arXiv subjects

A. Repko

Publications and source records attributed to A. Repko.

At least 19 recordsLinked to original sources

arXiv2025

Wavelet analysis of monopole strength in highly deformed $^{24}$Mg

Experimental data on $\alpha$-particle inelastic scattering for monopole excitations in $^{24}$Mg in the excitation-energy region $E_{\rm x}$$=$$9$$-$$25$ MeV, obtained at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS), have been analyzed within a fully self-consistent quasiparticle random-phase approximation (QRPA) framework using two Skyrme parametrizations. A good overall agreement with the experimental data is achieved, particularly with the SkP$^{\delta}$ force, which corresponds to a low nuclear incompressibility of $K_{\infty}$$=$$202$ MeV. Extraction of energy scales, by means of wavelet analysis, characterizing the observed fine structure of the isoscalar giant monopole resonance (ISGMR) as well as the low-energy region $10$$-$$18$ MeV of the deformation-induced monopole-quadrupole coupling (MQC) in order to investigate the damping mechanism contributing to their decay widths. Characteristic energy scales are extracted from the fine structure using continuous wavelet transforms. The experimental results are compared to QRPA calculations employing the Skyrme parameterizations SkP$^{\delta}$ and SVbas. A significant, if not decisive, impact of the MQC strength on the wavelet power spectra is observed across the entire excitation-energy range of $10$$-$$24$ MeV. Wavelet features derived from the QRPA and from unperturbed two-quasiparticle (2qp) monopole strengths are compared. The results demonstrate that the residual interaction plays a key role in reproducing realistic wavelet powers and characteristic energy scales. Overall, a continuous range of scales $\delta E$$=$$200$$-$$1000$ keV is obtained rather than distinct isolated scales. The deformation softness of $^{24}$Mg is found to significantly influence both the monopole strength distribution and the wavelet characteristics.

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arXiv2025

Low-energy spectra of nobelium isotopes: Skyrme random-phase-approximation analysis

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 SLy4, 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 where 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 forces SLy4 and SLy6. The disputed $8^-$ isomer in $^{254}$No is assigned as neutron two-quasiparticle configuration $nn[734\uparrow,613\uparrow]$. The isomers are additionally analyzed using Skyrme functionals UNEDF1, UNEDF2 and UNEDF1$^{\rm SO}$. 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 also 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 should exhibit essential irregularities caused by a noticeable shell gap in the neutron single-particle spectrum and corresponding reduction of the neutron pairing. In particular, low-energy pairing-vibrational $K^{\pi}=0^+$ states in $^{252,254}$No are predicted.

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arXiv2023

Candidate toroidal electric dipole mode in the spherical nucleus $^{58}$Ni

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.

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arXiv2023

Microscopic analysis of dipole electric and magnetic strengths in $^{156}$Gd

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.

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arXiv2023

Moments of inertia in light deformed nuclei: pairing and mean-field impacts

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.

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arXiv2022

Low-energy M1 states in deformed nuclei: spin-scissors or spin-flip?

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.

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arXiv2021

Isoscalar giant monopole resonance in $^{24}$Mg and $^{28}$Si: Effect of coupling between the isoscalar monopole and quadrupole strength

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.

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arXiv2021

Microscopic analysis of low-energy spin and orbital magnetic dipole excitations in deformed nuclei

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.

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arXiv2019

Individual dipole toroidal states: main features and search in (e,e') reaction

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.

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arXiv2019

Systematics of toroidal dipole modes in Ca, Ni, Zr, and Sn isotopes

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.

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arXiv2018

Elimination of spurious modes within QRPA

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.

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arXiv2018

Individual low-energy E1 toroidal and compression states in light nuclei: deformation effect, spectroscopy and interpretation

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.

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arXiv2017

Individual low-energy toroidal dipole state in $^{24}$Mg

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.

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arXiv2017

Pairing and deformation effects in nuclear excitation spectra

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.

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arXiv2016

Deformation-induced splitting of isoscalar E0 giant resonance: Skyrme random-phase-approximation analysis

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.

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arXiv2016

Toroidal resonance: relation to pygmy mode, vortical properties and anomalous deformation splitting

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.

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arXiv2016

Magnetic dipole excitations of $^{50}$Cr

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.

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arXiv2015

Deformation-induced splitting of the monopole giant resonance in 24Mg

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.

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