Self-consistent Quasiparticle Random-phase Approximation Research Articles

ISOSCALAR DIPOLE RESPONSE IN 92Mo AND 100Mo ISOTOPES

In this work, the Isoscalar (IS) Giant Dipole Resonance (GDR) and Pygmy Dipole Resonance (PDR) of 92Mo and 100Mo Isotopes were calculated in the farmwork of the self-consistent quasi-particle random phase approximation (QRPA) based on the results of Hartree-Fock-Bardeen, Cooper and Schrieffer (HF-BCS) using 10 Skyrme-type interactions: KDE0v1, eMSL08, SKX, SGOI, v080, SKP, SIV, SIII, SKIII, and SGI. The strength distributions of isoscalar dipole response were compared with the available experimental data. Also, we discussed the statistical relation between the centroid energy and the nuclear matter incompressibility KNM.

Low-Energy M1 States in Deformed Nuclei: Spin Scissors or Spin-Flip?

The low-energy $$M$$ 1 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 $$M$$ 1 excitations. The obtained results are compared with the prediction of the low-energy spin-scissors $$M$$ 1 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 $$M$$ 1 strength than by the occurrence of the collective spin-scissors resonance. In general, our calculations do not confirm the existence of this resonance.

Single-state or low-lying-states dominance mechanism of 2νββ -decay nuclear matrix elements

The $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements (NMEs) for 11 nuclei are studied with the self-consistent quasiparticle random phase approximation (QRPA) based on the Skyrme Hartree-Fock-Bogoliubov (Skyrme HFB) model. As a common feature pointed out by \ifmmode \check{S}\else \v{S}\fi{}imkovic, Smetana, and Vogel [Phys. Rev. C 98, 064325 (2018)], negative contributions in the running sums of NMEs are found, and play important roles in the fulfillment of the single-state dominance or low-lying-states dominance hypothesis. By comparing the results of the QRPA model and the quasiparticle Tamm-Dancoff approximation (QTDA) model, we find that the negative contributions are due to the enhanced ground-state correlations, which are brought by the backward amplitude in the QRPA model and tuned by strong isoscalar pairing interaction. The enhancement of ground-state correlations will change the signs of ${\mathrm{GT}}^{+}$ (Gamow-Teller) transition amplitudes of higher-lying states and leads to the negative contributions in the running sum.

Temperature effects on neutron-capture cross sections and rates through electric dipole transitions in hot nuclei

The temperature evolution of electric dipole transition strengths of Sn isotopes is studied using self-consistent quasiparticle random phase approximation (QRPA) and finite-temperature RPA models based on a relativistic density functional. For tin isotopes lighter than $^{132}\mathrm{Sn}$, temperature only shows its effect at high values of 2 MeV, while for neutron-rich tin isotopes heavier than $^{132}\mathrm{Sn}$, the low-lying strength distributions get fragmented and spread to the lower-energy region already at temperature of 1 MeV. Using these electric dipole transition strengths as inputs for the talys code, the temperature effects on $(n,\ensuremath{\gamma})$ cross sections are studied. For tin isotopes lighter than $^{132}\mathrm{Sn}$, temperature causes an enhancement of neutron-capture cross section at high temperatures of 2 MeV, while for neutron-rich tin isotopes heavier than $^{132}\mathrm{Sn}$, the cross section is largely enhanced already at temperature $T=1.0$ MeV, and the bump of cross section caused by the pygmy dipole resonance also becomes broader. The change in neutron-capture rate can be as large as 70% for $^{136}\mathrm{Sn}$, considering the temperature effects on electric dipole transition strength in the final compound nucleus with a temperature of 0.86 MeV (corresponding to $T=10$ GK in the astrophysical environment). The change is around 20% for tin isotopes lighter than $^{132}\mathrm{Sn}$ and above 40% for those heavier than $^{132}\mathrm{Sn}$.

Isoscalar monopole and quadrupole modes in Mo isotopes: Microscopic analysis

The recent RCNP (α,α′) data on the Isoscalar Giant Monopole Resonance (ISGMR) and Isoscalar Giant Quadrupole Resonance (ISGQR) in 92,94,96,98,100Mo 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.

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.

