Quasiparticle Random Phase Approximation Research Articles

Electron capture and β-decay rates for nuclei with A = 65–80

Recently a list of top 50 most important electron capture (ec) and β-decay (bd) nuclei, averaged throughout the stellar trajectory for 0.500 > Y e > 0.400, was published. The current study presents the calculation of ec and bd rates, from the published list with A = 65–80, on a detailed temperature-density grid. The ec and bd rates were calculated using the proton-neutron quasiparticle random phase approximation model (pn-QRPA). Our calculation did not employ the Brink-Axel hypothesis. A systematic comparison of the current calculation with the previous pn-QRPA and independent particle model (IPM) results is presented for the first time. The reported ec rates are almost the same when compared with the previous pn-QRPA calculation. On the other hand, the reported bd rates are generally smaller up to an order of magnitude. Comparison with IPM results show that our calculated rates are bigger, by two orders of magnitude. The current calculation may contribute to a more realistic simulation of late phases of stellar evolution and modeling of x-ray bursts.

Original e− Capture Cross Sections for Hot Stellar Interior Energies

The nuclear electron capture reaction possesses a prominent position among other weak interaction processes occurring in explosive nucleosynthesis, especially at the late stages of evolution of massive stars. In this work, we perform exclusive calculations of absolute e−-capture cross sections using the proton–neutron (pn) quasi-particle random phase approximation. Thus, the results of this study can be used as predictions for experiments operating under the same conditions and in exploring the role of the e−-capture process in the stellar environment at the pre-supernova and supernova phase of a massive star. The main goal of our study is to provide detailed state-by-state calculations of original cross sections for the e−-capture on a set of isotopes around the iron group nuclei (28Si, 32S, 48Ti, 56Fe, 66Zn and 90Zr) that play a significant role in pre-supernova as well as in the core–collapse supernova phase in the energy range 0≤E≤50 MeV.

Towards a Predictive HFB+QRPA Framework for Deformed Nuclei: Selected Tools and Techniques

Reliable predictions of the static and dynamic properties of a nucleus require a fully microscopic description of both ground and excited states of this complicated many-body quantum system. Predictive calculations are key to understanding such systems and are important ingredients for simulating stellar environments and for enabling a variety of contemporary nuclear applications. Challenges that theory has to address include accounting for nuclear deformation and the ability to describe medium-mass and heavy nuclei. Here, we perform a study of nuclear states in an Hartree-Fock-Bogoliubov (HFB) and Quasiparticle Random Phase Approximation (QRPA) framework that utilizes an axially-symmetric deformed basis. We present some useful techniques for testing the consistency of such calculations and for interpreting the results.

Calculation of β -decay half-lives within a Skyrme-Hartree-Fock-Bogoliubov energy density functional with the proton-neutron quasiparticle random-phase approximation and isoscalar pairing strengths optimized by a Bayesian method

Background: For data on radioactive nuclei, $\ensuremath{\beta}$ decay provides some of the most important information, applicable to various fields. However, some $\ensuremath{\beta}$-decay data are not available due to experimental difficulties. For this reason, theoretically calculated results have been embedded in the data on radioactive nuclear $\ensuremath{\beta}$ decay to compensate for the missing information.Purpose: It is necessary to treat various nuclear correlations as precisely as possible for theoretical $\ensuremath{\beta}$-decay calculations. In particular, the pairing correlation is one of the most important factors for reproducing $\ensuremath{\beta}$-decay half-lives correctly. Therefore, we first study the effect of zero- and finite-range isovector pairings on half-lives. Second, we investigate the isoscalar pairing strengths, which are determined through experimental data of half-lives. Finally, we predict the isoscalar pairing strengths and half-lives of neutron-rich nuclei.Methods: To calculate the $\ensuremath{\beta}$-decay half-lives, a proton-neutron quasiparticle random-phase approximation on top of a Skryme energy density functional is applied with an assumption of spherical symmetry. The half-lives are calculated by including the allowed and first-forbidden transitions. The isoscalar pairing strength is estimated by a Bayesian neural network (BNN). We verify the predicted isoscalar pairing strengths by preparing the training data and test data.Results: It was confirmed that the finite-range isovector pairing ensures that the $\ensuremath{\beta}$-decay half-lives are insensitive to the model space, while the zero-range one is largely dependent on it. The half-lives calculated with the BNN isoscalar pairing strengths reproduced most of the experimental data, although those of highly deformed nuclei were underestimated. We also studied the predictive performance on new experimental data that were not used for the BNN training and found that they were reproduced well.Conclusions: Our study demonstrates that the isoscalar pairing strengths determined by the BNN can reproduce experimental data with the same accuracy as other theoretical works. To achieve a more precise prediction, the nuclear deformation is important.

