matrices determined in the (n − 1)-phonon subspace. Their solution, therefore, yields states built out of particle-hole operators applied on top of the (n−1)phonons basis states. Because of this peculiar structure, the states so generated form an overcomplete set. The redundancy, however, is removed completely and efficiently by a procedure based on the Choleski decomposition. The phonon composition of the basis states allows to remove naturally and maximally the spurious admixtures induced by the center of mass motion. The iteration of the equations from n = 0 up to an arbitrary number N of phonons generates an orthogonal basis spanning a space which is the direct sum of 0+1+..+N phonon subspaces. This basis decomposes the full Hamiltonian into N diagonal blocks plus off-diagonal terms coupling the n-phonons with the (n ± 1)and (n ± 2)-phonon subspaces. These off-diagonal terms are easily computed by recursive relations. The Hamiltonian can, therefore, be easily diagonalized by resorting to importance sampling techniques [1,2], which allow to truncate the multiphonon space while monitoring the accuracy of the solutions. The method can be easily upgraded so as to generate a particle-hole or quasiparticle RPA multiphonon basis. It is suitable for describing with high accuracy low-lying multiphonon spectra, whose experimental evidence is rapidly growing, as well as high-energy resonances like the recently discovered double dipole giant resonance. It can account with great accuracy for the anharmonicities associated to all collective modes. Last, but not least, it yields a highly correlated ground state which contains explicitly up to N particle N hole configurations and, therefore, applies to the cases where the quasiboson approximation breaks down. For illustrative purposes, we apply the method to 16O, whose low-lying states are dominated by complex configurations containing up to 4 particle 4 hole states. Such a calculation probes the extreme accuracy of the method, on the one hand, and, on the other hand, provides a complete and exhaustive information on the microscopic structure of low and high energy states in 16O.

The method outlined here consists of constructing a set of equations of motion within a subspace spanned by states which are tensor products of n Tamm Dancoff phonons. Recursive relations allow to solve these equations iteratively, starting from the particle-hole vacuum, and, thereby, to generate a basis of microscopic multiphonon states. In such a basis, the Hamiltonian takes on a simple form and can be easily diagonalized. For illustrative purposes, we apply the method to 16 O .

The lowest quadrupole $\ensuremath{\gamma}$-vibrational ${K}^{\ensuremath{\pi}}={2}^{+}$ 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 ${E}_{\ensuremath{\gamma}}$ and reduced transition probabilities $B(E2)$ of ${2}_{\ensuremath{\gamma}}^{+}$ states are calculated with the Skyrme forces SV-bas and ${\mathrm{SkM}}^{*}$. 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 ${E}_{\ensuremath{\gamma}}$ 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 ${E}_{\ensuremath{\gamma}}$ and too weak collectivity of ${2}_{\ensuremath{\gamma}}^{+}$ states still persist. It is shown that domains of nuclei with low and high ${2}_{\ensuremath{\gamma}}^{+}$ collectivity are related to the structure of the lowest two-quasiparticle states and conservation of the Nilsson selection rules. The description of ${2}_{\ensuremath{\gamma}}^{+}$ states with SV-bas and ${\mathrm{SkM}}^{*}$ 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 ${2}_{\ensuremath{\gamma}}^{+}$ states.

Low-energy E1 strength in neutron-rich $^{132-164}$Sn isotopes is analyzed in the framework of the Skyrme random phase approximation (RPA) with different Skyrme forces. A double folding procedure is applied to take into account the energy-dependent width effects beyond RPA. All the considered Skyrme forces indicate a soft prolate deformation in the open shell isotopes $^{142-164}$Sn. The integrated E1 strength in the energy region of the pygmy resonance grows with the neutron number. The influence of deformation on the integrated strength near the particle emission thresholds (which is of a keen astrophysical interest) is strictly suppressed by the mutual compensation effect for the branches of the giant dipole resonance. The results obtained are in a good agreement with the previous findings of the relativistic mean field model., Comment: 12 pages, 6 figures, to be published in Int. J. Mod. Phys. E