Low-energy quadrupole states in neutron-rich tin nuclei

We present a study on the isoscalar quadrupole strength in tin nuclei, focusing mainly on the low-energy region. The calculations are performed using the Skyrme type energy density functionals within the fully self-consistent quasiparticle random phase approximation, allowing for a good description of the experimental data for the first 2$^+$ state and the isoscalar giant quadrupole resonance. It is found that the first $2^+$ state and the low-energy quadrupole states between 3 and 6 MeV display an opposite behavior with increasing neutron number. While the strength of the first $2^+$ state decreases, some excited states start to accumulate between 3 and 6 MeV, and increase their strength with increasing neutron number. This low-energy region between 3 and 6 MeV is quite sensitive to the changes in the shell structure with increasing neutron number. In particular, between $^{116}$Sn and $^{132}$Sn, the filling of the neutron orbitals with large values of $j$, has an important impact on the low-energy region. Our analysis shows that the low-energy states have a non-collective character, except the first 2$^+$ state. In addition, the states in the low-energy region above 5 MeV display an interesting pattern: with the increase of the neutron number, their strength increases and their nature changes, namely they switch from proton excitations to neutron-dominated one. We conclude that the low-energy quadrupole states between 3 and 6 MeV can provide information about the shell evolution in open-shell nuclei.

Self-consistent relativistic quasiparticle random-phase approximation and its applications to charge-exchange excitations

The self-consistent quasiparticle random-phase approximation (QRPA) approach is formulated in the canonical single-nucleon basis of the relativistic Hatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study the isobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Sn isotopes as examples. It is found that self-consistent treatment of the particle-particle residual interaction is essential to concentrate the IAS in a single peak for open-shell nuclei and the Coulomb exchange term is very important to predict the IAS energies. For the GTR, the isovector pairing can increase the calculated GTR energy, while the isoscalar pairing has an important influence on the low-lying tail of the GT transition. Furthermore, the QRPA approach is employed to predict nuclear $\beta$-decay half-lives. With an isospin-dependent pairing interaction in the isoscalar channel, the RHFB+QRPA approach almost completely reproduces the experimental $\beta$-decay half-lives for nuclei up to the Sn isotopes with half-lives smaller than one second. Large discrepancies are found for the Ni, Zn, and Ge isotopes with neutron number smaller than $50$, as well as the Sn isotopes with neutron number smaller than $82$. The potential reasons for these discrepancies are discussed in detail.

Quasiparticle random-phase approximation with quasiparticle-vibration coupling: Application to the Gamow-Teller response of the superfluid nucleusSn120

We propose a self-consistent quasi-particle random phase approximation (QRPA) plus quasi-particle-vibration coupling (QPVC) model with Skyrme interactions to describe the width and the line shape of giant resonances in open-shell nuclei, in which the effect of superfluidity should be taken into account in both the ground state and the excited states. We apply the new model to the Gamow-Teller resonance in the superfluid nucleus $^{120}$Sn, including both the isoscalar spin-triplet and the isovector spin-singlet pairing interactions. The strength distribution in $^{120}$Sn is well reproduced and the underlying microscopic mechanisms, related to QPVC and also to isoscalar pairing, are analyzed in detail.

Finite amplitude method applied to the giant dipole resonance in heavy rare-earth nuclei

Background: The quasiparticle random phase approximation (QRPA), within the framework of nuclear density functional theory (DFT), has been a standard tool to access the collective excitations of atomic nuclei. Recently, the finite amplitude method (FAM) was developed in order to perform the QRPA calculations efficiently without any truncation on the two-quasiparticle model space.Purpose: We discuss the nuclear giant dipole resonance (GDR) in heavy rare-earth isotopes, for which the conventional matrix diagonalization of the QRPA is numerically demanding. A role of the Thomas-Reiche-Kuhn (TRK) sum rule enhancement factor, connected to the isovector effective mass, is also investigated.Methods: The electric dipole photoabsorption cross section was calculated within a parallelized FAM-QRPA scheme. We employed the Skyrme energy density functional self-consistently in the DFT calculation for the ground states and FAM-QRPA calculation for the excitations.Results: The mean GDR frequency and width are mostly reproduced with the FAM-QRPA, when compared to experimental data, although some deficiency is observed with isotopes heavier than erbium. A role of the TRK enhancement factor in actual GDR strength is clearly shown: its increment leads to a shift of the GDR strength to higher-energy region, without a significant change in the transition amplitudes.Conclusions: The newly developed FAM-QRPA scheme shows remarkable efficiency, which enables one to perform systematic analysis of GDR for heavy rare-earth nuclei. The theoretical deficiency of the photoabsorption cross section could not be improved by only adjusting the TRK enhancement factor, suggesting the necessity of an approach beyond self-consistent QRPA and/or a more systematic optimization of the energy density functional (EDF) parameters.

