Quasiparticle Random Phase Approximation Research Articles

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.

Pygmy dipole resonance in the well-deformed even–even 152–162Gd

The electric dipole E1 strength in the well-deformed even–even 152–162Gd was calculated using a model based on translational and Galilean invariant quasi-particle random phase approximation (QRPA), where for the first time the highly-fragmented E1 strength has been predicted below the particle threshold energy. The predicted concentration of the electric dipole excitations exhausts less than 2% of the energy weighed sum rules (EWSR) below 20 MeV in rather good agreement with the experimental data for neighbor nuclei. Through cross sections, transition probabilities, and other properties, the electric dipole response was investigated in 152–162Gd for a wide range of excitation energies from 5 to 20 MeV. The calculation that was performed with the elimination of effects associated with deformation revealed that the effects associated with neutron excess play a more significant role in the formation of the pygmy dipole resonance (PDR) strength when compared to the effects associated with a changing deformation. The calculations indicate the presence of magnetic dipole excitations with summed M1 strengths in the energy region between 5 and 8 MeV was less than 10% of the total dipole strength in the same energy region. We also took into account a recent experimental study of 156Gd in our discussion and paid particular attention to this isotope.

Magnetic dipole excitations based on the relativistic nuclear energy density functional

Magnetic dipole (M1) excitations build not only a fundamental mode of nucleonic transitions, but they are also relevant for nuclear astrophysics applications. We have established a theory framework for description of M1 transitions based on the relativistic nuclear energy density functional. For this purpose the relativistic quasiparticle random phase approximation (RQRPA) is established using density dependent point coupling interaction DD-PC1, supplemented with the isovector-pseudovector interaction channel in order to study unnatural parity transitions. The introduced framework has been validated using the M1 sum rule for core-plus-two-nucleon systems, and employed in studies of the spin, orbital, isoscalar and isovector M1 transition strengths, that relate to the electromagnetic probe, in magic nuclei $^{48}$Ca and $^{208}$Pb, and open shell nuclei $^{42}$Ca and $^{50}$Ti. In these systems, the isovector spin-flip M1 transition is dominant, mainly between one or two spin-orbit partner states. It is shown that pairing correlations have a significant impact on the centroid energy and major peak position of the M1 mode. The M1 excitations could provide an additional constraint to improve nuclear energy density functionals in the future studies.

Analysis of two-nucleon transfer reactions in the Ne20+Cd116 system at 306 MeV

Background: Heavy-ion induced two-nucleon transfer reactions are powerful tools to reveal peculiar aspects of the atomic nucleus, such as pairing correlations, single-particle and collective degrees of freedom, and more. Also, these processes are in competition with the direct meson exchange in the double charge exchange reactions, which have recently attracted great interest due to their possible connection to neutrinoless double-beta decay. In this framework, the exploration of two-nucleon transfer reactions in the 20Ne+116Cd collision at energies above the Coulomb barrier is particularly relevant since the 116Cd nucleus is a candidate for the double-beta decay. Methods: We measured the excitation energy spectra and absolute cross sections for the two reactions using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. We performed direct coupled reaction channels and sequential distorted wave Born approximation calculations using the double folding S\~ao Paulo potential to model the initial and final state interactions. The spectroscopic amplitudes for two- and singleparticle transitions were derived by different nuclear structure approaches: microscopic large-scale shell model, interacting boson model-2 and quasiparticle random phase approximation. Results: The calculations are able to reproduce the experimental cross sections for both two-neutron and twoproton transfer reactions. The role of couplings with the inelastic channels are found to be important in the two-proton transfer case. A competition between the direct and the sequential process is found in the reaction mechanism. For the two-proton transfer case, the inclusion of the 1g7/2 and 2d5/2 orbitals in the model space is crucial.

