QRPA Calculations Research Articles

Ab initio description of monopole resonances in light- and medium-mass nuclei

Giant resonances (GRs) are a striking manifestation of collective motions in mesoscopic systems such as atomic nuclei. Until recently, theoretical investigations have essentially relied on the (quasiparticle) random phase approximation ((Q)RPA), and extensions of it, based on phenomenological energy density functionals (EDFs). As part of a current effort to describe GRs within an ab initio theoretical scheme, the present work promotes the use of the projected generator coordinate method (PGCM). This method, which can handle anharmonic effects while satisfying symmetries of the nuclear Hamiltonian, displays a favorable (i.e. mean-field-like) scaling with system’s size. Presently focusing on the isoscalar giant monopole resonance (GMR) of light- and medium-mass nuclei, PGCM’s potential to deliver wide-range ab initio studies of GRs in closed- and open-shell nuclei encompassing pairing, deformation, and shape coexistence effects is demonstrated. The comparison with consistent QRPA calculations highlights PGCM’s unique attributes and sheds light on the intricate interplay of nuclear collective excitations. The present paper is the first in a series of four and focuses on technical aspects and uncertainty quantification of ab initio PGCM calculations of GMR using the doubly open-shell 46\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{46}$$\\end{document}Ti as an illustrative example. The second paper displays results for a set of nuclei of physical interest and proceeds to the comparison with consistent (deformed) ab initio QRPA calculations. While the third paper analyzes useful moments of the monopolar strength function and different ways to access them within PGCM calculations, the fourth paper focuses on the effect of the symmetry restoration on the monopole strength function.

Roles of tensor and isoscalar pairing interactions in β-decay calculations for possible r-process waiting point nuclei with N ~ 82 and 126* *Supported by the National Natural Science Foundation of China (11575120, 11822504), and Science Specialty Program of Sichuan University (2020SCUNL210)

In this study, we adopt the self-consistent Hartree-Fock-Bogoliubov (HFB) theory with the proton-neutron quasi-particle random phase approximation (pnQRPA) based on the Skyrme force for calculation of the β − decay half-lives for nuclei with N ~ 82 and 126 on possible r-process paths. In the calculations, the Skyrme interaction (e.g., SKO') is adopted, and the tensor interaction is added self-consistently in both HFB and QRPA calculations. We systematically study how the half-life is changed by varying the strength of the triplet-even (TE) and triplet-odd (TO) components as well as the IS pairing. We find that a variation in strength of the IS pairing of approximately 20% does not produce a substantial effect on β-decay rates with or without the tensor force, while a strength variation of the TO tensor force considerably affects the change in the β-decay half-lives for the very neutron rich N ~ 82 and 126 isotonic chains. In addition, with the inclusion of the tensor force, the GT decay becomes dominant for very neutron-rich nuclei.

Total absorption gamma-ray spectroscopy study of the β-decay of 186Hg

The Gamow-Teller strength distribution of the decay of 186Hg into 186Au has been determined for the first time using the total absorption gamma spectroscopy technique and has been compared with theoretical QRPA calculations using the SLy4 Skyrme force. The measured Gamow-Teller strength distribution and the half-life are described by mixing oblate and prolate configurations independently in the parent and daughter nuclei. In this theoretical framework the best description of the experimental beta strength is obtained with dominantly prolate components for both parent 186Hg and daughter 186Au. The approach also allowed us to determine an upper limit of the oblate component in the parent state. The complexity of the analysis required the development of a new approach in the analysis of the X-ray gated total absorption spectrum.

