Quasiparticle Random Phase Approximation Research Articles

Axially deformed relativistic quasiparticle random-phase approximation based on point-coupling interactions

Axially deformed relativistic quasiparticle random-phase approximation based on point-coupling interactions

Higher forbidden unique β− decay transitions and shell-model interpretation

In the present work, we have predicted the half-lives for the β− decay for higher forbidden unique transitions in the mass range of nuclei from A = 40-138. For these transitions, the experimental data for half-lives are not available except for a few cases. The calculations for half-lives are performed within the framework of the nuclear shell model (SM). We have used the effective interactions sdpf-mu, gxpf1a, gwbxg, G-matrix, snet, sn100pn, and jj56pnb to perform the SM calculations in different mass regions. A comprehensive discussion has been made between the SM predicted half-lives and the scaled half-lives from proton-neutron quasiparticle random-phase approximation (pnQRPA). The results of the present study will be useful to plan new experiments to measure half-lives for these higher forbidden unique β− transitions.

Investigation of nuclear structure and [formula omitted]-decay properties of As isotopes

The nuclear ground state properties of 67−80As nuclei have been investigated within the framework of relativistic mean field (RMF) approach. The RMF model with density-dependent (DD-ME2) interaction is utilized for the calculation of potential energy curves and the nuclear ground-state deformation parameters (β2) of selected As isotopes. Later, the β-decay properties of As isotopes were studied using the proton–neutron quasi particle random phase approximation (pn-QRPA) model. These include Gamow Tellar (GT) strength distributions, log ft values, β-decay half-lives, stellar β± decays and stellar electron/positron capture rates. The β2 values computed from RMF model were employed in the pn-QRPA model as an input parameter for the calculations of β-decay properties for 67−80As. The calculated log ft values were in decent agreement with the measured data. The predicted β-decay half-lives matched the experimental values within a factor of 10. The stellar rates were compared with the shell model results. Only at high temperature and density values, the sum of β+ and electron capture rates had a finite contribution. On the other hand, the sum of β− and positron capture rates were sizeable only at low density and high temperature values. For all such cases, the pn-QRPA rates were found to be bigger than the shell model rates up to a factor of 33 or more. The findings reported in the current investigation could prove valuable for simulating the late-stage stellar evolution of massive stars.

Re-examination of nuclear structure properties and shape co-existence of nuclei around A ∼ 70

We re-examine the nuclear structure properties of waiting point nuclei around A ∼ 70 using the interacting boson model-1 (IBM-1) and the relativistic mean field (RMF) model. Effective density-dependent meson-exchange functional (DD-ME2) and density-dependent point-coupling functional (DD-PC1) were used for the RMF calculations. We calculated the energy levels, the geometric shapes, binding and separation energies of nucleons and quadrupole deformation parameters (β2). The shape co-existence phenomena in A ∼ 70 nuclei (68Se, 70Se, 70Br, 70Kr, 72Kr, 74Kr, 74Rb and 74Sr) was later investigated. Spherical and deformed shapes of the selected waiting point nuclei were computed using the IBM-1 and RMF models, respectively. The proton-neutron quasiparticle random phase approximation (pn-QRPA) model was used to calculate β-decay properties (Gamow-Teller strength distributions, β-decay half-lives and branching ratios) of selected nuclei as a function of β2. The results revealed a significant variation in calculated half-lives and Gamow-Teller strength distributions as the shape parameter was changed. The β2 computed via DD-ME2 functional resulted in half-lives in best agreement with the measured data.

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The strength distributions of charge exchange spin-dipole excitations are calculated in the continuum quasiparticle random-phase approximation based on the Fayans density functional with modified isovector part. An impact of the isovector parameter \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h_{2}^{-}$$\\end{document} of the DF3-f functional on the strength functions of charge-exchange spin-dipole excitations (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0^{-}$$\\end{document}, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1^{-}$$\\end{document}, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{-}$$\\end{document}) are studied for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{208}$$\\end{document}Pb, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{132}$$\\end{document}Sn and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{90}$$\\end{document}Zr. The sum rules are calculated using both ground state radii and direct integration of the total SD strength distributions. A comparison with the experimental SD sum rule in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{90}$$\\end{document}Zr gives one a possibility to check previously estimated \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h_{2}^{-}$$\\end{document} values which described well the recent combined estimate for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta R_{np}$$\\end{document} in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{208}$$\\end{document}Pb and corresponding equation of state parameters – symmetry energy \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_{0}=J(\\rho_{0})$$\\end{document} and a slope parameter \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_{0}=L(\\rho_{0})$$\\end{document}.

