Closed-shell Nuclei Research Articles

Symmetry breaking of Gamow-Teller and magnetic-dipole transitions and its restoration in calcium isotopes

Nuclear magnetic-dipole (M1) and Gamow-Teller (GT) transitions provide insight into the spin-isospin properties of atomic nuclei. By considering them as unified spin-isospin transitions, the M1/GT transition strengths and excitation energies are subject to isospin symmetry. The excitation properties associated to the M1/GT symmetry need to be clarified within consistent theoretical approach. In this work, the relationship between the M1 and GT transitions in Ca isotopes is investigated in a unified framework based on the relativistic energy-density functional (REDF) with point-coupling interactions, using the relativistic quasi-particle random-phase approximation (RQRPA). It is shown that the isovector-pseudovector (IV-PV) residual interaction affects both transitions, and the symmetry of M1 and giant-GT transitions is disrupted by this interaction in closed-shell nuclei. In open-shell Ca isotopes, the proton-neutron pairing in the residual RQRPA interaction also plays a role in GT transitions. Due to the interplay between these interactions, the M1/GT symmetry can be restored especially in the $^{42}$Ca nucleus, i.e., the giant-GT strength can become comparable to that of the M1 mode in terms of the unified spin-isospin transitions by adjusting the PN-pairing strength to reproduce the experimental low-lying GT-excitation energies. The mirror symmetry of both M1 and GT transitions is also demonstrated for open-shell mirror partners, $^{42}$Ca and $^{42}$Ti. Further improvements are required to achieve simultaneous reproduction of M1 and GT-transition energies in the REDF framework.

Theoretical study of ground state properties of odd-A Cu isotopes in an analytical approach

Copper isotopes have been studied within various theoretical approaches, including the Shell model. Here, we describe their static properties using a new analytical approach. In the proposed model, we consider odd-A Cu isotopes as closed-shell nuclei plus one proton outside the [Formula: see text] shell gap. We calculate their static properties such as ground state energies, electric quadrupole moments and charge radii. The obtained results show good agreement with the experimental data, thus suggesting that our approach can be applicable to similar isotopic chains.

Effects of ground-state correlations on the damping of giant dipole resonances in LS closed-shell nuclei

Abstract The effects of ground-state correlations on the damping of isovector giant dipole resonances in the LS closed-shell nuclei 16O and 40Ca are studied using extended random phase approximation (RPA) approaches derived from the time-dependent density matrix theory. It is pointed out that unconventional two-body amplitudes of one-particle–three-hole and three-particle–one-hole types that are neglected in most extended RPA theories play an important role in the fragmentation of isovector dipole strength.

Quenching of Gamow-Teller strengths and two-particle–two-hole configurations

We apply the charge-exchange subtracted second random-phase approximation (SSRPA), based on Skyrme functionals, to investigate Gamow-Teller resonances in several closed-shell and closed-subshell nuclei, located in different regions of the nuclear chart. After having discussed the SSRPA findings obtained within different approximation schemes in $^{48}$Ca, we compare our results with {\it{ab-initio}} coupled-cluster predictions available for C and O isotopes, where two-body currents are included. Our integrated strenghts, obtained by using one-body transition operators, are lower compared to the corresponding {\it{ab-initio}} results. This indicates that, within our model, quenching effects are mainly driven by the inclusion of two particle - two hole configurations and that the role of a two-body contribution in the transition operator is less important than in the coupled-cluster approach. By analyzing heavier nuclei, $^{90}$ Zr and $^{132}$Sn, we confirm the same conclusions that we have recently drawn for $^{48}$Ca: the inclusion of two particle - two hole configurations is very effective in our model for providing strengths which are significantly more quenched than in other theoretical models and, thus, in better agreement with the experimental measurements. This occurs because two particle - two hole configurations have a density which strongly increases with the excitation energy. Their inclusion thus pushes a significant amount of the strength to higher energies, compared to what happens in other theoretical models, reducing in this way the cumulative sum of the strength up to excitation energies around 20-30 MeV.

Magnetic moment predictions of odd-A nuclei with the Bayesian neural network approach * *Supported by the National Natural Science Foundation of China (11675063, 11875070, 11205068) and the Open fund for Discipline Construction, Institute of Physical Science and Information Technology, Anhui University

The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei. The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square (rms) deviations from data, i.e., 0.949 and 1.272 for odd-neutron nuclei and odd-proton nuclei, respectively. By including the dependence of the nuclear spin and Schmidt magnetic moment, the machine-learning approach precisely describes the magnetic moments of odd-A nuclei with rms deviations of 0.036 for odd-neutron nuclei and 0.061 for odd-proton nuclei. Furthermore, the evolution of magnetic moments along isotopic chains, including the staggering and sudden jump trend, which are difficult to describe using nuclear models, have been well reproduced by the Bayesian neural network (BNN) approach. The magnetic moments of doubly closed-shell nuclei, for example, isoscalar and isovector magnetic moments, have been well studied and compared with the corresponding non-relativistic and relativistic calculations.