Isoscalar and neutron modes in theE1spectra of Ni isotopes and the relevance of shell effects and the continuum

We study theoretically the electric dipole transitions of even Ni isotopes at low energies, using the self-consistent quasi-particle random-phase approximation (RPA) with the D1S Gogny interaction and a continuum-RPA model with the SLy4 Skyrme force. We analyze isoscalar states, isovector states, and the dipole polarizability. We define a reference value for the polarizability, to remove a trivial dependence on the mass number. We compare our results with data and other calculations, with a focus on collective states, shell effects, and threshold transitions. Our results support the presence of a strong isoscalar transition, with little or moderate E1 strength, as a universal feature of ordinary nuclei. In moderately neutron-rich Ni isotopes, namely 68Ni and neighboring isotopes, this transition is found bimodal due to couplings with surface neutrons. An adequate treatment of the continuum states appears essential for describing suprathreshold E1 strength, especially beyond 68Ni. Very exotic isotopes (N>50) are found highly polarizable, with practically all their E1 strength in the continuum. The dipole polarizability and the neutron skin thickness are influenced by shell structure in different ways, so they can appear anticorrelated. A comparison with existing results for lighter (Ca) and heavier (Sn) nuclei suggests that the so-called pygmy dipole strength is influenced strongly by shell effects and that, partly for that reason, its isospin structure depends on the mass region.

Gamow-Teller strength in deformed nuclei within the self-consistent charge-exchange quasiparticle random-phase approximation with the Gogny force

The charge-exchange excitations in nuclei are studied within the fully self-consistent proton-neutron quasiparticle random-phase approximation using the finite-range Gogny interaction. No additional parameters beyond those included in the effective nuclear force are included. Axially symmetric deformations are consistently taken into account, both in the description of the ground states and spin-isospin excitations. We focus on the isobaric analog and Gamow-Teller resonances. A comparison of the predicted strength distributions to the existing experimental data is presented and the role of nuclear deformation analyzed. The Gamow-Teller strength is used to estimate the beta-decay half-life of nuclei for which experimental data exist. A satisfactory agreement with experimental half-lives is found and justifies the additional study of the exotic neutron-rich N=82, 126 and 184 isotonic chains of relevance for the r-process nucleosynthesis.

Low-energy electric dipole response of Sn isotopes

We study the low-energy dipole (LED) strength distribution along the Sn isotopic chain in both the isoscalar (IS) and the isovector (IV, or E1) electric channels, to provide testable predictions and guidance for new experiments with stable targets and radioactive beams. We use the self-consistent Quasi-particle Random-Phase Approximation (QRPA) with finite-range interactions and mainly the Gogny D1S force. We analyze also the performance of a realistic two-body interaction supplemented by a phenomenological three-body contact term. We find that from N=50 and up to the N=82 shell closure (132Sn) the lowest-energy part of the IS-LED spectrum is dominated by a collective transition whose properties vary smoothly with neutron number and which cannot be interpreted as a neutron-skin oscillation. For the neutron-rich species this state contributes to the E1 strength below particle threshold, but much more E1 strength is carried by other, weak but numerous transitions around or above threshold. We find that strong structural changes in the spectrum take effect beyond N=82, namely increased LED strength and lower excitation energies. Our results with the Gogny interaction are compatible with existing data. On this basis we predict that a) the summed IS strength below particle threshold shall be of the same order of magnitude for N=50-82, b) the summed E1 strength up to approximately 12 MeV shall be similar for N=50-82 MeV, while c) the summed E1 strength below threshold shall be of the same order of magnitude for N ~ 64 - 82 and much weaker for the lighter, more-symmetric isotopes. We point out a general agreement of our results with other non-relativistic studies, the absence of a collective IS mode in some of those studies, and a possibly radical disagreement with relativistic models.