Strength of the isoscalar pairing interaction determined by a relation between double-charge change and double-pair transfer for double- β decay

A new method has been proposed to determine the strength of the isoscalar proton-neutron pairing interaction applicable to many nuclei. The principle is the equivalence between the double charge change and the double transfer of like-particle pair, and a constraint is derived to the effective interactions used in approximations. This method was applied to the quasiparticle random-phase approximation for determining that interaction strength. In this paper, detail of this method is explained thoroughly, and applications are made to nuclei of several instances of the double-$\beta$ decays. The systematics of the strengths determined for those nuclei is understood in terms of a midshell effect. The effect of the new interaction strength is examined in two examples of the Gamow-Teller strength function with comparisons with the experimental data. The nuclear matrix elements of the neutrinoless double-$\beta$ decay are also calculated.

Neutron-Proton, Neutron-Neutron, Proton-Proton QRPA for the Gamow-Teller and the M1 Spin Transitions of N ≃ Z Nuclei in the s — d Shell

We study the Gamow-Teller (GT) and the M1 spin transitions of the s — d shell nuclei $^{24}$Mg, $^{26}$Mg, $^{28}$Si, $^{32}$S, and $^{36}$Ar by using a quasiparticle random phase approximation (QRPA) scheme that comprises neutron-proton (np), neutron-neutron (nn) and proton-proton (pp) QRPA owing to the inclusion of the np pairing, as well as nn and pp pairing correlations. At present, we work in spherical symmetry under the assumption that the deformations of the nuclei considered in this work are small enough to neglect, as was customary in past applications. For the GT transition, as well as single and double beta decays, the neutron-proton QRPA (np QRPA) is usually employed. For the M1 spin transition, the pp and nn QRPA is needed due to its neutral current property. The np pairing correlations couple the np QRPA to the nn and pp QRPA. Therefore, the coupled np + nn + pp QRPA enables us to investigate simultaneously the GT and the M1 spin transitions. In particular, in this work, detailed analyses of particle-particle and particle-hole interactions at the QRPA stage are performed for the GT and the M1 spin transitions of the well-known s — d shell N ≃ Z nuclei, and the results are compared to available data. The roles of the np pairing correlations are also discussed for those transitions.

Lepton capture rates due to isotopes of vanadium in astrophysical environment

Lepton (electron and positron) capture rates on iron-regime nuclei are an essential element for modeling the late stages of progression of massive stars that become core collapse and thermonuclear supernova. As per previous simulation studies, lepton capture (LC) rates on isotopes of vanadium are believed to have a substantial effect in regulating the Ye (lepton to baryon fraction) during the final evolutionary phases. The present work involves the calculation of lepton capture rates for 22 isotopes of vanadium by making use of the proton-neutron (pn-) quasiparticle random phase approximation (QRPA) model. The covered mass range is from A = 43 to 64. The LC rates have been computed over stellar densities ranging from $10^{1}$ to $10^{11}$ (g/cm3) and for the temperature range $10^{7} - 3 \times 10^{10}$ (K). A comparison of our calculated LC rates to the rates computed using other models (IPM and LSSM) has also been presented. As compared to the rates calculated by other models, pn-QRPA rates at high temperature ( $3 \times 10^{10}$ K) are larger by up to 1-2 orders of magnitude.

Role of residual interaction in the relativistic description of M1 excitation

Magnetic dipole (M1) excitation is the leading mode of multi-nucleon excitations induced by the magnetic field, and is a phenomenon of the spin–orbit splitting and residual interactions involved. In this work, we investigate the effects of the residual interactions on the M1 excitation from a novel perspective, the framework of relativistic nuclear energy-density functional. The relativistic Hartree–Bogoliubov model is utilized to determine the nuclear ground state properties, while the relativistic quasi-particle random-phase approximation is employed for the description of M1-excitation properties. From the analysis of M1 mode in the Ca isotope chain, role of the isovector–pseudovector residual interaction is discussed. For open-shell nuclei, the pairing correlation also plays a noticeable role in the M1 mode. The experimental data on M1 mode is expected to provide a suitable reference to improve and optimize the theoretical models to describe the residual interactions.

Global description of β− decay with the axially deformed Skyrme finite-amplitude method: Extension to odd-mass and odd-odd nuclei

We use the finite amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute beta-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.