Impact of shell structure on the fusion of neutron-rich mid-mass nuclei

The influence of shell effects on fusion of mid-mass nuclei is explored using isotopic chains of K and Ar ions on an oxygen target. Comparison of the reduced excitation functions reveals that the fusion cross section for the open neutron-shell projectile nuclei $^{41}\mathrm{K}$ and $^{45}\mathrm{K}$ is systematically larger than for the closed neutron-shell projectiles $^{39}\mathrm{K}$ and $^{47}\mathrm{K}$. The S\~ao Paulo fusion model using matter densities from systematics fails to describe the measured excitation functions. Use of more realistic densities from a Dirac-Hartree-Bogoliubov (DHB) approach performs significantly better though it still overpredicts the closed-shell nuclei.

Microscopic shell-model counterpart of the Bohr–Mottelson model

In the present paper we demonstrate that there exists a fully microscopic shell-model counterpart of the Bohr-Mottelson model by embedding the latter in the microscopic shell-model theory of atomic nucleus within the framework of the recently proposed fully microscopic proton-neutron symplectic model (PNSM). For this purpose, another shell-model coupling scheme of the PNSM is considered in which the basis states are classified by the algebraic structure $SU(1,1) \otimes SO(6)$. It is shown that the configuration space of the PNSM contains a six-dimensional subspace that is closely related to the configuration space of the generalized quadrupole-monopole Bohr-Mottelson model and its dynamics splits into radial and orbital motions. The group $SO(6)$ acting in this space, in contrast, e.g., to popular IBM, contains an $SU(3)$ subgroup which allows to introduce microscopic shell-model counterparts of the exactly solvable limits of the Bohr-Mottelson model that closely parallel the relationship of the original Wilets-Jean and rotor models. The Wilets-Jean-type dynamics in the present approach, in contrast to the original collective model formulation, is governed by the microscopic shell-model intrinsic structure of the symplectic bandhead which defines the relevant Pauli allowed $SO(6)$, and hence $SU(3)$, subrepresentations. The original Wilets-Jean dynamics of the generalized Bohr-Mottelson model is recovered for the case of closed-shell nuclei, for which the symplectic bandhead structure is trivially reduced to the scalar or equivalent to it irreducible representation.

In-medium k-body reduction of n-body operators

The computational cost of ab initio nuclear structure calculations is rendered particularly acute by the presence of (at least) three-nucleon interactions. This feature becomes especially critical now that many-body methods aim at extending their reach beyond mid-mass nuclei. Consequently, state-of-the-art ab initio calculations are typically performed while approximating three-nucleon interactions in terms of effective, i.e. system-dependent, zero-, one- and two-nucleon operators. While straightforward in doubly closed-shell nuclei, existing approximation methods based on normal-ordering techniques involve either two- and three-body density matrices or a symmetry-breaking one-body density matrix in open-shell systems. In order to avoid such complications, a simple, flexible, universal and accurate approximation technique involving the convolution of the initial operator with a sole symmetry-invariant one-body matrix is presently formulated and tested numerically. Employed with a low-resolution Hamiltonian, the novel approximation method is shown to induce errors below $2-3\%$ across a large range of nuclei, observables and many-body methods.

Constraining the density dependence of the symmetry energy with nuclear data and astronomical observations in the Korea-IBS-Daegu-SKKU framework

The KIDS framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore symmetry-energy (SE) parameters such as J (value at saturation density), L (slope), Ksym (curvature) and so on independently of each other and of assumptions about the effective mass. Here we examine the performance of EoSs with different SE parameters in reproducing nuclear properties and astronomical observations in an effort to constrain especially L and Ksym or the droplet-model counterpart Ktau. Assuming a standard EoS for symmetric matter, we explore several points on the hyperplane of (J,L,Ksym or Ktau) values. For each point, the corresponding EDF parameters and a pairing parameter are obtained for applications in spherical even-even nuclei. This is the first application of KIDS EDFs with pairing correlations. The EoSs are tested successively on properties of closed-shell nuclei, along the Sn isotopic chain, and on astronomical observations, in a step-by-step process of elimination and correction. A small regime of best-performing parameters is determined. The results strongly suggest that Ksym is negative and no lower than -200MeV, that Ktau lies between roughly -400 and -300MeV and that L lies between 40 and 65MeV with L<55MeV more likely. Correlations between symmetry-energy parameters are critically discussed. Predictions for the position of the neutron drip line and the neutron skin thickness of selected nuclei are reported. They are only weakly affected by the choice of effective mass values. Parts of the drip line can be sensitive to the SE parameters. The results underscore the role of Ktau and of precise astronomical input. Better constraints are possible with precise fits to nuclear energies and, in the future, more-precise input from astronomy.

