Quasiparticle Random Phase Approximation Research Articles

Electric dipole polarizability in neutron-rich Sn isotopes as a probe of nuclear isovector properties

The determination of nuclear symmetry energy, and in particular, its density dependence, is a long-standing problem for nuclear physics community. Previous studies have found that the product of electric dipole polarizability $\alpha_D$ and symmetry energy at saturation density $J$ has a strong linear correlation with $L$, the slope parameter of symmetry energy. However, current uncertainty of $J$ hinders the precise constraint on $L$. We investigate the correlations between electric dipole polarizability $\alpha_D$ (or times symmetry energy at saturation density $J$) in Sn isotopes and the slope parameter of symmetry energy $L$ using the quasiparticle random-phase approximation based on Skyrme Hartree-Fock-Bogoliubov. A strong and model-independent linear correlation between $\alpha_D$ and $L$ is found in neutron-rich Sn isotopes where pygmy dipole resonance (PDR) gives a considerable contribution to $\alpha_D$, attributed to the pairing correlations playing important roles through PDR. This newly discovered linear correlation would help one to constrain $L$ and neutron-skin thickness $\Delta R_\textnormal{np}$ stiffly if $\alpha_D$ is measured with high resolution in neutron-rich nuclei. Besides, a linear correlation between $\alpha_D J$ in a nucleus around $\beta$-stability line and $\alpha_D$ in a neutron-rich nucleus can be used to assess $\alpha_D$ in neutron-rich nuclei.

Discerning nuclear pairing properties from magnetic dipole excitation

Pairing correlation of Cooper pair is a fundamental property of multi-fermion interacting systems. For nucleons, two modes of the Cooper-pair coupling may exist, namely of $$S_{12}=0$$ with $$L_{12}=0$$ (spin-singlet s-wave) and $$S_{12}=1$$ with $$L_{12}=1$$ (spin-triplet p-wave). In nuclear physics, it has been an open question whether the spin-singlet or spin-triplet coupling is dominant, as well as how to measure their role. We investigate a relation between the magnetic-dipole (M1) excitation of nuclei and the pairing modes within the framework of relativistic nuclear energy-density functional (RNEDF). The pairing correlations are taken into account by the relativistic Hartree-Bogoliubov (RHB) model in the ground state, and the relativistic quasi-particle random-phase approximation (RQRPA) is employed to describe M1 transitions. We have shown that M1 excitation properties display a sensitivity on the pairing model involved in the calculations. The systematic evaluation of M1 transitions together with the accurate experimental data enables us to discern the pairing properties in finite nuclei.

Comparison of Microscopic Interacting Boson Model and Quasiparticle Random Phase Approximation 0νββ Decay Nuclear Matrix Elements

The fundamental nature of the neutrino is presently a subject of great interest. A way to access the absolute mass scale and the fundamental nature of the neutrino is to utilize the atomic nuclei through their rare decays, the neutrinoless double beta (0νββ) decay in particular. The experimentally measurable observable is the half-life of the decay, which can be factorized to consist of phase space factor, axial vector coupling constant, nuclear matrix element, and function containing physics beyond the standard model. Thus reliable description of nuclear matrix element is of crucial importance in order to extract information governed by the function containing physics beyond the standard model, neutrino mass parameter in particular. Comparison of double beta decay nuclear matrix elements obtained using microscopic interacting boson model (IBM-2) and quasiparticle random phase approximation (QRPA) has revealed close correspondence, even though the assumptions in these two models are rather different. The origin of this compatibility is not yet clear, and thorough investigation of decomposed matrix elements in terms of different contributions arising from induced currents and the finite nucleon size is expected to contribute to more accurate values for the double beta decay nuclear matrix elements. Such comparison is performed using detailed calculations on both models and obtained results are then discussed together with recent experimental results.