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

The paper is the third of a series dedicated to the ab initio description of monopole giant resonances in mid-mass closed- and open-shell nuclei via the so-called projected generator coordinate method. The present focus is on the computation of the moments mk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_k$$\\end{document} of the monopole strength distribution, which are used to quantify its centroid energy and dispersion. First, the capacity to compute low-order moments via two different methods is developed and benchmarked for the m1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_1$$\\end{document} moment. Second, the impact of the angular momentum projection on the centroid energy and dispersion of the monopole strength is analysed before comparing the results to those obtained from consistent quasi-particle random phase approximation calculations. Next, the so-called energy weighted sum rule (EWSR) is investigated. First, the appropriate ESWR in the center-of-mass frame is derived analytically. Second, the intrinsic EWSR is tested in order to quantify the (unwanted) local-gauge symmetry breaking of the presently employed chiral effective field theory (χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}EFT) interactions. Finally, the infinite nuclear matter incompressibility associated with the employed χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}EFT interactions is extracted by extrapolating the finite-nucleus incompressibility computed from the monopole centroid energy.

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

Giant resonances (GRs) are a striking manifestation of collective motions in atomic nuclei. The present paper is the second in a series of four dedicated to the use of the projected generator coordinate method (PGCM) for the ab initio determination of the isoscalar giant monopole resonance (GMR) in closed- and open-shell mid-mass nuclei. While the first paper was dedicated to quantifying various uncertainty sources, the present paper focuses on the first applications to three doubly-open shell nuclei, namely 46Ti\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{46}\\hbox {Ti}$$\\end{document}, 28Si\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{28}\\hbox {Si}$$\\end{document} and 24Mg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{24}\\hbox {Mg}$$\\end{document}. In particular, the goal is to investigate, starting from chiral effective field theory nuclear interactions, (i) the coupling of the GMR with the giant quadrupole resonance (GQR) in intrinsically-deformed nuclei, (ii) the possible impact of shape coexistence and shape mixing on the GMR, (iii) the GMR based on shape isomers and (iv) the impact of anharmonic effects on the monopole response. The latter is studied by comparing PGCM results to those obtained via the quasi-particle random phase approximation (QRPA), the traditional many-body approach to giant resonances, performed in a consistent setting. Eventually, PGCM results for sd-shell nuclei are in good agreement with experimental data, which is attributed to the capacity of the PGCM to capture the important fragmentation of the monopole response in light, intrinsically-deformed systems. Still, the comparison to data in 28Si\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{28}\\hbox {Si}$$\\end{document} and 24Mg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{24}\\hbox {Mg}$$\\end{document} illustrates the challenge (and the potential benefit) of extracting unambiguous experimental information.

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.

Re-analysis of temperature dependent neutron capture rates and stellar β-decay rates of 95-98Mo

The neutron capture rates and temperature dependent stellar beta decay rates of Mo isotopes are investigated within the framework of the statistical code TALYS v1.96 and the proton neutron quasi particle random phase approximation (pn-QRPA) model. The Maxwellian average cross-section (MACS) and neutron capture rates for the Mo(n,γ) Mo radiative capture process are analyzed within the framework of the statistical code TALYS v1.96 based on the phenomenological nuclear level density model and gamma strength functions. The present model-based computations for the MACS are comparable to the existing measured data. The sensitivity of stellar weak interaction rates to various densities and temperatures is investigated within the framework of the pn-QRPA model. Particular attention is paid to the impact of thermally filled excited states in the decaying nuclei ( Mo) on electron emission and positron capture rates. Furthermore, we compare the neutron capture rates and stellar beta decay rates. It is found that neutron capture rates are higher than stellar beta decay rates at both lower and higher temperatures.

Re-examination of effects of pairing gaps on charge-changing transitions

We re-examine the effects of pairing gaps on charge-changing transitions and the associated β-decay half-lives. Calculations are performed using the proton-neutron quasiparticle random phase approximation (pn-QRPA) model for 250 nuclei possessing astrophysical significance. Pairing gaps between like nucleons are key model parameters in the pn-QRPA approach. Three different values of empirically computed pairing gaps were used as input parameters in our nuclear model. Changing the pairing gap values significantly altered the Gamow-Teller distributions including the total strength and centroid values. The β-decay half-lives also changed substantially. The half-lives computed via the three-term pairing formula, based on separation energies of nucleons, were in best agreement with the measured data.