Electron scattering is a tool that can provide relatively clean view of the nuclear structure in both ground and excited states, as it depends on the well-known electromagnetic interaction. But since the common expressions for its cross section were derived with certain assumptions, in this paper we describe several nontrivial steps necessary for a proper theoretical calculation within the current density-functional framework, namely with Skyrme QRPA for axial nuclei, with aim to enable comparison of the theoretically predicted low-lying $1^-$ toroidal modes with future (e,e') experiments., 10 pages, 5 figures, to be published in the proceedings of XXV Nuclear Physics Workshop (25-30 September 2018), Kazimierz Dolny, Poland; now slightly improved wording in introduction

This contribution deals with the predictive power of the Skyrme-Hartree-Fock model. First, we discuss the phenomenological adjustment of the Skyrme energy-functional and the choice of proper fit data. Then, we check the reliability in extrapolations to other observables and nuclei, using two strategies: first, comparison with data for observables not included in the fit, and second, an estimate of the extrapolation error by virtue of the least-squares fitting techniques. Test cases will be energies of extremely neutron rich Sn isotopes as well as energies, giant resonances, and fission properties of super-heavy elements.

The self-consistent separable random-phase approximation (SRPA) with Skyrme forces is extended to the case of magnetic excitations and applied to the description of spin-flip and orbital M1 giant resonances in the isotopic chain 142-152 Nd . The Skyrme forces SkT6, SkM*, SLy6 and SkI3 are used. The calculations show an onset of the scissors mode with increasing deformation. A specific three-peak structure of the spin-flip response is found and explained by particular neutron and proton spin-flip transitions. Although the employed forces provide an acceptable qualitative description, the Skyrme functional still needs further improvement to reproduce quantitatively the experiment for spin modes.

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.

The lowest γ -vibrational states with Kπ = 2+ γ in well-deformed Dy, Er and Yb isotopes are investigated within the self-consistent separable quasiparticle random-phase-approximation (QRPA) approach based on the Skyrme functional. The energies Eγ and reduced transition probabilities B(E2) γ of the states are calculated with the Skyrme force SV-mas10. We demonstrate the strong effect of the pairing blocking on the energies of γ -vibrational states. It is also shown that collectivity of γ -vibrational states is strictly determined by keeping the Nilsson selection rules in the corresponding lowest 2qp configurations.

10 pags.; 6 figs.; 4 tabs. ; Open Access funded by Creative Commons Atribution Licence 4.0, We have applied the fast timing β(t) technique to remeasure lifetimes of selected states in Ra populated in the β decay of Fr. T = 587(12) ps and 210(13)ps have been obtained for the 3/2 and 5/2 states at 50.1 and 79.7 keV, that are more accurate than the previous values of 630(70)ps and 166(55)ps, respectively. Our |D| value of 0.155(10) e·fm obtained for the K=3/2 configuration together with the available values of |D| for the K=1/2 and K=5/2 parity doublet bands establish the configuration dependence of |D| at low spins in this nucleus. Results of theoretical calculations performed for Ra, using the quasiparticle-phonon model (QPM) with inclusion of the Coriolis coupling, reasonably well reproduce octupole correlations in this nucleus. © The Author(s), 2016, This work was supported in part by the Swedish Natural Science Research Council, Norwegian Scientific Research Committee, the Nansen Foundation, the CICYT “Plan Nacional de Altas Energias” Spain (under contract AEN94-0833-C02-02), the U.K. Engineering and Physical Sciences Research Council, and the Polish Scientific Research Committee.

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

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"

In the cranked Nilsson-plus-random-phase approximation, we study low-lying quadrupole excitations of positive parity and negative signature in 156Dy and 162Yb at high spins. Special attention is paid to a consistent description of wobbling excitations and their identification among excited states. A good agreement between the available experimental data and the results of calculations is obtained. We find that the lowest odd-spin γ-vibrational states in 156Dy transform into wobbling excitations after the backbending associated with the transition from an axially symmetric shape to a nonaxial shape. Similar results are predicted for 162Yb. The analysis of electromagnetic transitions uniquely determines the sign of the γ deformation in both nuclei after the transition point.

We propose a method for deriving a set of eigenvalue equations within a subspace spanned by states which are tensor products of n Tamm–Dancoff phonons. Recursive relations allow to one solve these equations iteratively, starting from the particle–hole vacuum, and, thereby, to generate a basis of microscopic multiphonon states. The Hamiltonian has a simple spectral decomposition in such a basis and can be easily brought into diagonal form. 16O is chosen as testing ground for the method.

