Nuclear Ground-state Properties Research Articles

High-Precision Mass Measurements of Neutron Deficient Silver Isotopes Probe the Robustness of the N=50 Shell Closure.

High-precision mass measurements of exotic ^{95-97}Ag isotopes close to the N=Z line have been conducted with the JYFLTRAP double Penning trap mass spectrometer, with the silver ions produced using the recently commissioned inductively heated hot cavity catcher laser ion source at the Ion Guide Isotope Separator On-Line facility. The atomic mass of ^{95}Ag was directly determined for the first time. In addition, the atomic masses of β-decaying 2^{+} and 8^{+} states in ^{96}Ag have been identified and measured for the first time, and the precision of the ^{97}Ag mass has been improved. The newly measured masses, with a precision of ≈1 keV/c^{2}, have been used to investigate the N=50 neutron shell closure, confirming it to be robust. Empirical shell-gap and pairing energies determined with the new ground-state mass data are compared with the state-of-the-art abinitio calculations with various chiral effective field theory Hamiltonians. The precise determination of the excitation energy of the ^{96m}Ag isomer in particular serves as a benchmark for abinitio predictions of nuclear properties beyond the ground state, specifically for odd-odd nuclei situated in proximity to the proton dripline below ^{100}Sn. In addition, density functional theory calculations and configuration-interaction shell-model calculations are compared with the experimental results. All theoretical approaches face challenges to reproduce the trend of nuclear ground-state properties in the silver isotopic chain across the N=50 neutron shell and toward the proton dripline.

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.

High voltage determination and stabilization for collinear laser spectroscopy applications.

Fast beam collinear laser spectroscopy is the established method to investigate nuclear ground state properties such as the spin, the electromagnetic moments, and the charge radius of exotic nuclei. These are extracted with high precision from atomic observables, i.e., the hyperfine splitting and the isotope shift, which become possible due to a large reduction of the Doppler broadening by compressing the velocity width of the ion beam through electrostatic acceleration. With the advancement of experimental methods and applied devices, e.g., to measure and stabilize the laser frequency, the acceleration potential became the dominant systematic uncertainty contribution. To overcome this, we present a custom-built high-voltage divider, which was developed and tested at the German metrology institute, and a feedback loop that enabled collinear laser spectroscopy to be performed at a 100-kHz level. Furthermore, we describe the impact of field penetration into the laser-ion interaction region. This affects the determined isotope shifts and hyperfine splittings if Doppler tuning is applied, i.e., the ion beam energy is altered instead of scanning the laser frequency. Using different laser frequencies that were referenced to a frequency comb, the field penetration was extracted laser spectroscopically. This allowed us to define an effective scanning potential to still apply the faster and easier Doppler tuning without introducing systematic deviations.

High-resolution laser spectroscopy on the hyperfine structure and isotope shift of 237,239\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{237,239}$$\\end{document}Np

Nuclear ground state properties of 237,239\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{237,239}$$\\end{document}Np were investigated by high-resolution laser spectroscopy at the RISIKO mass separator off-line radioactive beam facility of the University of Mainz. The isotope shifts and the hyperfine parameters were determined in two different atomic ground-state transitions at 398.80 nm and 395.61 nm. The data allowed for calculation of the so far unknown nuclear moments of the short-lived isotope 239\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{239}$$\\end{document}Np, i.e. the nuclear magnetic dipole moment of μI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _I$$\\end{document} = +3.18(2) μN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _N$$\\end{document} and the electric quadrupole moment of QS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_S$$\\end{document} = +4.05(8) eb, using the known nuclear moments of 237\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{237}$$\\end{document}Np as a reference, which were determined by electron paramagnetic resonance and investigations of muonic X-ray hyperfine structures, respectively.

Re-examination of β-decay in Hg, Pb and Po Isotopes

This study re-examines the effect of nuclear deformation on the calculated Gamow-Teller (GT) strength distributions of neutron-deficient (178−192Hg, 185−194Pb and 196−206Po) nuclei. The nuclear ground state properties and shape parameters were calculated using the Relativistic Mean Field model. Three different density-dependent interactions (D3C, DD-ME2 and DD-PC1) were used in the calculation. Estimated shape parameters were later used within the framework of deformed proton-neutron quasi-random phase approximations model, with a separable interaction, to calculate the GT strength distributions, half-lives and branching ratios for these neutron–deficient isotopes. It was concluded that half-lives and GT strength distributions vary considerably with change in shape parameter.