The TDHF code Sky3D version 1.2

The Sky3D code has been widely used to describe nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The approach is based on Skyrme forces or related energy density functionals. The static and dynamic equations are solved on a three-dimensional grid, and pairing is been implemented in the BCS approximation. This updated version of the code aims to facilitate the calculation of nuclear strength functions in the regime of linear response theory, while retaining all existing functionality and use cases. The strength functions are benchmarked against available RPA codes, and the user has the freedom of choice when selecting the nature of external excitation (from monopole to hexadecapole and more). Some utility programs are also provided that calculate the strength function from the time-dependent output of the dynamic calculations of the Sky3D code. New version program summaryProgram Title: Sky3DCPC Library link to program files:https://doi.org/10.17632/vzbrzvyrn4.2Developer's repository link:https://github.com/manybody/sky3dLicensing provisions: GPLv3Programming language: Fortran, with one post-processing utility in Python.Journal reference of previous version:: Schuetrumpf, B., Reinhard, P.G., Stevenson, P.D., Umar, A.S., and Maruhn, J.A. (2018). The TDHF code Sky3D version 1.1. Comput. Phys. Commun. 229 (2018) 211–213.Does the new version supersede the previous version?: Yes.Reasons for the new version: The capability of reproducing the nuclear strength function for a variety of newly-coded external boosts has been added.Nature of problem: Calculating nuclear multipole strength functions is a crucial probe that can help model the nuclear system and its structure properties. A variety of models exist for this task, such as QRPA (Quasiparticle Random Phase Approximation) and its variants, but such approaches are often limited due to symmetry constraints. Time-dependent Hartree Fock (TDHF) has been used to simulate nuclear vibrations and collisions between nuclei for low energies without assuming any symmetry in the system. This code extends the TDHF to calculate the multi-pole strength functions of atomic nuclei. We showcase its reliability by comparing it with the established RPA codes for the calculation of such strength functions.Solution method: We extended previous versions of the Sky3D code [1,2] to include an external boost of multipole type where the user can provide custom input that decides the nature of the multipole (monopole, quadrupole, octupole, and so on) boost. The principal aim is to calculate the multipole strength function, which is the Fourier transform of the time-dependent expectation value of the multipole operator, which has the same form as the external boost. The proper unit conversion is done so that one can extract the exact unit of the thus calculated strength function, which is comparable to the available literature in the field. The boundary conditions are chosen such that a Woods-Saxon-like function cuts off the external field, driving it to zero at the boundary.Summary of revisions: The ability to give a more general external field for excitation has been implemented, which can be of a chosen multipolarity and isospin nature. Then, as a function of time, moments for both isospins and for multipolarities up to L=5 are followed. A new analysis program is included to calculate strength functions and energy weighted sum rules. The ability to specify a mixing parameter in the pairing force is included. This allows a mixed surface-volume pairing to be selected in a way more compatable with QRPA codes for comparison. An updated Makefile is included which makes compilation on Apple silicon computers easier.

Nuclear structure properties and weak interaction rates of even–even Fe isotopes

Nuclear structure properties and weak interaction rates of neutron-rich even–even iron (Fe) isotopes (A = 50 – 70) are investigated using the Interacting Boson Model-1 (IBM-1) and the proton–neutron Quasiparticle Random Phase Approximation (pn-QRPA) model. The IBM-1 is used for the calculation of energy levels and the B(E2) values of neutron-rich Fe isotopes. Later their geometry was predicted within the potential energy formalism of the IBM-1 model. Weak interaction rates on neutron-rich nuclei are needed for the modeling and simulation of presupernova evolution of massive stars. In the current study, we investigate the possible effect of nuclear deformation on stellar rates of even–even Fe isotopes. The pn-QRPA model is applied to calculate the weak interaction rates of selected Fe isotopes using three different values of deformation parameter. It is noted that, in general, bigger deformation values led to smaller total strength and larger centroid values of the resulting Gamow–Teller distributions. This later translated to smaller computed weak interaction rates. The current finding warrants further investigation before it may be generalized. The reported stellar rates are up to 4 orders of magnitude smaller than previous calculations and may bear astrophysical significance.