Lepton emission rates of [formula omitted]v isotopes under stellar conditions

In astrophysical conditions prevalent during the late times of stellar evolution, lepton (e− and e+) emission processes compete with the corresponding lepton capture processes. Prior to the collapse, lepton emissions significantly affect the cooling of the core and reduce its entropy. Therefore the lepton emission rates for Fe-group nuclei serve as an important input for core-collapse simulations of high-mass stars. From earlier simulation studies, isotopes of vanadium (V) have great astrophysical significance in regard to their weak-decay rates which substantially affect Ye (fraction of lepton to baryon number) during the final developmental stages of massive stars. The current study involves the computation of the weak lepton emission (LE) rates for V-isotopes by employing the improved deformed proton-neutron Quasi-particle Random Phase Approximation (pn-QRPA) model. The mass numbers of the selected isotopes range from 43 to 64. The LE rates on these isotopes have been estimated for a broad spectrum of density and temperature under astrophysical conditions. The ranges considered for density and temperature are 101 to 1011 (g/cm3) and 107 to 3 × 1011 (K), respectively. The lepton emission rates from the present study were also compared to the rates previously estimated by using the independent-particle model (IPM) and large-scale shell model (LSSM). IPM rates are generally bigger than QRPA rates, while LSSM rates are overall in good comparison with the reported rates. We attribute these differences to correct placement of GT centroid in LSSM and QRPA models.

Nuclear matrix elements for the 0νββ(0+→2+) decay of Ge76 within the two-nucleon mechanism

In this work we present the first beyond closure calculation for the neutrinoless double beta decay ($0\nu\beta\beta$) of $^{76}$Ge to the first $2^+$ states of $^{76}$Se. The isospin symmetry restored Quasi-particle random phase approximation (QRPA) method with the CD-Bonn realistic force is adopted for the nuclear structure calculations. We analyze the structure of the two nucleon mechanism nuclear matrix elements, and estimate the uncertainties from the nuclear many-body calculations. We find $g_{pp}$ plays an important role for the calculations and if quenching is included, suppression for the transition matrix element $M_{\lambda}$ is found. Our results for the transition matrix elements are about one order of magnitude larger than previous projected Hatree-Fock-Boglyubov results with the closure approximation.

Investigation of Important Weak Interaction Nuclei in Presupernova Evolution

Abstract This project aims to investigate the most important weak interaction nuclei in the presupernova evolution of massive stars. To achieve this goal, an ensemble containing 728 nuclei in the mass range of A = 1–100 was considered. We computed the mass fractions of these nuclei using Saha’s equation for predetermined values of T, ρ, and Y e and assuming nuclear statistical equilibrium. The nuclear partition functions were obtained using a newly introduced recipe where excited states, up to 10 MeV, were treated as discrete. The weak interaction rates (electron capture (ec) and β-decay (bd)) were calculated in a totally microscopic fashion using the proton–neutron quasiparticle random phase approximation model and without assuming the Brink–Axel hypothesis. The calculated rates were coupled with the computed mass fractions to investigate the time rate of change of lepton to baryon fraction of the stellar matter. We compare our results with the previous calculations reported in the literature. Noticeable differences up to orders of magnitude are reported with previous calculations. These differences may influence the evolution of the star in the later stages of presupernova. We present a list of the top 50 ec and bd nuclei, which have the largest effect on Y e for conditions after silicon core burning. The competition between the ec and bd rates in the stellar core was investigated and it was found that Y e = 0.424–0.455 is the interval where the bd results are bigger than the ec rates.

Comparative Analysis of Nuclear Matrix Elements of 0νβ+β+ Decay and Muon Capture in 106Cd

Comparative analyses of the nuclear matrix elements (NMEs) related to the 0νβ+β+ decay of 106Cd to the ground state of 106Pd and the ordinary muon capture (OMC) in 106Cd are performed. This is the first time the OMC NMEs are studied for a nucleus decaying via positron-emitting/electron-capture modes of double beta decay. All the present calculations are based on the proton-neutron quasiparticle random-phase approximation with large no-core single-particle bases and realistic two-nucleon interactions. The effect of the particle-particle interaction parameter gpp of pnQRPA on the NMEs is discussed. In the case of the OMC, the effect of different bound-muon wave functions is studied.

β -decay feeding intensity distributions for Nb103,104m

The $\ensuremath{\beta}$ decays of $^{103,104m}\mathrm{Nb}$ were studied with the Summing NaI(Tl) (SuN) detector at the National Superconducting Cyclotron Laboratory. The $\ensuremath{\beta}$-decay feeding intensity distribution ${I}_{\ensuremath{\beta}}(E)$ for each isotope was extracted by measuring $\ensuremath{\gamma}$ rays in coincidence with an emitted electron. The ${I}_{\ensuremath{\beta}}(E)$ was extracted via the total absorption spectroscopy technique. The ${I}_{\ensuremath{\beta}}(E)$ for each nucleus was compared to predictions made by the quasiparticle random-phase approximation (QRPA) model which is commonly used to calculate $\ensuremath{\beta}$-decay properties for astrophysical applications. The main goal was to provide experimental data for neutron-rich nuclei, relevant to the astrophysical $r$ process. In addition, the extracted $\ensuremath{\beta}$-decay feeding intensity distributions can lead to a better understanding of nuclear structure in a region of rapid structure changes around $A=100$. Finally, experimental data for $^{104m}\mathrm{Nb}$ are also of interest to antineutrino studies of nuclear reactors.