Chebyshev kernel polynomial method for efficient calculation of the quasiparticle random phase approximation response function

Efficient and accurate algorithms for the calculation of the multipole response of deformed atomic nuclei are very important tools in nuclear structure, especially for large scale calculations. In this paper we present an implementation of the algorithm based on the expansion of the response function in terms of the Chebyshev polynomials in conjunction with the kernel polynomial method for a very efficient calculation of the quasiparticle random phase approximation response function. Several test calculations are performed in order to asses the applicability and feasibility of this algorithm, already used successfully in the field of computational solid state physics, in various nuclear structure calculations.

Two-neutrino double- β decay matrix elements based on a relativistic nuclear energy density functional

Nuclear matrix elements (NMEs) for two-neutrino double-beta decay ($2\nu\beta\beta$) are studied in the framework of relativistic nuclear energy density functional (REDF). The properties of nuclei involved in the decay are obtained using the relativistic Hartree-Bardeen-Cooper-Schrieffer theory and relevant nuclear transitions are described using the relativistic proton-neutron quasiparticle random phase approximation based on relativistic energy density functional (REDF-QRPA). Three effective interactions have been employed, including density-dependent meson-exchange (DD-ME2) and point coupling interactions (DD-PC1 and DD-PCX), and pairing correlations are described consistently both in $T=1$ and $T=0$ channels using a separable pairing interaction. The optimal values of $T=0$ pairing strength parameter $V_{0pp}$ are constrained by the experimental data on $\beta$-decay half lives. The $2\nu\beta\beta$ matrix elements and half-lives are calculated for several nuclides experimentally known to undergo this kind of decay: $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Xe, $^{128}$Te, $^{130}$Te, $^{136}$Xe and $^{150}$Nd. The model dependence of the NMEs and their sensitivity on $V_{0pp}$ is investigated, and the NMEs obtained using optimal values of $V_{0pp}$ are discussed in comparison to previous studies. The results of the present work represent an important benchmark for the future applications of the relativistic framework in studies of neutrinoless double-beta decay.

Symmetry breaking of Gamow-Teller and magnetic-dipole transitions and its restoration in calcium isotopes

Nuclear magnetic-dipole (M1) and Gamow-Teller (GT) transitions provide insight into the spin-isospin properties of atomic nuclei. By considering them as unified spin-isospin transitions, the M1/GT transition strengths and excitation energies are subject to isospin symmetry. The excitation properties associated to the M1/GT symmetry need to be clarified within consistent theoretical approach. In this work, the relationship between the M1 and GT transitions in Ca isotopes is investigated in a unified framework based on the relativistic energy-density functional (REDF) with point-coupling interactions, using the relativistic quasi-particle random-phase approximation (RQRPA). It is shown that the isovector-pseudovector (IV-PV) residual interaction affects both transitions, and the symmetry of M1 and giant-GT transitions is disrupted by this interaction in closed-shell nuclei. In open-shell Ca isotopes, the proton-neutron pairing in the residual RQRPA interaction also plays a role in GT transitions. Due to the interplay between these interactions, the M1/GT symmetry can be restored especially in the $^{42}$Ca nucleus, i.e., the giant-GT strength can become comparable to that of the M1 mode in terms of the unified spin-isospin transitions by adjusting the PN-pairing strength to reproduce the experimental low-lying GT-excitation energies. The mirror symmetry of both M1 and GT transitions is also demonstrated for open-shell mirror partners, $^{42}$Ca and $^{42}$Ti. Further improvements are required to achieve simultaneous reproduction of M1 and GT-transition energies in the REDF framework.

Role of the quadrupole deformation in γ-soft nuclei: The case of 124−134Xe

Observation of the scissors mode in the γ-soft and transition nuclei provides the reasoning for investigating the possibility of quadrupole deformation in such nuclei. Using a deformed-based model for an investigation of the scissors mode, the goal of this work was to analyze the effects associated with quadrupole deformation for the so-called “γ-soft” nuclei in the example of even-even 124−134Xe isotopes. Here, the well-known properties of the scissors mode were investigated using just the quadrupole deformed-based rotational, invariant quasiparticle random phase approximation (QRPA) method. The properties of the scissors mode were clearly seen for all the investigated xenon isotopes, demonstrating that quadrupole deformed-based models can easily explain the nature of the low-lying M1 strength for γ-soft nuclei and indicating that quadrupole deformation plays a non-negligible role in the formation of the low-lying dipole strength for such nuclei.