Properties of isoscalar giant multipole resonances in medium-heavy closed-shell nuclei: A semimicroscopic description

The semimicroscopic particle-hole dispersive optical model (PHDOM) is implemented to describe main properties of Isoscalar Giant Multipole Resonances (up to L=3) in medium-heavy closed-shell nuclei. The main properties are characterized by the strength distribution, transition density, partial and total probabilities of direct one-nucleon decay. Calculation results obtained for the 208Pb nucleus are compared with available experimental data.

Ultraviolet suppression and nonlocality in optical model potentials for nucleon-nucleus scattering

We investigate the role of high momentum components of optical model potentials for nucleon-nucleus scattering and its incidence on their nonlocal structure in coordinate space. The study covers closed-shell nuclei with mass number in the range $4\leq A\leq 208$, for nucleon energies from tens of MeV up to 1 GeV. To this purpose microscopic optical potentials are calculated using density-dependent off-shell $g$ matrices in Brueckner-Hartree-Fock approximation and based on Argonne $v_{18}$ as well as chiral 2$N$ force up to next-to-next-to-next-to-leading order. We confirm that the gradual suppression of high-momentum contributions of the optical potential results in quite different coordinate-space counterparts, all of them accounting for the same scattering observables. We infer a minimum cutoff momentum $Q$, function of the target mass number and energy of the process, that filters out irrelevant ultraviolet components of the potential. We find that when ultraviolet suppression is applied to Perey-Buck nonlocal potential or local Woods-Saxon potentials, they also result nonlocal with similar appearance to those obtained from microscopic models in momentum space. We examine the transversal nonlocality, quantity that makes comparable the intrinsic nonlocality of any potential regardless of its representation. We conclude that meaningful comparisons of nonlocal features of alternative potentials require the suppression of their ultraviolet components.

Investigation of the cold valley paths for the synthesis of isotopes of Ubh in optimum orientations

Cold valley paths have been investigated for the synthesis of isotopes of superheavy element Unbihexium using quantum mechanical fragmentation theory, which suggests the fusion of fission fragments belonging to the cold valleys in the potential energy surfaces with at least one spherical closed shell nucleus as the reaction partner for the nuclear synthesis. For the suitability of the cold valley fission fragments for the synthesis of isotopes of Ubh, first the fragmentation potentials, preformation probabilities and fission barriers of the fission fragments of 314Ubh and 326Ubh compound systems in their ground states have been compared by keeping the fragments either in hot or cold optimum orientations. The comparison suggests 138Ba + 176Yb and 132Sn + 194Os reactions in hot optimum orientations for the synthesis of isotopes of Ubh due to their highest values of preformation probabilities, lowest values of the fragmentation potentials and relatively good values of the fission barriers. Also, the reactions 68Ni + 246Cf and 70Ni + 256Cf have been considered for the comparison with 138Ba + 176Yb and 132Sn + 194Os reactions due to their relatively smaller values of the Coulomb potential, higher mass-asymmetry and fission barrier, and shell closures next to 48Ca which has been used in most of the experiments for the synthesis of superheavy elements. Finally, the excitation functions for the neutron evaporation from the compound systems formed in these reactions, the probabilities of the formation and survival of the compound nuclei have been compared to suggest the suitable cold valley paths energies for the synthesis of the isotopes of Ubh.

Shell corrections with finite temperature covariant density functional theory * *Supported by Natural Science Foundation of Henan Province (202300410480, 202300410479), the National Natural Science Foundation of China (U2032141), the Foundation of Fundamental Research for Young Teachers of Zhengzhou University (JC202041041), and the Physics Research and Development Program of Zhengzhou University (32410217)

The temperature dependence of the shell corrections to the energy , entropy , and free energy is studied by employing the covariant density functional theory for closed-shell nuclei. Taking Sm as an example, studies have shown that, unlike the widely-used exponential dependence , exhibits a non-monotonous behavior, i.e., first decreasing 20% approaching a temperature of MeV, and then fading away exponentially. Shell corrections to both free energy and entropy can be approximated well using the Bohr-Mottelson forms and , respectively, in which . Further studies on the shell corrections in other closed-shell nuclei, Sn and Pb, are conducted, and the same temperature dependencies are obtained.