Isoscalar monopole and dipole transitions in Mg24 , Mg26 , and Si28

Nuclei in the $sd$-shell demonstrate a remarkable interplay of cluster and mean-field phenomena. The $N=Z$ nuclei, such as $^{24}$Mg and $^{28}$Si, have been the focus of the theoretical study of both these phenomena in the past. The cluster and vortical mean-field phenomena can be probed by excitation of isoscalar monopole and dipole states in scattering of isoscalar particles such as deuterons or $\alpha$ particles. Inelastically scattered $\alpha$ particles were momentum-analysed in the K600 magnetic spectrometer at iThemba LABS, Cape Town, South Africa. The scattered particles were detected in two multi-wire drift chambers and two plastic scintillators placed at the focal plane of the K600. In the theoretical discussion, the QRPA and AMD+GCM were used. The QRPA calculations lead us to conclude that: i) the mean-field vorticity appears mainly in dipole states with $K=1$, ii) the dipole (monopole) states should have strong deformation-induced octupole (quadrupole) admixtures, and iii) that near the $\alpha$-particle threshold, there should exist a collective state (with $K=0$ for prolate nuclei and $K=1$ for oblate nuclei) with an impressive octupole strength. The results of the AMD+GCM calculations suggest that some observed states may have a mixed (mean-field + cluster) character or correspond to particular cluster configurations. A tentative correspondence between observed states and theoretical states from QRPA and AMD+GCM was established. The QRPA and AMD+GCM analysis shows that low-energy isoscalar dipole states combine cluster and mean-field properties. The QRPA calculations show that the low-energy vorticity is well localized in $^{24}$Mg, fragmented in $^{26}$Mg, and absent in $^{28}$Si.

Statistical properties of the well deformed Sm153,155 nuclei and the scissors resonance

The Nuclear Level Densities (NLDs) and the $\gamma$-ray Strength Functions ($\gamma$SFs) of $^{153,155}$Sm have been extracted from (d,p$\gamma$) coincidences using the Oslo method. The experimental NLD of $^{153}$Sm is higher than the NLD of $^{155}$Sm, in accordance with microscopic calculations. The $\gamma$SFs of $^{153,155}$Sm are in fair agreement with QRPA calculations based on the D1M Gogny interaction. An enhancement is observed in the $\gamma$SF for both $^{153,155}$Sm nuclei around 3 MeV in excitation energy and is attributed to the M1 Scissors Resonance (SR). Their integrated strengths were found to be in the range 1.3 - 2.1 and 4.4 - 6.4 $\mu^{2}_{N}$ for $^{153}$Sm and $^{155}$Sm, respectively. The strength of the SR for $^{155}$Sm is comparable to those for deformed even-even Sm isotopes from nuclear resonance fluorescence measurements, while that of $^{153}$Sm is lower than expected.

2νββ-decay to first 2+ states with partial isospin symmetry restoration from spherical QRPA calculations * * Supported by National Natural Science Foundation of China (11505078, 1164730), “Light of West China” Program and key research program (XDPB09-2) from Chinese Academy of Sciences

Using partially restored isospin symmetry, we calculate the nuclear matrix elements for a special decay mode of a two-neutrino double beta decay – the decay to the first 2+ excited states. Employing the realistic CD–Bonn nuclear force, we analyze the dependence of the nuclear matrix elements on the isovector and isoscalar parts of proton–neutron particle–particle interactions. The dependence on the different nuclear matrix elements is observed, and the results are explained. We also provide the phase space factors using numerical electron wavefunctions and properly chosen excitation energies. Finally, we present our results for the half-lives of this decay mode for different nuclei.

Coherent and incoherent channels of neutrino-nucleus reactions

Inelastic neutrino-nucleus scattering cross sections at low and intermediate energies are investigated for currently interesting nuclei employed in neutrino-detection experiments. This is an extension to charged current processes of our previous QRPA calculations referred to neutral current neutrino/antineutrino-nucleus reactions. Our preliminary results for the reactions 56Fe(νe, e−)56Co and 40Ar(νe, e−)40K compare rather well with similar calculations obtained in the context of continuum RPA.