Investigation of Gamow–Teller strength of 186Hg within deformed pn-QRPA

Recently, the total absorption gamma spectroscopy technique was used to determine the Gamow–Teller (GT) distribution of β-decay of 186Hg. It was concluded that the best description of the measured data was obtained with dominantly prolate components for both parent 186Hg and daughter 186Au. Motivated by the recent findings, we investigate the effect of nuclear deformation on the energy distribution of the GT strength of the decay of 186Hg into 186Au within the framework of proton–neutron quasiparticle random phase approximation (pn-QRPA) based on the deformed Nilsson potential. To do the needful, we first calculate the energy levels and shape prediction of 186Hg within the interacting boson model. The computed GT strength distribution satisfied the model-independent Ikeda sum rule 100% (99.98%) for the prolate (oblate) case. Based on the strength distributions, the deformed pn-QRPA model with separable interaction prefers a prolate shape for the ground state of 186Hg and supports the shape coexistence for this nucleus.

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.

Many-body approach to superfluid nuclei in axial geometry

Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov's quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon's characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in nonspherical geometries. In this paper, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov's Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point-coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of $^{38}\mathrm{Si}$ and $^{250}\mathrm{Cf}$ are presented and discussed.

The β-decay of 70Kr into 70Br: Restoration of the pseudo-SU(4) symmetry

The β-decay of the even-even nucleus 70Kr with Z=N+2, has been investigated at the Radioactive Ion Beam Factory (RIBF) of the RIKEN Nishina Center using the BigRIPS fragment separator, the ZeroDegree Spectrometer, the WAS3ABI implantation station and the EURICA HPGe cluster array. Fifteen γ-rays associated with the β-decay of 70Kr into 70Br have been identified for the first time, defining ten populated states below Eexc=3300 keV. The half-life of 70Kr was derived with increased precision and found to be t1/2=45.19±0.14 ms. The β-delayed proton emission probability has also been determined as εp=0.545(23)%. An increase in the β-strength to the yrast 1+ state in comparison with the heaviest Z=N+2 system studied so far (62Ge decay) is observed that may indicate increased np correlations in the T=0 channel. The β-decay strength deduced from the results is interpreted in terms of the proton-neutron quasiparticle random-phase approximation (pnQRPA) and also with a schematic model that includes isoscalar and isovector pairing in addition to quadrupole deformation. The application of this last model indicates an approximate realization of pseudo-SU(4) symmetry in this system.

How effective is the Brink–Axel hypothesis for astrophysical weak rates?

Abstract We explore the effectiveness of the Brink–Axel hypothesis (BAH) for the computation of stellar electron capture (EC) and β-decay (BD) rates, namely that the transition strength function depends only upon the transition energy and not upon the details of the initial state. For this purpose, we calculated Gamow–Teller (GT) strength distributions for a selection of sd-shell nuclides, using two different microscopic models, namely the proton–neutron quasiparticle random phase approximation and the full configuration-interaction shell model, taking into account the first 100 states of both the initial and final nuclides. The GT transition strengths among these levels evolve with initial state energy. These transition strength functions we folded into weak-interaction mediated rates in stellar matter, specifically EC and BD rates, for a range of densities 10 g cm−3 ⩽ ρ ⩽ 1011 g cm−3 and range of temperatures 1 GK ⩽ T ⩽ 30 GK. When transitions from excited states were approximated using the BAH, augmented by so-called ‘back-resonance’ transitions, the rates were affected by up to three orders of magnitude or more at high temperatures and densities. Thus the BAH is not a reliable approximation for the calculation of stellar rates, especially in high temperature–density environments.

Global calculation of two-neutrino double- β decay within the finite amplitude method in nuclear density functional theory

Two-neutrino double-beta ($2\nu\beta\beta$) decay has been used to constrain the neutron-proton part of effective interactions, which in turn is used to compute the nuclear matrix elements for neutrinoless double-beta decay, the observation of which would have important consequences for fundamental physics. We carefully examine $2\nu\beta\beta$ matrix elements within the proton-neutron quasiparticle random-phase approximation with nuclear energy density functionals. We work with functionals that are fit globally to single-beta-decay half-lives and charge-exchange giant-resonance energies, but not to $2\nu\beta\beta$ half-lives themselves, to evaluate the $2\nu\beta\beta$ nuclear matrix elements for all important nuclei, including those whose half-lives have not yet been measured. Such a comprehensive evaluation in large model spaces without configuration truncation requires an efficient computational scheme; we employ a double contour integration within the finite amplitude method. The results generally reproduce the nuclear matrix element extracted from half-lives well, without the use of any of those half-lives in the fitting procedure. We present predictions of the matrix elements in a total of 27 nuclei with half-lives that are still unmeasured.