The giant dipole resonance (GDR) in deformed nuclei is analyzed using the self-consistent separable random-phase-approximation (SRPA) with Skyrme forces SkT6, SkM$^*$, SLy6 and SkI3. The deformed nuclei $^{150}$Nd and $^{238}$U are used as representative rare-earth and actinide samples. Dependencies of the dipole strength distributions on some basic characteristics of the Skyrme functional and nuclear matter properties (isoscalar and isovector effective masses, time-odd contributions) are discussed. Particular attention is paid to the fragmentation structure of the GDR strength which are shown to depend sensitively to spin-orbit intruder states with large angular momentum., 12 pages, 3 figures

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)

The energies of negative-parity levels based on two-particle states exhibit a nonlinear behavior at low spins versus the core-rotation energy because the alignment process has not yet been completed for them. This behavior of negative-parity levels in the low-spin region is satisfactorily described upon the inclusion of octupole-octupole interactions. This is demonstrated within the rotational model involving the Coriolis mixing of states for the even-even isotopes 162–168Hf.

We extend the classical Landau theory for rotating nuclei and show that the backbending in 162Yb, which comes about as a result of the two-quasiparticle alignment, is identified with the second-order phase transition. We found that the backbending in 156Dy, caused by the instability of γ vibrations in the rotating frame, corresponds to the first-order phase transition. We suggest an empirical rule to determine the type of the phase transition in rotating nuclei undergoing backbending.

We propose a self-consistent practical method to study collective excitations in rotating nuclei within the cranking + random phase approximation approach. It consists in solving the cranking Hartree-Bogolyubov equations for the modified Nilsson potential + monopole pairing forces. Further, the mean field results are used to construct collective vibrations treated in the random phase approximation (RPA). Special attention is paid to fulfill all conservation laws in the RPA to separate spurious and physical solutions. We demonstrate that the backbending in 156Dy can be explained as a result of the disappearance of collective γ vibrations of the positive signature in the rotating frame.

Minor changes in the assignments of gamma rays following the alpha decay of228Pa in two previous studies make possible a reinterpretation of224Ac into two alternative level schemes. The resulting level structures arise from the reflection asymmetric configurations π3/2±(0.0 −0.3)−ν3/2±(−0.1 0.6), π5/2±(0.0 −0.2)±ν3/2±(−0.1 0.6) and π5/2±(0.0 −0.2)±ν1/2±(0.2 −0.1 3) which give rise to eitherK=0± or 1±,K=4±,K=2± andK=3± parity doublet bands. The bands with appreciable band structure, namelyK=0± or 1± andK=3±, have average parity doublet splittings of 11.0 and 5.8 keV respectively. These are extremely small values and suggest that224Ac is the most octupole deformed nucleus studied thus far. A method of calculating the parity doublet splitting in odd-odd nuclei is suggested and tested for224Ac. It seems to work remarkably well. The systematics of the hindrance factors for the bands with extended band structures confirm their interpretations as band structures. Finally, the two alternative level schemes are analyzed in the framework of the axially-symmetric rigid rotor model including the Coriolis interaction.

The level structure of 231 Pa was investigated by Coulomb excitation using 148 MeV 32 S and 255, 260 and 261 MeV 58 Ni projectiles and the NORDBALL detector array. The 1/2[530] ground-state rotational band was excited up to spin 39/2 − . The 3/2[651] band, established up to spin 37/2 + , was observed to be populated apart from direct Coulomb excitation by the de-excitation of the 1/2[530] band. The 1/2[400] band could be followed up to spin 23/2 + . Weak excitation of the bands 5/2[642], 5/2[512], 3/2[532] and 3/2[521] was seen up to spins 11/2 + , 15/2 − , 9/2 − and 9/2 − , respectively. Matrix elements were extracted from the γ -ray yields with the help of the semi-classical Coulomb-excitation least-squares search code GOSIA. The level scheme and transition intensities were analyzed in the framework of the quasiparticle-plus-phonon model including Coriolis-coupling (QPMC).

A basis of multiphonon states is generated by constructing and solving iteratively a set of equations of motion. Represented in this basis, the Hamiltonian has a simple structure and can be easily brought to diagonal form. The method is adopted to compute the energy levels and the electromagnetic responses in 16O, chosen as test ground because of its complex structure.