Constraints for stellar electron-capture rates on Kr86 via the Kr86(t,He3+γ)Br86 reaction and the implications for core-collapse supernovae

In the late stages of stellar core-collapse, prior to core bounce, electron captures on medium-heavy nuclei drive deleptonization and simulations require the use of accurate reaction rates. Nuclei with neutron number near $N=50$, just above atomic number $Z=28$, play an important role, but rates used in astrophysical simulations rely primarily on a relatively simple single-state approximation. In order to improve the accuracy of astrophysical simulations, experimental data are needed to test the electron-capture rates and to guide the development of better theoretical models. This work presents the results of the $^{86}$Kr($t$,$^{3}$He+$\gamma$) experiment at the NSCL, from which an upper limit for the Gamow-Teller strength up to an excitation energy in $^{86}$Br of 5 MeV is extracted. The derived upper limit for the electron-capture rate on $^{86}$Kr indicates that the rate estimated through the single-state approximation is too high and that rates based on Gamow-Teller strengths estimated in shell-model and QRPA calculations are more accurate. The QRPA calculations tested in this manner were used for estimating the electron capture rates for 78 isotopes near $N=50$ and above $Z=28$. The impact of using these new electron-capture rates in simulations of supernovae instead of the rates based on the single-state approximation is investigated, indicating a significant reduction in the deleptonization that affects multi-messenger signals, such as the emission of neutrinos and gravitational waves.

Interplay of quasiparticle and vibrational excitations: First observation of isomeric states in 168Dy and 169Dy

The neutron-rich dysprosium isotopes 168Dy102 and 169Dy103 have been investigated using the EURICA γ-ray spectrometer, following production via in-flight fission of a high-intensity uranium beam in conjunction with isotope separation through the BigRIPS separator at RIBF in RIKEN Nishina Center. For 168Dy, a previously unreported isomer with a half-life of 0.57(7) μs has been identified at an excitation energy of 1378 keV, and its presence affirmed independently using γ-γ-γ coincidence data taken with Gammasphere via two-proton transfer from an enriched 170Er target performed at Argonne National Laboratory. This isomer is assigned Jπ=Kπ=(4−) based on the measured transition strengths, decay patterns, and the energy systematics for two-quasiparticle states in N=102 isotones. The underlying mechanism of two-quasiparticle excitations in the doubly midshell region is discussed in comparison with the deformed QRPA and multi-quasiparticle calculations. In 169Dy, the B(E2) value for the transition de-exciting the previously unreported Kπ=(1/2−) isomeric state at 166 keV to the Kπ=(5/2−) ground state is approximately two orders of magnitude larger than the E2 strength for the corresponding isomeric-decay transition in the N=103 isotone 173Yb, suggesting the presence of a significant γ-vibrational admixture with a dominant neutron one-quasiparticle component in the isomeric state.

Influence of octupole vibration on the low-lying structure of Fm251 and other heavy N=151 isotones

The structure of low-lying excited states in $^{251}\mathrm{Fm}$, populated by the $\ensuremath{\alpha}$ decay of $^{255}\mathrm{No}$, has been investigated by means of combined $\ensuremath{\gamma}$ and internal conversion electron spectroscopy. The values for the internal conversion coefficients for the $1/{2}^{+}\ensuremath{\rightarrow}5/{2}^{+}$ and $5/{2}^{+}\ensuremath{\rightarrow}9/{2}^{\ensuremath{-}}$ transitions have been measured. The determined $M2/E3$ mixing ratio and lifetime for the $5/{2}^{+}$ decay to the ground state allowed to determine the corresponding reduced transitions strengths of $B(E3)=18(6)$ W.u. and $B(M2)=3.0(6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ W.u. These results, as well as the results of previous studies in $N=151$ isotopes, are compared to theoretical calculations beyond the mean-field approach, including the first QRPA calculations using the Gogny D1M parametrization for such heavy odd-$N$ nuclei. The comparison points to the importance of accounting for the octupole vibrations for a proper understanding of the low-lying nuclear structure of some of the heaviest elements.