Effects of Residual Tensor and Pairing Forces on the Gamow–Teller states in Magic Nuclei, 48Ca, 90Zr, 132Sn, and 208Pb

Abstract We investigate the effects of residual tensor force (TF) and pairing force on the Gamow–Teller (GT) transitions in four magic nuclei, 48Ca, 90Zr, 132Sn and 208Pb. The TF is taken into account by using the Brückner G-matrix theory with the charge-dependent (CD) Bonn potential as the residual interaction of charge-exchange quasiparticle random phase approximation (QRPA). We found that particle–particle (p–p) tensor interaction does not affect the GT transitions because of the closed shell nature in the nuclei, but repulsive particle–hole (p–h) residual interaction for the p–h configuration of spin-orbit partners dominates the high-lying giant GT states for all of the nuclei. It is also shown that appreciable GT strengths are shifted to a lower energy region by the attractive p–h TF for the same jπ = jν configuration, and produce the low-lying GT peak about 2.5 MeV in 48Ca. Simultaneously, in 90Zr and 132Sn, the low-energy GT strength appears as a lower energy shoulder near the main GT peak. On the other hand, the shift of the low-lying GT state is not seen clearly for 208Pb because of the strong spin-orbit splitting of high j orbits, which dominates the GT strength.

Isoscalar giant quadrupole resonance of even-even 112-124Sn isotopes using BCS-QRPA

Using self-consistent Bardeen - Cooper - Schriffer + Hartree - Fock and quasiparticle random phase approximation, the isoscalar giant quadrupole resonance in the isotopes of 112,114,116,118,120,122,124Sn has been studied in this work. Five sets of Skyrme-type interactions of different values of the nuclear matter incompressibility coefficient KNM and effective mass m*/m are used in the calculations. Additionally, the impact of different types of pairing forces (i.e., volume, surface, and mixed) is examined. Comparisons are made between the computed strength distributions, centroid energies Ecen, scaled energies Es, and constrained energies Econ of the isoscalar giant quadrupole resonance and the available experimental data. Analysis is done on the relationships between KNM and m*/m, and the estimated properties.

Toward a new approach for the pygmy dipole resonance in even–even nuclei. Application to isotopes 144,148,150,152,154Sm

A many-body Hamiltonian consisting of a spherical shell model mean-field term, a pairing interaction for alike nucleons and a dipole–dipole interaction, with the dipole operator involving a cubic term in the radial coordinate, was studied within a quasiparticle random-phase approximation and applied numerically to five even–even isotopes of Sm. The resulting wavefunctions were further used to calculate the B(E1) values, which at their turn were employed to calculate the photoabsorption cross section, integrated moments of the cross section and energy weighted sum rule (EWSR). The calculated cross section and its integrated moments were compared with the available data, and a good agreement was observed. Two regions were distinguished: one corresponding to the pygmy dipole resonance (PDR) (1–10 MeV) and the other to the giant dipole resonance (GDR) (10–20 MeV), which were studied separately. The peaks belonging to each of the two ranges were analyzed in detail. The PDR states were located around the neutron separation energy and were mainly formed by the collective isoscalar and neutron collective states. The PDR states describe oscillations of the neutron excess against protons from the isospin-saturated core. The character of the states from the GDR region, isoscalar or isovector, is also pointed out. The PDR states carry only 0.8%–2.7% of the total EWSR and 0.4%–5.9% of the total E1 strength. The dependence of the dipole strength on nuclear deformation is evidenced. A comment on the cross section splitting into two branches for deformed isotopes is included. The r-cubic term and nuclear deformation have opposite effects on the dipole strength. In addition, it diminishes the effect of nonconservation of the center of mass momentum. The famous Thomas–Reiche–Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new sum rule is well satisfied. The projected spherical single-particle basis used in our formalism allows for a unified description of spherical transitional and deformed isotopes.

Re-Examination of the Effect of Pairing Gaps on Gamow–Teller Strength Distributions and β-Decay Rates

β-decay is one of the key factors for understanding the r-process and evolution of massive stars. The Gamow–Teller (GT) transitions drive the β-decay process. We employ the proton–neutron quasiparticle random phase approximation (pn-QRPA) model to calculate terrestrial and stellar β-decay rates for 50 top-ranked nuclei possessing astrophysical significance according to a recent survey. The model parameters of the pn-QRPA model affect the predicted results of β-decay. The current study investigates the effect of nucleon–nucleon pairing gaps on charge-changing transitions and the associated β decay rates. Three different values of pairing gaps, namely TF, 3TF, and 5TF, were used in our investigation. It was concluded that both GT strength distributions and half-lives are sensitive to pairing gap values. The 3TF pairing gap scheme, in our chosen nuclear model, resulted in the best prediction with around 80% of the calculated half-lives within a factor 10 of the measured ones. The 3TF pairing scheme also led to the calculation of the biggest β-decay rates in stellar matter.