Axially-deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (IV) hfbtho (v4.0): A new version of the program

We describe the new version 4.0 of the code hfbtho that solves the nuclear Hartree-Fock-Bogoliubov problem by using the deformed harmonic oscillator basis in cylindrical coordinates. In the new version, we have implemented the restoration of rotational, particle number, and reflection symmetry for even-even nuclei. The restoration of rotational symmetry does not require using bases closed under rotation. Furthermore, we added the SeaLL1 functional and improved the calculation of the Coulomb potential. Finally, we refactored the code to facilitate maintenance and future developments. New version program summaryProgram title:hfbtho v4.0CPC Library link to program files:https://doi.org/10.17632/c5g2f92by3.2Code Ocean capsule:https://codeocean.com/capsule/5389629Licensing provisions: GPLv3Programming language: Fortran 2003Journal reference of previous version: R.N. Pérez, N. Schunck, R.-D. Lasseri, C. Zhang and J. Sarich, Comput. Phys. Commun. 220 (2017) 363Does the new version supersede the previous version: YesReasons for the new version: This version adds new capabilities to restore broken symmetries and determine corresponding quantum numbers of even-even nucleiSummary of revisions:1.Angular momentum projection for even-even nuclei in a deformed basis;2.Particle number projection for even-even nuclei in the quasiparticle basis;3.Implementation of the SeaLL1 functional;4.Expansion of the Coulomb potential onto Gaussians;5.MPI-parallelization of a single hfbtho execution;6.Code refactoring.Nature of problem:hfbtho is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of hfbtho, the energy density is derived either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear superfluidity is treated at the Hartree-Fock-Bogoliubov (HFB) approximation. Constraints on the nuclear shape allow probing the potential energy surface of the nucleus as needed, e.g., for the description of shape isomers or fission. A local scale transformation of the single-particle basis in which the HFB solutions are expanded provides a tool to properly compute the structure of weakly-bound nuclei. Restoration of the rotational, particle number, and reflection symmetry for even-even nuclei enables recovering the quantum numbers that are lost at the HFB approximation.Solution method: The program uses the axial harmonic oscillator (HO) or the transformed harmonic oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the HFB Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. Lagrange parameters are used to impose constraints on HFB solutions, and their value is updated at each iteration from an approximation of the quasiparticle random phase approximation (QRPA) matrix. Symmetry restoration is implemented through standard projection techniques. Previous versions of the program were presented in [1-3].Additional comments including restrictions and unusual features: Axial and time-reversal symmetries are assumed in HFB calculations; y-simplex symmetry and even particle numbers are assumed in angular momentum projection.

Low-energy monopole strength in spherical and axially deformed nuclei: Cluster and soft modes

Background: Several recent experiments report significant low-energy isoscalar monopole strength, below the giant resonance, in various nuclei. In light $\ensuremath{\alpha}$-conjugate nuclei, these low-energy resonances were recently interpreted as cluster vibration modes. However, the nature of these excitations in neutron-rich nuclei remains elusive.Purpose: The present work provides a systematic analysis of the low-energy monopole strength in isotopic chains, from neon to germanium, in order to monitor and understand its nature and conditions of emergence.Methods: We perform covariant quasiparticle random phase approximation calculations, formulated within the finite amplitude method, on top of constrained relativistic Hartree-Bogoliubov (RHB) reference states.Results: Neutron excess leads to the appearance of low-energy excitations according to a systematic pattern reflecting the single-particle features of the underlying RHB reference state. With the onset of deformation, these low-energy resonances get split and give rise to more complex patterns, with possible mixing with the giant resonance. At lower energy, clusterlike excitations found in $N=Z$ systems survive in neutron-rich nuclei, with valence neutrons arranging in molecularlike orbitals. Finally, at very low energy, pair excitations are also found in superfluid nuclei, but remain negligible in most of the cases.Conclusions: The low-energy part of the monopole strength exhibits various modes, from cluster vibrations ($\ensuremath{\approx}$5--10 MeV) to components of the giant resonance downshifted by the onset of deformation, including soft modes ($\ensuremath{\approx}$10--15 MeV) as well as pair excitation ($<$5 MeV), with possible mixing, depending on neutron excess, deformation, and pairing energy.