Cross-section measurements of the 94Mo(γ,n) and 90Zr(γ,n) reactions using real photons at the HIγS facility

The photodisintegration reaction cross-sections for 94Mo(γ,n) and 90Zr(γ,n) have been experimentally investigated with quasi-monochromatic photon beams at the High Intensity γ-Ray Source (HIγS) facility, Triangle University Nuclear Laboratory (TUNL). The measurements were focused primarily on studying the energy dependence of the photoneutron cross sections, which is the most direct way of testing statistical models, and were performed close to the respective neutron thresholds and above up to ~ 20 MeV. Neutrons from the (γ,n) reactions were detected using a 4π assembly of 3He proportional counters developed at Los Alamos National Laboratory and presently available at TUNL. While the 94Mo(γ,n) cross section measurement aims to contribute to a broader investigation for understanding the γ-process (the mechanism responsible for the nucleosynthesis of the so-called p-nuclei), the information from the 90Zr(γ,n) data is relevant to constrain QRPA calculations of γ-ray strength functions in this mass region. In this contribution, we will present our preliminary results of the total (γ,n) excitation functions for the two photoneutron reactions on 94Mo and 90Zr.

Unexpected high-energy γ emission from decaying exotic nuclei

The N=52Ga83β decay was studied at ALTO. The radioactive 83Ga beam was produced through the ISOL photofission technique and collected on a movable tape for the measurement of γ-ray emission following β decay. While β-delayed neutron emission has been measured to be 56–85% of the decay path, in this experiment an unexpected high-energy 5–9 MeV γ-ray yield of 16(4)% was observed, coming from states several MeVs above the neutron separation threshold. This result is compared with cutting-edge QRPA calculations, which show that when neutrons deeply bound in the core of the nucleus decay into protons via a Gamow–Teller transition, they give rise to a dipolar oscillation of nuclear matter in the nucleus. This leads to large electromagnetic transition probabilities which can compete with neutron emission, thus affecting the β-decay path. This process is enhanced by an excess of neutrons on the nuclear surface and may thus be a common feature for very neutron-rich isotopes, challenging the present understanding of decay properties of exotic nuclei.

Quasiparticle random phase approximation predictions of the gamma-ray strength functions using the Gogny force

Dipole excitations of nuclei are crucial since they play an important role in nuclear reaction modeling in connection with the photoabsorption and the radiative capture processes. We present here results for the gamma-ray strength function obtained in large-scale axially-symmetric deformed quasiparticle (qp) random phase approximations approach using the finite-range Gogny force, with a particular emphasis on the E1 mode. The convergence with respect to the number of harmonic oscillator shells adopted and the cut-off introduced in the 2-quasiparticle excitation energy space is analyzed. The microscopic nature of our self-consistent Hartree-Fock-Bogoliubov plus QRPA (HFB+QRPA) calculation has unfortunately to be broken, some phenomenological corrections being needed to take into account effects beyond the standard 2-qp QRPA excitations and the coupling between the single-particle and low-lying collective phonon degrees of freedom. The corresponding phenomenological parameters are adjusted on experimental photoabsorption data. In such a procedure, a rather satisfactory description of experimental data is obtained. To study the sensitivity of these phenomenological corrections on the extrapolation, both at low energies and towards exotic neutron-rich nuclei, three different prescriptions are considered. They are shown to lead to rather similar predictions of the E1 strength at low energies as well as for exotic neutron-rich nuclei. The Gogny-HFB+QRPA strength is finally applied to the calculation of radiative neutron capture cross sections and the predictions compared with those obtained with more traditional Lorentzian-type approaches.

Proton-hole and core-excited states in the semi-magic nucleus 131In82

The β decay of the N = 83 nucleus 131Cd has been studied at the RIBF facility at the RIKEN Nishina Center. The main purpose of the study was to identify the position of the 1p3/2 and 0f5/2 protonhole states and the energies of core-excited configurations in the semi-magic nucleus 131In. From the radiation emitted following the β decay, a level scheme of 131In was established and the β feeding to each excited state determined. Similarities between the single-particle transitions observed in the β decays of the N = 83 isotones 132In and 131Cd are discussed. Finally the excitation energies of several core-excited configurations in 131In are compared to QRPA and shell-model calculations.