Impact of complex many-body correlations on electron capture in thermally excited nuclei around Ni78

We link complex many-body correlations, which play a decisive role in the structural properties of atomic nuclei, to the electron capture occurring during star evolution. The recently developed finite-temperature response theory, taking into account the coupling between single-nucleon and collective degrees of freedom, is applied to spin-isospin transitions, which dominate the electron capture rates. Calculations are performed for $^{78}\mathrm{Ni}$ and for the surrounding even-even nuclei associated with a high-sensitivity region of the nuclear chart in the context of core-collapse supernova simulations. The obtained electron capture rates are compared to those of a simpler thermal quasiparticle random phase approximation (TQRPA), which is standardly used in such computations. The comparison indicates that correlations beyond TQRPA lead to significantly higher electron capture rates under the typical thermodynamical conditions.

Total absorption spectroscopy of the β decay of Zr101,102 and Tc109

The $\ensuremath{\beta}$ decay of $^{101,102}\mathrm{Zr}$ and $^{109}\mathrm{Tc}$ was studied using the technique of total absorption spectroscopy. The experiment was performed at the National Superconducting Cyclotron Laboratory using the Summing NaI(Tl) (SuN) detector in the first-ever application of total absorption spectroscopy with a fast beam produced via projectile fragmentation. The $\ensuremath{\beta}$-decay feeding intensity and Gamow-Teller transition strength distributions were extracted for these three decays. The extracted distributions were compared to three different quasiparticle random-phase approximation (QRPA) models based on different mean-field potentials. A comparison with calculations from one of the QRPA models was performed to learn about the ground-state shape of the parent nucleus. For $^{101}\mathrm{Zr}$ and $^{102}\mathrm{Zr}$, calculations assuming a pure shape configuration (oblate or prolate) were not able to reproduce the extracted distributions. These results may indicate that some type of mixture between oblate and prolate shapes is necessary to reproduce the extracted distributions. For $^{109}\mathrm{Tc}$, a comparison of the extracted distributions with QRPA calculations suggests a dominant oblate configuration. The other two QRPA models are commonly used to provide $\ensuremath{\beta}$-decay properties in $r$-process network calculations. This work shows the importance of making comparisons between the experimental and theoretical $\ensuremath{\beta}$-decay distributions, rather than just half-lives and $\ensuremath{\beta}$-delayed neutron emission probabilities, as close to the $r$-process path as possible.

Deducing primary γ -ray intensities and the dipole strength function in Mo94 via radiative proton capture

Background: The nucleosynthesis of heavy nuclei is affected by the reaction rates of radiative capture reactions. Many of the astrophysical relevant rates cannot be obtained from experiments but are obtained from theoretical models. The $\ensuremath{\gamma}$-decay widths that are derived from radiative strength functions are one of the key nuclear physics input parameters in those calculations. The explicit study of $\ensuremath{\gamma}$-ray strength functions has been thoroughly addressed in the last decade and various methods have been established to extract the dipole strength in atomic nuclei.Purpose: The investigation of primary $\ensuremath{\gamma}$-ray transitions from the $^{93}\mathrm{Nb}(p,\ensuremath{\gamma})^{94}\mathrm{Mo}$ reaction allows deducing the $\ensuremath{\gamma}$-ray strength function in $^{94}\mathrm{Mo}$. The results are compared to results obtained using other techniques and the impact of level densities, excitation mechanism, and excitation energy will be thoroughly investigated.Method: The proton beam was delivered by the 10 MV FN-Tandem accelerator located at the Institute for Nuclear Physics at the University of Cologne, Germany. By means of in-beam $\ensuremath{\gamma}$-ray spectroscopy the intensity of primary $\ensuremath{\gamma}$ rays is determined. Additionally, the first generation $\ensuremath{\gamma}$-ray intensity is deduced from the secondary $\ensuremath{\gamma}$ rays using their branching and the coincidence detection efficiency. Absolute $\ensuremath{\gamma}$-ray strength function values as well as relative values using the ratio method will be extracted.Results: Numerous states in $^{94}\mathrm{Mo}$ at excitation energies above 3 MeV have been identified for the first time and their decay behavior has been studied. We disentangled the effects of $M1$ and $E1$ radiation for the $\ensuremath{\gamma}$-ray emission channel in $^{94}\mathrm{Mo}$ and extracted strength function curves for both radiation types. Our results are in good agreement with experimental results using the Oslo method and photoinduced experiments as well as with recent theoretical quasiparticle random-phase approximation (QRPA) calculations. An enhancement of the $\ensuremath{\gamma}$-ray strength below the neutron separation energy was found that is most likely of $E1$ character. In addition, a significant increase of the dipole strength at low $\ensuremath{\gamma}$-ray energies was found which is most likely due to $M1$ strength.Conclusion: Radiative proton capture reactions are a well-suited tool to study the $\ensuremath{\gamma}$-ray strength function in atomic nuclei. From the intensity of primary $\ensuremath{\gamma}$-ray transitions as well as from secondary $\ensuremath{\gamma}$-rays, information about the radiative dipole strength can be extracted. The $\ensuremath{\gamma}$-ray emission seems to be independent of the excitation energy in the studied mass and energy range. Detailed knowledge about the intrinsic properties of the nuclear states is very important and their uncertainties affect the uncertainty of the extracted $\ensuremath{\gamma}$-ray strength functions heavily.