Resolution Characterizations of JetRIS in Mainz Using 164Dy

Laser spectroscopic studies of elements in the heavy actinide and transactinide region help understand the nuclear ground state properties of these heavy systems. Pioneering experiments at GSI, Darmstadt identified the first atomic transitions in the element nobelium. For the purpose of determining nuclear properties in nobelium isotopes with higher precision, a new apparatus for high-resolution laser spectroscopy in a gas-jet called JetRIS is under development. To determine the spectral resolution and the homogeneity of the gas-jet, the laser-induced fluorescence of 164Dy atoms seeded in the jet was studied. Different hypersonic nozzles were investigated for their performance in spectral resolution and efficiency. Under optimal conditions, a spectral linewidth of about 200–250 MHz full width at half maximum and a Mach number of about 7 was achieved, which was evaluated in context of the density profile of the atoms in the gas-jet.

The nuclear ground-state properties and stellar electron emission rates of 76Fe, 78Ni, 80Zn, 126Ru, 128Pd and 130Cd using RMF and pn-QRPA models

Our study consists of investigations of nuclear ground state properties and weak transition rates of even-even waiting point nuclei. The calculation was performed for N=50 and N=82 nuclei. The Relativistic Mean Field (RMF) model was used to explore the nuclear ground state properties of selected nuclei. The proton-neutron quasi particle random phase (pn-QRPA) model was used for the computation of allowed Gamow Teller (GT) and unique first-forbidden (U1F) transitions of the selected waiting point nuclei. The RMF approach with different density-dependent interactions, DD-ME2 and DD-PC1, was used to compute potential energy curves and surfaces, quadrupole moments, deformation parameters, binding energies, proton-neutron separation energies, charge, and radii. The RMF computed deformation parameters were used in the pn-QRPA model, as a free parameter, for the computation of GT and U1F weak transitions. We investigated three different sets of deformation parameter for the calculation of electron emission rates. The rates changed considerably with change in deformation parameter. We later investigated contribution of allowed GT and U1F rates and competition between positron capture and electron emission rates at high stellar temperatures. The computed positron capture rates were significant especially at low densities and high temperatures. The contribution of U1F rates to allowed GT appreciably reduced the total calculated half-lives. The comparison of our results with previous calculations and measurement is also shown. The pn-QRPA calculation including U1F contribution is in good agreement with the experimental data.

Investigation Some Nuclear Ground State Properties of The 89Y, 138,139La and 175,176La Rare Earth Elements

One of the important arguments that will carry today's world to the high technology of the future is the rare earth elements. However, energy will be the most important field in future technology and also, the most important issue in the field will be fusion energy. Of course, as all areas of technology, the rare earth elements will make an important contribution to the development of fusion technology. Also, the nuclear structure of the rare earth elements in nuclear physics has always been the focus of interest and is still a subject that is frequently studied today. Therefore, in this study, nuclear ground state properties such as the binding energies per particle, the rms charge proton and neutron density radii, the deformation parameters and the quadrupole moments of the rare earth nuclei as 89Y, 138,139La and 175,176Lu are calculated using the Skyrme-Hartree-Fock-Bogolyubov method. The calculations are performed with HFB9, SIII, SKI3, SKM *, SKO, SKP, SKX, SLY4, SLY5, SLY6, SLY7, UNE0 and UNE1 Skyrme force parameters. Also, the results are discussed and compared with the available experimental data.

Nuclear Equation of State in the Relativistic Point-Coupling Model Constrained by Excitations in Finite Nuclei

Nuclear equation of state is often described in the framework of energy density functional. However, the isovector channel in most functionals has been poorly constrained, mainly due to rather limited available experimental data to probe it. Only recently, the relativistic nuclear energy density functional with an effective point-coupling interaction was constrained by supplementing the ground-state properties of nuclei with the experimental data on dipole polarizability and isoscalar monopole resonance energy in 208Pb, resulting in DD-PCX parameterization. In this work, we pursue a complementary approach by introducing a family of 8 relativistic point-coupling functionals that reproduce the same nuclear ground-state properties, including binding energies and charge radii, but in addition have a constrained value of symmetry energy at saturation density in the range J = 29, 30, …, 36 MeV. In the next step, this family of functionals is employed in studies of excitation properties such as dipole polarizability and magnetic dipole transitions, and the respective experimental data are used to validate the optimal choice of functional as well as to assess reliable values of the symmetry energy and slope of the symmetry energy at saturation.

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.