Large-scale calculations of the double- β decay of 76 Ge , 130 Te , 136 Xe , and 150 Nd in the deformed self-consistent Skyrme quasiparticle random-phase approximation

Large-scale calculations of the double- β decay of 76 Ge , 130 Te , 136 Xe , and 150 Nd in the deformed self-consistent Skyrme quasiparticle random-phase approximation

Specific shear viscosity in hot rotating systems of paired fermions

The specific shear viscosity $\bar\eta$ of a classically rotating system of nucleons that interact via a monopole pairing interaction is calculated including the effects of thermal fluctuations and coupling to pair vibrations within the selfconsistent quasiparticle random-phase approximation. It is found that $\bar\eta$ increases with angular momentum $M$ at a given temperature $T$. In medium and heavy systems, $\bar\eta$ decreases with increasing $T$ at $T\geq$ 2 MeV and this feature is not affected much by angular momentum. But in lighter systems (with the mass number $A\leq$ 20), $\bar\eta$ increases with $T$ at a value of $M$ close to the maximal value $M_{max}$, which is defined as the limiting angular momentum for each system. The values of $\bar\eta$ obtained within the schematic model as well as for systems with realistic single-particle energies are always larger than the universal lower-bound conjecture $\hbar/(4\pi k_B)$ up to $T$=5 MeV.

Testing Skyrme Energy-Density Functionals with the QRPA in Low-lying Vibrational States of Rare-Earth Nuclei

Although nuclear energy density functionals are determined primarily by fitting to ground state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random phase approximation (QRPA). Here we test the Skyrme functionals SkM∗ and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with γ-vibrational states, but our results are not perfect and indicate the presences of multi-particle-hole correlations that are not included in the QRPA. The Skyrme functional SkM∗ performs noticeably better than SLy4. In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with “β-vibrational” states than with the γ-vibrational states.

Monopole strength function of deformed superfluid nuclei

We present an efficient method for calculating strength functions using the finite amplitude method (FAM) for deformed superfluid heavy nuclei within the framework of the nuclear density functional theory. We demonstrate that FAM reproduces strength functions obtained with the fully self-consistent quasi-particle random-phase approximation (QRPA) at a fraction of computational cost. As a demonstration, we compute the isoscalar and isovector monopole strength for strongly deformed configurations in $^{240}$Pu by considering huge quasi-particle QRPA spaces. Our approach to FAM, based on Broyden's iterative procedure, opens the possibility for large-scale calculations of strength distributions in well-bound and weakly bound nuclei across the nuclear landscape.

Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

Although nuclear energy-density functionals are determined primarily by fitting to ground-state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random-phase approximation (QRPA). Here we test the Skyrme functionals SkM${}^{*}$ and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with $\ensuremath{\gamma}$-vibrational states, but our results are not perfect and indicate the presence of multiparticle-hole correlations that are not included in the QRPA. The Skyrme functional SkM${}^{*}$ performs noticeably better than SLy4. In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with ``$\ensuremath{\beta}$-vibrational'' states than with the $\ensuremath{\gamma}$-vibrational states.

Thermodynamic properties of hot nuclei within the self-consistent quasiparticle random-phase approximation

The thermodynamic properties of hot nuclei are described within the canonical and microcanonical ensemble approaches. These approaches are derived based on the solutions of the BCS and self-consistent quasiparticle random-phase approximation at zero temperature embedded into the canonical and microcanonical ensembles. The obtained results agree well with the recent data extracted from experimental level densities by Oslo group for $^{94}$Mo, $^{98}$Mo, $^{162}$Dy and $^{172}$Yb nuclei.

Self-consistent Skyrme quasiparticle random-phase approximation for use in axially symmetric nuclei of arbitrary mass

We describe a new implementation of the quasiparticle random phase approximation (QRPA) in axially-symmetric deformed nuclei with Skyrme and volume-pairing energy-density functionals. After using a variety of tests to demonstrate the accuracy of the code in ^{24,26}Mg and ^{16}O, we report the first fully self-consistent application of the Skyrme QRPA to a heavy deformed nucleus, calculating strength distributions for several K^pi in ^{172}Yb. We present energy-weighted sums, properties of gamma-vibrational and low-energy K^pi=0^+ states, and the complete isovector E1 strength function. The QRPA calculation reproduces the properties of the low-lying 2^+ states as well or better than it typically does in spherical nuclei.