Reaction channel contributions to the triton optical potential

Background: The well-established coupled channel and coupled reaction channel processes contributing to direct reactions make particular contributions to elastic scattering that are absent from local density folding models. Very little has been established concerning the contribution of these processes to the optical model potentials (OMPs) for 3He scattering. For studying such processes, spin-saturated closed shell nuclei such as 16O and 40Ca are particularly suitable target nuclei and the (3He, 4He) reaction is easily handled within conventional reaction theory because it avoids complications such as breakup. Purpose: To establish and characterize the contribution to the 3He-nucleus interaction generated by coupling to neutron pickup (outgoing 4He) channels; also to study the contribution of collective states and identify effects of dynamical nonlocality from these couplings. Methods: Coupled reaction channel (CRC) calculations, including coupling to collective states, will provide the elastic channel S-matrix Sl j resulting from the included processes. Inversion of Sl j will produce the local potential that yields, in a single channel calculation, the elastic scattering observables from the coupled channel calculation. Subtracting the bare potential from the CRC calculations yields a local and l-independent representation of the dynamical polarization potential (DPP). From the DPPs, because of a range of combinations of channel couplings, the influence of dynamically generated nonlocality can be identified. Results: Coupling to 4He channels systematically induces repulsion and absorption in the 3He OMP and also a reduction in the rms radius of the real part. The repulsion and absorption is less for 208Pb than for the lighter target nuclei although the qualitative effects, including the general undularity of the DPPs, are similar for all cases; therefore coupling to these channels cannot be represented by renormalizing folding model potentials. Evidence is presented for substantial dynamical nonlocality of the induced DPPs; for 40Ca this modifies direct reaction angular distributions. The local equivalent DPPs for individual couplings cannot be added to give the overall DPP for the complete set of couplings. For the 208Pb case, channel coupling reduces the reaction cross section although it increases it for 16O, with 40Ca an intermediate case. Conclusions: The DPPs established here strongly challenge the notion that folding models, in particular local density models, provide a satisfactory description of elastic scattering of 3He from nuclei. Coupling to neutron pickup channels induces dynamical nonlocality in the 3He OMP with implications for direct reactions involving 3He. Departures from a smooth radial form for the 3He OMP should be apparent in good fits to suitable elastic scattering data.

Ternary Fission Mass Distributions of Superheavy Nuclei Within a Statistical Model

Theoretical models predict the existence of an island of stability at the proton shell closures Z = 114 or 120 or 126 and at the neutron shell closure N = 184 due to the microscopic shell effects. In this article, mass distributions of fragments from ternary fission of superheavy nuclei are investigated with the aid of the statistical theory. We have computed the fission mass distributions for the simultaneous decay into three fragments of nuclei 298Fl, $^{304}_{120}$ X and $^{310}_{126} $ X, at the two excitation energies E∗ = 20 and 50 MeV, with the constraint on one of the fragment to be 50Ca and 72Ni. With the fixed third fragments of mass number A3 = 50, 72, asymmetric breakup (A1 ≠ A2) has a larger ternary fission yield for Z = 114, 120 and 126 isotopes. Predominantly, one of the fragments with the neutron closed-shell nucleus (N ≈ 82, 50) is favoured at higher excitation energies. Subsequently, we have considered the ternary fragmentation of the neutron-rich superheavy elements $^{314}_{120}$ X and $^{320}_{126} $ X again for the same excitation energies and fixed third fragment. Interestingly, for the superheavy nucleus $^{314}_{120}$ X, symmetric fission (A1 ≈ A2) with doubly closed-shell nuclei 132Sn for the third fragment 50Ca is favoured at higher E∗. For the isotope $^{320}_{126} $ X, relative yields of fragments with closed shell increase at higher excitation energy.

Investigation of Nuclear Structures of Self-conjugate Zn, Ge, Se, Kr, Sr Nuclei

Nuclear structures of the atomic nuclei can be theoretically investigated by using nuclear shell model. Generally, a doubly closed-shell nucleus has been considered as inert core and the nucleons outside the core are taken into account in the calculation. It is assumed that the nucleons in the inert core do not move but each valance nucleon out of the core moves under an average potential created by the others. The self-conjugate (N=Z) moderate mass nuclei region is one of the region for the investigation of several phenomena because of the maximum spatial overlap of neutrons and protons. In this study, the nuclear structures of the moderate mass N=Z have been analyzed in the scope of the nuclear shell model by using KSHELL computer code. In the calculations, doubly magic 56Ni were taken as core and p3/2, f5/2 and p1/2 single particle orbits were used as valance orbits. Different two-body interactions have been taken into account. The results have been compared with each other and the available values existing in the literature.