Charge radii of Ca isotopes and correlations

We study the effects of short- and long-range correlations on the charge radii of Ca isotopes. We start our investigation with an independent particle model consisting in Hartree-Fock plus Bardeen-Cooper-Schrieffer calculations with finite-range effective nucleon-nucleon interactions of Gogny type. The short-range correlations effects are evaluated by considering all the terms of a cluster expansion containing a single correlation line. The long-range correlations are taken into account by including the coupling with the quasi-particle random phase approximation phonons. While the effects of the short-range correlations are negligible, those of the long-range correlations largely modify the independent particle model results and improve the agreement with the experimental data.

High-precision Q-value measurement and nuclear matrix element calculations for the double-beta decay of ^{98}Mo

The ^{98}Mo double-beta decay Q-value has been measured, and the corresponding nuclear matrix elements of neutrinoless double-beta (0nu beta beta ) decay and the standard two-neutrino double-beta (2nu beta beta ) decay have been provided by nuclear theory. The double-beta decay Q-value has been determined as Q_{beta beta }=113.668(68) keV using the JYFLTRAP Penning trap mass spectrometer. It is in agreement with the literature value, Q_{beta beta }=109(6) keV, but almost 90 times more precise. Based on the measured Q-value, precise phase-space factors for 2nu beta beta decay and 0nu beta beta decay, needed in the half-life predictions, have been calculated. Furthermore, the involved nuclear matrix elements have been computed in the proton–neutron quasiparticle random-phase approximation (pnQRPA) and the microscopic interacting boson model (IBM-2) frameworks. Finally, predictions for the 2nu beta beta decay are given, suggesting a much longer half-life than for the currently observed cases.

Isoscalar giant monopole resonance inMg24andSi28: 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∞ and the coupling between IS0 and isoscalar quadrupole (IS2) strength. Purpose: This study aims to investigate the two-peaked structure of the ISGMR in the prolate Mg24 and oblate Si28 nuclei and identify among a variety of energy density functionals based on Skyrme parametrizations 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 analyzed. Methods: The ISGMR was excited in Mg24 and Si28 using α-particle inelastic scattering measurements acquired with an Eα=196 MeV beam at scattering angles θLab=0∘ and 4∘. The K600 magnetic spectrometer at iThemba LABS was used to detect and momentum analyze the inelastically scattered α particles. An experimental energy resolution of ≈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-spectra (DoS) technique. The theoretical comparison is based on the quasiparticle random-phase approximation (QRPA) with a representative set of Skyrme forces. Results: IS0 strength distributions for Mg24 and Si28 are extracted and compared to previously published results from experiments with a lower energy resolution. With some exceptions, a reasonable agreement is obtained. The IS0 strength is found to be separated into a narrow structure at about 13–14 MeV in Mg24, 17–19 MeV in Si28, and a broad structure at 19–26 MeV in both nuclei. The data are compared with QRPA results. The results of the calculated characteristics of IS0 states demonstrate the strong IS0/IS2 coupling in strongly prolate Mg24 and oblate Si28. The narrow IS0 peaks are shown to arise due to the deformation-induced IS0/IS2 coupling and strong collective effects. The cluster features of the narrow IS0 peak at 13.87MeV in Mg24 are also discussed. The best description of the IS0 data is obtained using the Skyrme force SkPδ with an associated low nuclear incompressibility K∞=202MeV allowing for both the energy of the peak and integral IS0 strength in Mg24 and Si28 to be reproduced. The features of the ISGQR in these nuclei are also investigated. An anomalous deformation splitting of the ISGQR in oblate Si28 is found. The observed structure of ISGQR in Mg24 is described. Conclusions: The ISGMR and ISGQR in light deformed nuclei are coupled and thus need to be described simultaneously. Only such a description is relevant and consistent. The deformation-induced narrow IS0 peaks can serve as an additional sensitive measure of the nuclear incompressibility.8 MoreReceived 13 November 2021Revised 20 December 2021Accepted 25 January 2022DOI:https://doi.org/10.1103/PhysRevC.105.024311©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsNuclear forcesNuclear many-body theoryNuclear spin & parityNuclear structure & decaysNucleon induced nuclear reactionsNucleon-nucleon interactionsResonance reactionsProperties20 ≤ A ≤ 38Accelerators & BeamsNuclear Physics

The electric dipole response of even-even 154–164Dy isotopes

The excitation of pygmy dipole resonance (PDR) and giant dipole resonance (GDR) in even–even 154–164Dy isotopes is examined through quasiparticle random-phase approximation (QRPA) with the effective interactions that restore the broken translational and Galilean invariances. In each isotope, an electric response emerges by showing ample distribution at energies below and above 10 MeV. We, therefore, study the transition cross-sections and probabilities, photon strength functions, transition strengths, isospin character, and collectivity of the predicted E1 responses.