Low-lying electric and magnetic dipole strengths in Pb207

Low-lying dipole transitions in $^{207}\mathrm{Pb}$ were measured via nuclear photon scattering using a quasimonochromatic, linearly polarized photon beam. The spins and/or parities of the states observed in $^{207}\mathrm{Pb}$ were determined from the intensity asymmetry of resonantly scattered $\ensuremath{\gamma}$ rays with respect to the polarization plane of the incident photon beam. The electric ($E1$) and magnetic ($M1$) dipole strengths were obtained for excitation energies from 5.49 to 6.75 MeV. The present experimental results, combined with $(\ensuremath{\gamma},n)$ data from the literature, were used to investigate the $E1$ and $M1$ photoabsorption cross sections near the neutron separation energy by comparison with predictions from the particle-vibration coupling with the quasiparticle random-phase approximation model.

Isovector giant dipole resonances in proton-rich Ar and Ca isotopes * *This work is partly Supported by the National Natural Science Foundation of China (11975096, 11775014) and the Fundamental Research Funds for the Central Universities (2020NTST06)

The isovector giant dipole resonances (IVGDR) in proton-rich Ar and Ca isotopes have been systematically investigated using the resonant continuum Hartree-Fock+BCS (HF+BCS) and quasiparticle random phase approximation (QRPA) methods. The Skyrme SLy5 and density-dependent contact pairing interactions are employed in the calculations. In addition to the giant dipole resonances at energy around 18 MeV, pygmy dipole resonances (PDR) are found to be located in the energy region below 12 MeV. The calculated energy-weighted moments of PDR in nuclei close to the proton drip-line exhaust about 4% of the TRK sum rule. The strengths decrease with increasing mass number in each isotopic chain. The transition densities of the PDR states show that motions of protons and neutrons are in phase in the interiors of nuclei, while the protons give the main contribution at the surface. By analyzing the QRPA amplitudes of proton and neutron 2-quasiparticle configurations for a given low-lying state, we find that only a few proton configurations give significant contributions. They contribute about 95% to the total QRPA amplitudes, which indicates that the collectivity of PDR states is not strong in proton-rich nuclei in the present study.

Finite-amplitude method for collective inertia in spontaneous fission

Background: Microscopic description of spontaneous fission is one of the most challenging subjects in nuclear physics. It is necessary to evaluate the collective potential and the collective inertia along a fission path for a description of quantum tunneling in spontaneous or low-energy fission. In past studies of the fission dynamics based on nuclear energy density functional (EDF) theory, the collective inertia has been evaluated with the cranking approximation, which neglects dynamical residual effects. Purpose: The purpose is to provide a reliable and efficient method to include dynamical residual effects in the collective inertia for fission dynamics. Methods: We use the local quasiparticle random-phase approximation (LQRPA) to evaluate the collective inertia along a fission path obtained by the constrained Hartree-Fock-Bogoliubov method with the Skyrme EDF. The finite-amplitude method (FAM) with a contour integration technique enables us to efficiently compute the collective inertia in a large model space. Results: We evaluate the FAM-QRPA collective inertia along a symmetric fission path in $^{240}$Pu and $^{256}$Fm. The FAM-QRPA inertia is significantly larger than the one of the cranking approximation, and shows pronounced peaks around the ground state and the fission isomer. This is due to dynamical residual effects. Conclusions: To describe the spontaneous or low-energy fission, we provide a reliable and efficient method to construct the collective inertia with dynamical residual effects that have been neglected in most of EDF-based works in the past. We show the importance of dynamical residual effects to the collective inertia. This work will be a starting point for a systematic study of fission dynamics in heavy and superheavy nuclei to microscopically describe the nuclear large-amplitude collective motions.