Electric dipole transitions in the relativistic quasiparticle random-phase approximation at finite temperature

Electric dipole transitions in the relativistic quasiparticle random-phase approximation at finite temperature

Re-analysis of the Gamow-Teller distributions for [formula omitted] nuclei, 24Mg, 28Si, and 32S

The Gamow-Teller (GT) strength distributions of sd-shell N=Z nuclei (24Mg, 28Si, and 32S) are investigated within the framework of proton–neutron quasi-particle random phase approximation (pn-QRPA) using a deformed basis. The nuclear properties of these special nuclei were investigated by the Relativistic Mean Field (RMF) model. The RMF framework with density-dependent interactions (DD-PC1 and DD-ME2) was employed to compute ground-state deformation parameters (β2) using potential energy curves. The β2 values computed from the RMF and the finite range droplet model (FRDM) were employed as a free parameter in the pn-QRPA calculation to investigate the resulting GT strength distributions. The present model-based analyses compare well with the observed data.

An empirical formula of nuclear <i>β</i>-decay half-lives

Nuclear <i>β</i>-decay half-lives play an important role not only in nuclear physics, but also in astrophysics. The <i>β</i>-decay half-lives of many nuclei involved in the astrophysical rapid neutron-capture (r -process) still cannot be measured experimentally, so the theoretical predictions of nuclear <i>β</i>-decay half-lives are inevitable for r-process studies. Theoretical models for studying the nuclear <i>β</i>-decay half-lives include the empirical formula, the gross theory, the quasiparticle random phase approximation (QRPA), and the shell model. Compared with other theoretical models of <i>β</i>-decay half-lives, the empirical formula has high computational efficiency, and its prediction accuracy can be improved by introducing more and more physical information. In this work, an empirical formula without free parameters is proposed to calculate the nuclear <i>β</i>-decay half-lives based on the Fermi theory of <i>β</i> decay. By including the pairing effect, the shell effect, and the isospin dependence, the newly proposed empirical formula significantly improves the accuracy of predicting the nuclear <i>β</i>-decay half-life. For the nuclei with half-lives less than 1 second, the root-mean-square deviation of the common logarithms of the nuclear <i>β</i>-decay half-life predicted by the new empirical formula from the experimental data decreases to 0.220, which is improved by about 54% compared with that by the empirical formula without free parameters, even better than those by other existing empirical formulas and microscopic QRPA approaches. In the unknown region, the nuclear <i>β</i>-decay half-lives predicted by the new empirical formula are generally shorter than those predicted by the microscopic models in the light nuclear region, while those predicted by the new empirical formula in the heavy nuclear region are generally in agreement with those predicted by the microscopic models. The half-lives of neutron-rich nuclei on the nuclear chart are then predicted by the new empirical formula, providing nuclear <i>β</i>-decay half-life inputs for the r-process simulations.

Predicting nucleon-nucleus scattering observables using nuclear structure theory

Developing a predictive capability for inelastic scattering will find applications in multiple areas. Experimental data for neutron-nucleus inelastic scattering is limited and thus one needs a robust theoretical framework to complement it. Charged-particle inelastic scattering can be used as a surrogate for (n, γ) reactions to predict capture cross sections for unstable nuclei. Our work uses microscopic nuclear structure calculations for spherical nuclei to obtain nucleon-nucleus scattering potentials and calculate cross sections for these processes. We implement the Jeukenne, Lejeune, Mahaux (JLM) semi-microscopic folding approach, where the medium effects on nuclear interaction are parameterized in nuclear matter to obtain the nucleon-nucleon (NN) interaction in a medium at positive energies. We solve for the nuclear ground state using the Hartree-Fock-Bogliubov (HFB) many-body method, assuming the nucleons within the nucleus interact via the Gogny-D1M potential. The vibrational excited states of the target nucleus are calculated using the quasi-particle random phase approximation (QRPA). We demonstrate our approach for spherical nuclei in the medium-mass region, showing scattering results for the 90Zr nucleus.