The cranked Skyrme III effective Hamiltonian is applied for the analysis of the rotational dependence of the quadrupole and octupole moments in Ra, Th, and U isotopes. A comparison of the intrinsic electric dipole moments calculated in the model with available experimental and theoretical values is presented. It is found that the non-axial octupole deformation $Y_{32}$ becomes favorable at high spins for the actinide nuclei.

The γ -rays following the β − decay of 229 Ac have been investigated by means of γ -ray singles and γγ -coincidence measurements using Ge detectors. Multipolarities of 40 transitions in 229 Th have been established by measuring conversion electrons with a mini-orange electron spectrometer. The half-lives of the 146.35, 164.53 and 261.96 keV levels have been measured using the advanced time delayed βγγ (t) method. The low-lying states in 229 Th and observed transition rates have been interpreted within the quasiparticle–phonon model with inclusion of Coriolis coupling. Two octupole correlated parity partner bands, with K π =5/2 ± and K π =3/2 ± , were identified in 229 Th.

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., 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]

The structure of 231 Ra, the heaviest odd Ra nucleus currently accessible for detailed spectroscopic investigation, has been studied in the β − decay of 231 Fr. The main purpose has been to verify whether fast B (E1) rates and significant octupole correlations recently established in 229 Ra persist in 231 Ra. The excited states in 231 Ra have been determined for the first time. Spins and parities have been deduced from conversion electron measurements, while level half-lives in the ps and ns ranges have been measured with the Advanced Time Delayed βγγ (t) method. The moderately fast B (E1) rates found for transitions connecting the lowest-lying K π =5/2 ± and K π =1/2 ± bands, reveal the persistence of octupole collective effects in 231 Ra, although the B (E1) rates are lower than in 229 Ra. These findings reinforce the differences in the B (E1) systematics between isotonic Ra and Th nuclei.

The interchange of two sets of spins in the level structure of219Ra observed following the alpha decay of223Th and the suggestion that the ground state of219Ra was not observed in the heavy ion reaction spectroscopy208Pb(14C, 3n), allow the correlation of these levels which were previously unconnected. The resulting level structure is interpreted in terms of $$K = \tfrac{1}{2}^ \pm $$ and $$K = \tfrac{5}{2}^ \pm $$ parity doublet bands which evolve from anomalous rotational structures into vibrational-like structures with alternating spins and parities. The level structure of219Ra is successfully interpreted both in terms of octupole deformed (e 3=0.08) Nilsson levels and in terms of intermediate coupling using normal Nilsson levels with very strong octupole correlations. The levels in219Ra are then compared to the corresponding levels in a series of isotopic and isotonic nuclei to trace the collapse of octupole-quadrupole deformed nuclear structure into the more degenerate shell-model spectroscopy.

The collective properties of excited superdeformed bands have been investigated in the framework of self-consistent cranked Nilsson plus quasiparticle random-phase approximation. The expected octupole nature of some bands observed recently in some nuclei has been confirmed by a comparative analysis of their E1 decays to the yrast band and of the anomalous behavior of their dynamical moment of inertia. It is also shown that the onset of supederformation affects considerably the structure of the giant resonances and greatly enhances the collectivity of the low-lying scissors mode.

The electromagnetic response in 16O is studied within a recently developed approach that generates iteratively a microscopic multiphonon basis well suited for reformulating and solving exactly the nuclear eigenvalue problem within spaces of large dimensions spanned by complex configurations. These multiphonon configurations are seen to modify appreciably, dramatically in some cases, the mean field response. This is shown to be increasingly affected by the center-of-mass motion as the number of phonons increases. The method for removing such a spurious motion is briefly outlined and the effects discussed.

The remarkable features of the spectra of the odd-A Fr isotopes from213Fr (with 126 neutrons) through225Fr (with 138 neutrons) serve as a sequence of examples for the application of a variety of nuclear models. As the shapes vary from spherical to spherical with strong octupole correlations to octupole-deformed, the corresponding symmetry breaking leads to increasingly complex spectra. Of considerable interest is the fact that the219Fr 9/2− ground state has the character of an h9/2 shell model state while still having the rotational properties appropriate as a legitimate member of a reflection asymmetric K=1/2− band. It is also possible to follow the expansion of the more degenerate shell model states into the less degenerate reflection asymmetric states. This results from dramatic decreasing in decoupling parameters with increasing mass number.