Stellar electron-capture rates based on finite-temperature relativistic quasiparticle random-phase approximation

The electron capture process plays an important role in the evolution of the core collapse of a massive star that precedes the supernova explosion. In this study, the electron capture on nuclei in stellar environment is described in the relativistic energy density functional framework, including both the finite temperature and nuclear pairing effects. Relevant nuclear transitions $J^\pi = 0^\pm, 1^\pm, 2^\pm$ are calculated using the finite temperature proton-neutron quasiparticle random phase approximation with the density-dependent meson-exchange effective interaction DD-ME2. The pairing and temperature effects are investigated in the Gamow-Teller transition strength as well as the electron capture cross sections and rates for ${}^{44}$Ti and ${}^{56}$Fe in stellar environment. It is found that the pairing correlations establish an additional unblocking mechanism similar to the finite temperature effects, that can allow otherwise blocked single-particle transitions. Inclusion of pairing correlations at finite temperature can significantly alter the electron capture cross sections, even up to a factor of two for ${}^{44}$Ti, while for the same nucleus electron capture rates can increase by more than one order of magnitude. We conclude that for the complete description of electron capture on nuclei both pairing and temperature effects must be taken into account.

E1 moments from a coherent set of measured photoneutron cross sections

Recently, the $E1$ photoneutron cross sections were measured consistently using quasimonochromatic laser Compton-scattering $\ensuremath{\gamma}$-ray beams at NewSUBARU (Japan) for a set of ten odd-even nuclei, spherical as well as deformed, covering relatively widely light to heavy species and at energies ranging between the neutron threshold and 40 MeV. This consistent set of experimental photoneutron cross sections allow us to estimate the total $E1$ photoabsorption cross sections, through validated theoretical models, by excluding the quasideuteron component and by including the missing low-energy and charged-particle emission contributions. In turn, the total $E1$ photoabsorption cross sections are used to derive the three main moments of the $E1$ distributions, namely the integrated cross section, the centroid energy, and the polarizability. These so-called model-dependent experimental moments follow a rather smooth trend with atomic mass, as theoretically expected, except for the specific case of $^{209}\mathrm{Bi}$ which presents a surprising 10% increase of both the integrated strength and the polarizability with respect to its even-even spherical neighbor $^{208}\mathrm{Pb}$. A rather consistent value for the enhancement factor of the $E1$ energy-weighted sum rule could be extracted from the present experimental data. The experimentally derived moments are compared for the ten odd-even systems with calculations based on the mean-field plus quasiparticle random phase approximation (QRPA). Spherical as well as axially deformed predictions based on the Skyrme and Gogny interactions are considered to discuss the results. Special attention is also paid to the approximate treatment of odd systems of nucleons in this context. It is found that in general theoretical predictions can rather well describe the data for the full set of nuclei, except for $^{209}\mathrm{Bi}$ presenting a kink in all the three main $E1$ moments with respect to the well-studied $^{208}\mathrm{Pb}$ case. Such an experimental determination cannot be explained by mean-field plus QRPA calculations. New measurements of photoabsorption cross section on $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ in the 14--19 MeV range as well as future theoretical calculations, in particular of odd-even systems, may help to solve such a mystery. The present data are also used to reinvestigate the correlation between the nuclear matter symmetry energy and its slope at saturation density. The analysis based on both Skyrme and Gogny Hartree-Fock-Bogolyubov (HFB) plus QRPA calculations confirm previous results, though quantitatively larger variations of the correlation parameters are found.

Nuclear incompressibility from spherical and deformed nuclei

We present an analysis based on the deformed Quasi Particle Random Phase Approximation, on top of a deformed Hartree-Fock-Bogoliubov description of the ground state, aimed at studying the isoscalar monopole and quadrupole response in a deformed nucleus. This analysis is motivated by the need of understanding the coupling between the two modes and how it might affect the extraction of the nuclear incompressibility from the monopole distribution. After discussing this motivation, we present the main ingredients of our theoretical framework, and we show some results obtained with the SLy4 and SkM* interactions for the nucleus 24Mg.