The Axial Hartree–Fock + BCS Code SkyAx

The nuclear mean-field model based on Skyrme forces can predict a variety of properties of nuclear ground states. We present the Code SkyAx solving the Hartree–Fock equations in two spatial dimensions assuming axial symmetry. Pairing can be included in the BCS approximation. The code is implemented with a view on computational speed. Program summaryProgram title: SkyAxCPC Library link to program files:http://dx.doi.org/10.17632/fd453hc4jb.1Licensing provisions: GPLv3Programming language: Fortran 90 and parallel version with OpenMP.External routines/libraries: BLAS, LAPACK.Nature of problem: The Hartree–Fock equations can be used to determine static properties of nuclei all over the nuclear chart, e.g., nuclear masses, charge radii and deformations. This code implements the widely used Skyrme forces as interaction model and offers in addition to include the pairing interaction through the BCS theory. Due to its two-dimensional nature, the code allows only for axial deformations, which is suitable for most nuclei in the chart of nuclides.Solution method: The nucleonic wave functions are represented on a two-dimensional mesh assuming axial symmetry. The Coulomb potential is calculated for an isolated charge distribution by splitting the problem into a short-range and a long-range part. All spatial derivatives are evaluated using the finite Fourier transform method. The code solves the static Hartree–Fock equations with a damped gradient iteration method. It also allows for constraint iterations, where the monopole, quadrupole, octupole and hexadecapole moments can be fixed.Additional comments including restrictions and unusual features: The current implementation is restricted to even–even nuclei. Furthermore the Hartree–Fock + BCS model is valid only for well-bound nuclei. For nuclei near the neutron and proton drip lines, a full Hartree–Fock–Bogolyubov treatment would be more suitable.The code allows for multipole constraints up to l=4. Furthermore the code can be used to calculate fission paths or landscapes of deformations (potential energy surfaces) in one single run.

Systematic study of nuclear structure properties of proton-rich even-even tellurium isotopes with the Gogny energy density functional

The ground state nuclear structure properties of the proton rich even-even tellurium isotopes are studied by using Gogny energy density functional within the framework of Hartree-Fock-Bogoliubov (HFB) method. The HFB equations are solved by using the axial cylindrical transformed deformed harmonic oscillator basis. The full parameterization of Gogny energy density functional is employed in the present study. The evolution of the neutron density distributions with an increase in neutron number is studied and emergence of various nuclear structure phenomena is investigated. Besides this, the ground state nuclear structure properties such as nuclear multipole moments, deformation parameters, binding energies, pairing energies, root mean square radii and charge radii are obtained for the even-even proton-rich tellurium isotopes. The theoretical results on the nuclear ground state properties are compared with the available experimental data and good agreement is found.

The influence of the nuclear surface diffuseness on the transition charge densities.

Proton partial occupancies of the nuclear surface orbits are used in a modified shell model approach to study isoscalar dipole transition charge densities and form factors for self-conjugate nuclei. The energy-weighted sum-rules of Harakeh-Dieperink for both the transition form factor and transition charge density are modified so as fractional occupation probabilities of the states may be used. The partial occupancies of the surface n/j-levels are determined by fitting to the experimental inelastic scattering data and compared with those found previously in the study of nuclear ground state properties

Investigation of the Static Nuclear Properties of Some Cr-Isotopes Using Skyrme-Hartree-Fock Method

The self-consistent Hartree-Fock (HF) calculations with several Skyrme parameterizations; SKM, SKM*, SLY4, SKxs25, MSK7, SKO, SKxta, and SKxtb have been used to investigate some static nuclear ground-state properties of some Chromium (50-54Cr) isotopes. The nuclear ground state charge, mass, neutron and proton densities with the corresponding root mean square radii, the charge form factors, the total binding energies and the neutron skin thickness can be calculated. The calculations are performed using NuShellX@MSU code, where the deduced results led to specifying one set or more of Skyrme parameterizations that used to achieve the best agreement with the available experimental data.

Optimizing the relativistic energy density functional with nuclear ground state and collective excitation properties

We introduce a new relativistic energy density functional constrained by the ground state properties of atomic nuclei along with the isoscalar giant monopole resonance energy and dipole polarizability in $^{208}$Pb. A unified framework of the relativistic Hartree-Bogoliubov model and random phase approximation based on the relativistic density-dependent point coupling interaction is established in order to determine the DD-PCX parameterization by $\chi^2$ minimization. This procedure is supplemented with the co-variance analysis in order to estimate statistical uncertainties in the model parameters and observables. The effective interaction DD-PCX accurately describes the nuclear ground state properties including the neutron-skin thickness, as well as the isoscalar giant monopole resonance excitation energies and dipole polarizabilities. The implementation of the experimental data on nuclear excitations allows constraining the symmetry energy close to the saturation density, and the incompressibility of nuclear matter by using genuine observables on finite nuclei in the $\chi^2$ minimization protocol, rather than using pseudo-observables on the nuclear matter, or by relying on the ground state properties only, as it has been customary in the previous studies.