Large-scale deformed quasiparticle random-phase approximation calculations of theγ-ray strength function using the Gogny force

Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we present large-scale calculations of the $E1$ $\gamma$-ray strength function obtained in the framework of the axially-symmetric deformed QRPA based on the finite-range Gogny force. This approach is applied to even-even nuclei, the strength function for odd nuclei being derived by interpolation. The convergence with respect to the adopted number of harmonic oscillator shells and the cut-off energy introduced in the 2-quasiparticle (2-$qp$) excitation space is analyzed. The calculations performed with two different Gogny interactions, namely D1S and D1M, are compared. A systematic energy shift of the $E1$ strength is found for D1M relative to D1S, leading to a lower energy centroid and a smaller energy-weighted sum rule for D1M. When comparing with experimental photoabsorption data, the Gogny-QRPA predictions are found to overestimate the giant dipole energy by typically $\sim$2 MeV. Despite the microscopic nature of our self-consistent Hartree-Fock-Bogoliubov plus QRPA calculation, some phenomenological corrections need to be included to take into account the effects beyond the standard 2-$qp$ QRPA excitations and the coupling between the single-particle and low-lying collective phonon degrees of freedom. For this purpose, three prescriptions of folding procedure are considered and adjusted to reproduce experimental photoabsorption data at best. All of them are shown to lead to rather similar predictions of the $E1$ strength, both at low energies and for exotic neutron-rich nuclei. Predictions of $\gamma$-ray strength functions and Maxwellian-averaged neutron capture rates for the whole Sn isotopic chain are also discussed and compared with previous theoretical calculations.

Weakly bound nuclei: Exotic ground state properties and collective excitations

Weakly bound nuclei are open quantum many-body systems and can have exotic structures and dynamics in contrast to our knowledges of stable nuclei. Currently the related studies are among the central topics in nuclear physics and are important for further improvements of nuclear theory and understandings of element enrichment processes in astrophysical environments. Since the improvements of intensity and quality of radioactive nuclear beams are very difficult, theoretical studies will be very helpful for planning experiments and the interpretation of results. Here we review recent developments of continuum density functional theory and studies of weakly bound nuclei. The theoretical challenge is to self-consistently describe the weak-binding effects, exotic shapes, continuum effects and dynamics together. To this end, our main work is to solve the Hartree-Fock-Bogoliubov equation in non-spherical coordinate- spaces and then to describe the ground state properties as well as collective excitations of weakly bound nuclei. In the 2D lattice, we solved the HFB equation with the B-spline techniques. More recently, we solved the HFB equation in the 3D coordinate-space with the adaptive multi-resolution multi-wavelet techniques, which is novel and much more efficient. Based on our calculations, we discussed the exotic egg-like deformed halo structures, the core-halo deformation decoupling, and the role of continuum contributions. We also see pairing density distributions have remarkable deformed halo structures. The deformed cores are not so favorable for the formation of 2 n -halos, in particular heavy 2 n -halos. The non-resonant continuum rather than the resonant continuum is mainly responsible for halo features. With the quasiparticle blocking calculations, we also studied the deformed 1 n -halo nuclei, in which the pairing density is unusual due to the spin polarization. In addition, we developed the deformed continuum FAM-QRPA calculations in coordinate spaces and studied the emergent soft monopole collective excitations. The soft collective modes are unique in weakly bound nuclei and are useful for studies of nuclear properties in extreme conditions. Compared to the conventional QRPA diagonalization method, the FAM-QRPA solves the QRPA equation iteratively and is more efficient. Otherwise the deformed QRPA calculations with continuum would be very challenging. We see the pairing density halos and non-resonant continuum play an important role in these soft collective excitations. Our studies involved large coordinate-space calculations in Tianhe supercomputers to take into account shape deformations, large spatial extensions and continuum spectra. Otherwise, calculations within small coordinate spaces would produce a coarse continuum discretization and even false resonance peaks. Finally we give some persectives on studies of weakly bound nuclei and our plans. Since weakly bound nuclei exhibit few-body physics in many-body systems, the conventional shell-structure picture breaks down in this respect. Theorefore new many-body techniques, time-dependent 3D dynamics and improved effective interactions are very desirable. The studies of weakly bound nuclei as open quantum systems that involve threshold effects and continuum contributions can have broad interdisciplinary interests.