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.

Dipole response of Rb87 and its impact on the Rb86(n,γ)Rb87 cross section

Background: Detailed information on the low-lying dipole response in atomic nuclei along isotonic or isotopic chains is well suited to systematically investigate the structure and evolution of the pygmy dipole resonance (PDR). Moreover, the dipole strength below and around the neutron separation energy Sn has impact on statistical model calculations for nucleosynthesis processes. Purpose: The photon strength function (PSF) of Rb87, which is directly connected to the photoabsorption cross section, is a crucial input for statistical model calculations constraining the Maxwellian-averaged cross section (MACS) of the neutron capture of the unstable s-process branching-point nucleus Rb86. Within this work, the photoabsorption cross section is investigated. Methods: The photoabsorption cross section of the N=50 nucleus Rb87 was determined from photon-scattering experiments via the nuclear resonance fluorescence (NRF) technique. Bremsstrahlung beams at the γELBE facility in conjunction with monoenergetic photon beams at the HIγS facility were used to determine the integrated cross sections Is of isolated states as well as the averaged cross section as function of the excitation energy. Decays to the ground state were disentangled from decays to first low-lying excited states. Statistical and experimental approaches for the γ-decay properties at various excitation energies were applied. The linearly polarized photon beams at HIγS provide information on the ratio of electric and magnetic type of radiation. Results: Within this work, more than 200 ground-state decays and associated levels in Rb87 were identified. Moreover, transitions below the sensitivity limit of the state-by-state analysis were taken into account via a statistical approach from the bremsstrahlung data as well as model-independently from the HIγS data. The photoabsorption cross sections at various excitation energies were determined. The dipole response between 6 and 10 MeV of Rb87 is in agreement with assuming contributions of electric multipolarity, only. Conclusions: The photoabsorption cross section of Rb87 does not contradict with the trend of decreasing E1 strength with increasing proton number along the N=50 isotonic chain but might also be associated with a constant trend. The experimental γ decay at various excitation energies of the HIγS data supports the statistical approach but does not provide a stringent proof due to the limited sensitivity in the decay channels. The additional E1 strength observed in the present experiments significantly enhances the MACSs compared only to recent microscopic HFB+QRPA (Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation) calculations using the D1M interaction. Moreover, theoretical estimations provided by the KADoNiS project could be significantly improved.6 MoreReceived 18 June 2020Revised 24 August 2020Accepted 28 September 2020DOI:https://doi.org/10.1103/PhysRevC.102.044327©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectromagnetic transitionsEnergy levels & level densitiesNuclear astrophysicsPhotonuclear reactionsRadiative captureProperties59 ≤ A ≤ 89Nuclear Physics

Implementation of nuclear time-dependent density-functional theory and its application to the nuclear isovector electric dipole resonance

Following a previous paper [Y. Shi, Phys. Rev. C 98, 014329(2018)], we present an extension of the density-functional theory to allow for dynamic calculations based on the obtained static Hartree-Fock results. We perform extensive benchmark calculations, by comparing the calculated results with that of an existing code Sky3D. To perform linear-response calculations using the TDDFT method, comparisons have been made with the finite-amplitude quasiparticle random-phase approximation (FAM-QRPA) method. We plan to apply the TDDFT method to a systematic description of the IVD resonances in the Zr, Mo, and Ru isotopes. The strengths of IVD resonances are calculated using two complementary methods: TDDFT and FAM-QRPA methods. For the TDDFT results, additional benchmark calculations have been performed using the well-tested code Sky3D. In these three models, the important ingredients which have major influence on the results, such as time-odd potentials, boundary conditions, smoothing procedures, spurious peaks etc., have been carefully examined. The current TDDFT and the Sky3D codes yield almost identical response functions once both codes use the same time-odd mean fields and absorbing boundary conditions. The strengths of the IVD resonances calculated using the TDDFT and FAM-QRPA methods agree reasonably well with the same position of the giant dipole resonance. Upon seeing a reasonable accuracy offered by the implemented code, we perform systematic TDDFT calculations for spherical Zr and Mo isotopes near $N=50$, where experimental data exist. For neutron-rich Zr, Mo, and Ru isotopes where shape evolution exist we predict the photoabsorption cross sections based on oblate and triaxial minima.