Evolution of nuclear spin-orbit splittings with Skyrme functional SAMi-T

A new Skyrme functional has been developed with tensor term guided by ab initio relativistic Brueckner-Hartree-Fock (RBHF) studies on neutron-proton drops. Instead of extracting information on the tensor force from experimental single-particle energy splittings, the RBHF calculations do not contain beyond mean-field effects such as particle-vibration coupling and therefore the information on the tensor force can be obtained without ambiguities. The new functional gives a good description of nuclear ground-state properties aswell as various giant resonances. The description for the evolution of single-particle energy splittings is also improved by the new functional.

Modeling baryonic interactions with the Clausius-type equation of state

The quantum statistical Clausius-based equation of state is used to describe the system of interacting nucleons. The interaction parameters $a$, $b$, and $c$ of the model are fixed by the empirically known nuclear ground state properties and nuclear incompressibility modulus. The model is generalized to describe the baryon-baryon interactions in the hadron resonance gas (HRG). The predictions of such a Clausius-HRG model are confronted with the lattice QCD data at zero and at small chemical potentials, and are also contrasted with the standard van der Waals approach. It is found that the behavior of the lattice QCD observables in a high-temperature hadron gas is sensitive to the nuclear matter properties. An improved description of the nuclear incompressibility factor correlates with an improved description of the lattice QCD data in the crossover transition region.

Constraints on the nuclear equation of state from nuclear masses and radii in a Thomas-Fermi meta-modeling approach

The question of correlations among empirical equation of state (EoS) parameters constrained by nuclear observables is addressed in a fully empirical meta-modeling approach. A recently proposed meta-modeling for the nuclear EoS in nuclear matter, is augmented with a single finite size term to produce a minimal unified EoS functional able to describe the smooth part of the nuclear ground state properties. This meta-model can reproduce the predictions of a large variety of models, and interpolate continuously between them. The parameter space is sampled and filtered through the constraint of nuclear mass reproduction. We show that this simple analytical meta-modeling has a predictive power on masses, radii, and skins comparable to full HF or ETF calculations with realistic energy functionals. The covariance analysis on the posterior distribution shows that no physical correlation is present between the different EoS parameters. Concerning nuclear observables, a strong correlation between the slope of the symmetry energy and the neutron skin is observed, in agreement with previous studies.

Higher-order baryon number susceptibilities: Interplay between the chiral and the nuclear liquid-gas transitions

We use an improved version of the SU(3) flavour parity-doublet quark-hadron model to investigate the higher order baryon number susceptibilities near the chiral and the nuclear liquid-gas transitions. The parity-doublet model has been improved by adding higher-order interaction terms of the scalar fields in the effective mean field Lagrangian, resulting in a much-improved description of nuclear ground-state properties, in particular the nuclear compressibility. The resulting phase diagram of the model agrees qualitatively with expectations from lattice QCD, i.e., it shows a crossover at zero net baryo-chemical potential and a critical point at finite density. Using this model, we investigate the dependence of the higher-order baryon number susceptibilities as function of temperature and chemical potential. We observe a strong interplay between the chiral and liquid-gas transition at intermediate baryo chemical potentials. Due to this interplay between the chiral and the nuclear liquid-gas transitions, the experimentally measured cumulants of the net baryon number may show very different beam energy dependence, subject to the actual freeze-out temperature.

Investigation of Nuclear Ground State Properties of Fuel Materials of 232Th and 238U Using Skyrme-Extended-Thomas-Fermi Approach Method

It has been performed the nuclear ground state properties investigation of 232Th and 238U using Skyrme interaction. The local density, the kinetic energy density, and the spin-orbit density for proton and neutron have been calculated using Extended-Thomas-Fermi approach method. Then the calculation results have been compared with Skyrme-Hartree-Fock results (using HAFOMN and HFBRAD codes). Total energy calculations obtained from this research are -1792.973947 MeV (for 232Th) deviated 0.29244% from experiment energy and -1761.519459 MeV (for 238U) deviated 0.48369% from experiment energy. The distribution profiles of local density and local potential for 232Th and 238U are quite similar with Skyrme- Hartree-Fock results. It is indicated that Skyrme-Extended-Thomas-Fermi method can be used to study the nuclear ground state properties, especially even nuclei.