Global description ofβ−decay in even-even nuclei with the axially-deformed Skyrme finite-amplitude method

We use the finite amplitude method for computing charge-changing Skyrme-QRPA transition strengths in axially-deformed nuclei together with a modern Skyrme energy-density functional to fit several previously unconstrained parameters in the charge-changing time-odd part of the functional. With the modified functional we then calculate rates of beta-minus decay for all medium-mass and heavy even-even nuclei between the valley of stability and the neutron drip line. We fit the Skyrme parameters to a limited set of beta-decay rates, a set of Gamow-Teller resonance energies, and a set of spin-dipole resonance energies, in both spherical and deformed nuclei. Comparison to available experimental beta-decay rates shows agreement at roughly the same level as in other global QRPA calculations. We estimate the uncertainty in our rates all the way to the neutron drip line through a construction that extrapolates the errors of known beta-decay rates in nuclei with intermediate Q values to less stable isotopes with higher Q values.

Large-scale deformed QRPA calculations of the gamma-ray strength function based on a Gogny force

The dipole excitations of nuclei play an important role in nuclear astrophysics processes in connection with the photoabsorption and the radiative neutron capture that take place in stellar environment. We present here the results of a large-scale axially-symmetric deformed QRPA calculation of the γ-ray strength function based on the finite-range Gogny force. The newly determined γ-ray strength is compared with experimental photoabsorption data for spherical as well as deformed nuclei. Predictions of γ-ray strength functions and Maxwellian-averaged neutron capture rates for Sn isotopes are also discussed.

First-forbidden transitions and stellar β-decay rates of Zn and Ge isotopes

First-forbidden (FF) charge-changing transitions become relatively important for nuclei as their proton number increases. This is because the strength of allowed Gamow–Teller (GT) transitions decreases with increasing Z. The FF transitions play an important role in reducing the half-lives compared to those calculated from taking the GT transitions alone into account. In this paper we calculate allowed GT as well as and transitions for neutron-rich Zn and Ge isotopes. Two different pn-QRPA models were used with a schematic separable interaction to calculate GT and FF transitions. Half-lives calculated after inclusion of FF transitions were in excellent agreement with the experimental data. Our calculations were also compared to previous QRPA calculations and were found to be in better agreement with measured data. Stellar β-decay rates were calculated for these nuclei including allowed GT and unique FF transitions for astrophysical applications. 86,88Ge has a sizeable contribution to the total stellar rate from unique FF transitions.

An analysis of β-delayed neutron emission of even–even neutron-rich nuclei with proton-neutron QRPA

β-delayed neutron emission probabilities of even–even nuclei are examined with a proton-neutron quasi-particle random-phase-approximation (pnQRPA). To calculate a light particle evaporation from excited states of daughter nucleus populated by β-decay, the Hauser-Feshbach statistical model is used. We discuss effects of isospin T = 0 pairing, tensor force and nuclear deformation on the β-delayed neutron emission probability. We find that the effect of nuclear deformation is essential rather than the that of isospin T = 0 pairing and tensor force to give an appropriate β-feedings to energy window of neutron emission. The obtained β-delayed neutron emission probabilities are in reasonable agreement with the experimental data of several typical delayed neutron emitters. The results are also compared with the FRDM + QRPA calculation. We conclude that the present approach is promising to calculate β-delayed neutron.