Muon capture rates: Evaluation within the quasiparticle random phase approximation

The Quasiparticle Random Phase Approximation (QRPA) is used in evaluation of the total muon capture ratesfor the final nuclei participating in double-beta decay. Several variants of the method are used, depending on the size of the single particle model space used, or treatment of the initial bound muon wave function. The resulting capture rates are all reasonably close to each other. In particular, the variant that appears to be most realistic, results in rates in good agreement with the experimental values. There is no necessity for an empirical quenching of the axial current coupling constant $g_A$. Its standard value $g_A$ = 1.27 seems to be adequate.

Global Calculations of Beta-Decay Properties Based on the Fayans Functional

An effective approximation to a fully self-consistent global description of beta-decay properties of nuclei within the theory of finite Fermi systems is presented. It is based on describing the ground state properties within the energy density functional proposed by Fayans and coauthors (DF3) and on the continuum quasiparticle random-phase approximation (CQRPA). The accuracy of global DF3 $$+$$ CQRPA calculations is analyzed. For more than 200 (quasi)spherical nuclei with $$Z=18$$ to 51 having half-lives in the range of $$T_{1/2}<5$$ s, the experimental half-lives and delayed neutrons emission probabilities are described within a factor of two and three, respectively. A comparison is performed with the results of similar calculations based on state-of-the-art self-consistent models : the relativistic spherical RHB $$+$$ RQRPA approach and deformed finite-amplitude method (FAM) and HFB $$+$$ QRPA approaches, as well as the interacting shell model. A detailed analysis of beta-decay properties in the nickel isotopic chain that were obtained in various calculations allows us for determining basic mechanisms responsible for the sudden shortening of the half-lives that was found experimentally at RIKEN for isotopes heavier than the doubly magic $${}^{78}$$ Ni nucleus. These are the contributions of first-forbidden (FF) transitions and multiphonon configurations and spin inversion of the respective ground states. The acceleration effect in question is highly sensitive to the balance of the contributions of Gamow–Teller (GT) and FF transitions to the total beta-decay rate. It is shown that, in nickel isotopes, the ratio of these contributions takes different values before and after the neutron-shell crossing at $$N=50$$ .

Comparative analysis of muon-capture and 0νββ -decay matrix elements

Average matrix elements of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of current experimental interest are computed and compared with the corresponding energy and multipole decompositions of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements (NMEs). The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ NMEs include the appropriate short-range correlations, nuclear form factors, and higher-order nucleonic weak currents. The nuclear wave functions are obtained in extended no-core single-particle model spaces using the spherical version of the proton-neutron quasiparticle random-phase approximation with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. Both the OMC and $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes involve 100-MeV-range momentum exchanges and hence similarities could be expected for both processes in the feeding of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ intermediate states. These similarities may help improve the accuracy of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ NME calculations by using the data from the currently planned OMC experiments.

Signatures of enhanced octupole correlations at high spin in Nd136

Experimental signatures of moderately enhanced octupole correlations at high spin in Nd136 are indicated for the first time. The extracted dipole moments of two negative-parity bands are only two times smaller than those of the lanthanide nuclei with N≈90 which present well-established octupole correlations. Calculations using the cranked quasiparticle random phase approximation and a model of quadrupole-octupole rotations with octupole vibrations reveal the structure of the bands and the enhanced octupole correlations at high spin in Nd136.

Nuclear structure properties of even-even chromium isotopes and the effect of deformation on calculated electron capture cross sections

In this study, we investigate the role of the nuclear deformation on the calculated electron capture cross section (ECC) of even-even chromium (Cr) isotopes. We first determined the nuclear structure properties of these nuclei within the interacting boson model-1 (IBM-1). The energy spectra and E2 transition probabilities were calculated by fitting the parameters in the model formalism. The analysis of the potential energy surface were also performed to predict the geometric shape of the Cr nuclei by plotting their contour plot in the plane of (β, γ) deformation parameters. Later, we calculated the ECC within the proton-neutron quasiparticle random phase approximation (pn-QRPA) model. In particular we studied how the calculated ECC changed with different values of nuclear deformation parameter. The calculated Gamow-Teller (GT) strength distributions were widely spread among the daughter states. The total GT strength decreased with increasing value of the β parameter. The computed ECC values, however, increased with increase in the β value of the Cr isotopes.