A solvable model for octupole phonons

A solvable model is proposed for the description of octupole phonons in closed-shell nuclei, formulated in terms of shell-model par\-ticle--hole excitations. With some simple assumptions concerning single-particle energies and two-body interactions, closed expressions are derived for the energy and wave function of the octupole phonon. In particular, it is shown that the components of the octupole phonon are proportional to Wigner $3j$ coefficients. This analytic wave function is proven to be exactly valid in light nuclei, which have $LS$ shell closures that coincide with those of the three-dimensional harmonic oscillator, and to be valid to a good approximation in heavier nuclei, which have $jj$ shell closures due to the spin--orbit interaction. The properties of the solvable model are compared with the results of a realistic shell-model calculation for $^{208}$Pb.

Ab initio leading order effective potentials for elastic nucleon-nucleus scattering

Background: Calculating microscopic effective interactions (optical potentials) for elastic nucleon-nucleus scattering has already in the past led to a large body of work. For first-order calculations a nucleon-nucleon (\textit{NN}) interaction and a one-body density of the nucleus were taken as input to rigorous calculations of microscopic full-folding calculations. Purpose: Based on the spectator expansion of the multiple scattering series we employ a chiral next-to-next-to-leading order (NNLO) nucleon-nucleon interaction on the same footing in the structure as well as in the reaction calculation to obtain an in leading-order consistent effective potential for nucleon-nucleus elastic scattering, which includes the spin of the struck target nucleon. Methods: The first order effective folding potential is computed by first deriving a nonlocal scalar density as well as a spin-projected momentum distribution. Those are then integrated with the off-shell Wolfenstein amplitudes $A$, $C$, and $M$. The resulting nonlocal potential serves as input to a momentum-space Lippmann-Schwinger equation, whose solutions are summed to obtain the nucleon-nucleus scattering observables. Results: We calculate elastic scattering observables for $^4$He, $^6$He, $^8$He, $^{12}$C, and $^{16}$O in the energy regime between 100 and 200 MeV projectile kinetic energy, and compare to available data. We also explore the extension down to about 70 MeV, and study the effect of ignoring the spin of the struck nucleon in the nucleus. Conclusions: In our calculations we contrast elastic scattering off closed-shell and open-shell nuclei. We find that for closed-shell nuclei the approximation of ignoring the spin of the struck target nucleon is excellent. We only see effects of the spin of the struck target nucleon when considering $^6$He and $^8$He, which are nuclei with a $N/Z$ ratio larger than 1.

Effects of velocity-dependent and spin-orbit terms of the Skyrme interaction on neutron elastic scattering observables

Elastic scattering of a series of doubly closed-shell nuclei at low energy has been described in the framework of optical potential model generated from the particle-vibration coupling approach on top of the collective excited states obtained from the random-phase approximation. We focus on the effects of the spin-orbit and velocity-dependent interaction on the angular distributions and analyzing powers by comparing these observables with experimental data. It has been found that the contribution of the two-body velocity-dependent and two-body spin-orbit terms are important to improve results for $^{16}\mathrm{O},\phantom{\rule{0.16em}{0ex}}^{40}\mathrm{Ca},\phantom{\rule{0.16em}{0ex}}^{48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$. The velocity-dependent interactions strongly reduce the absorption on the surface while the spin-orbit interactions sightly increase the absorption in the interior.

Ne İzotoplarının Nükleer Yapı Özelliklerinin Nükleer Kabuk Modeli ile İncelenmesi

One of the common methods used to investigate the nuclear structures of atomic nuclei is the nuclear shell model. Similar to the placement of atomic electrons into orbits, in the nuclear shell model, protons and neutrons are thought to fill the orbits within the nucleus, following the principle of Pauli's exclusion. These orbits are grouped to form shells, which are said to be closed if all possible places in a shell are full. Atomic nuclei with closed shells are very stable and valence nucleons that are more than these nuclei are included in the nuclear shell model calculations. In this study, the nuclear shell model was used to investigate the nuclear structure of even-even Ne nuclei by considering the 16O core as a closed-shell nucleus. Single-particle orbits d5/2, s1/2 and d3/2 are taken into account and different parameter sets are used for two-body interactions between valance nucleons. The results were compared with each other and with current literature values. It was seen that the closest results to the experimental values were obtained with parameter sets of usdb and sdnn. In the 18Ne isotope with magic neutron number, it was seen that the first excited level energy was found to be large as expected. Then, this excitation energy decreases for the 20Ne and 22Ne nuclei and rises again when the orbits become full.