Closed-shell Nuclei Research Articles

Zeeman Effect at Explosive Nuclide Formation

Nuclear structure and composition in ultra-strong magnetic fields relevant for heavy-ion collisions, supernovae, andmagnetar crusts are analyzed. For field intensities exceeding 0.1 teratesla (TT) nuclear magnetic response is represented as combined reactivity of valent outer-shell nucleons, exhibits linear regime up to a strength of ~10 TT and exceeds significantly nuclear g factor. The Zeeman effect leads to an increase of binding energies for open shell nuclei and a decrease for closed-shell nuclei. Noticeable enhancement and suppression in a yield of corresponding explosive nucleosynthesis products with antimagic and magic numbers corroborate with observational results.

Validity of the distorted-wave impulse-approximation description of Ca40(e,e′p)K39 data using only ingredients from a nonlocal dispersive optical model

The nonlocal implementation of the dispersive optical model (DOM) provides all the ingredients for distorted-wave impulse-approximation (DWIA) calculations of the $(e,e'p)$ reaction. It provides both the overlap function, including its normalization, and the outgoing proton distorted wave. This framework is applied to describe the knockout of a proton from the $0\textrm{d}\frac{3}{2}$ and $1\textrm{s}\frac{1}{2}$ orbitals in ${}^{40}$Ca with fixed normalizations of 0.71 and 0.60, respectively. Data were obtained in parallel kinematics for three outgoing proton energies: 70, 100, and 135 MeV. Agreement with the data is as good as, or better than, previous descriptions employing local optical potentials and overlap functions from Woods-Saxon potentials - both with standard nonlocality corrections - whose normalization (spectroscopic factor) and radius were fitted to the data. The present analysis suggests that slightly larger spectroscopic factors are obtained when nonlocal optical potentials are employed than those generated with local potentials. The results further suggest that the chosen kinematical window around 100 MeV proton energy provides the best and cleanest method to employ the DWIA for the analysis of this reaction. The conclusion that substantial ground-state correlations cannot be ignored when describing a closed-shell atomic nucleus is therefore confirmed in detail. To reach these conclusions, it is essential to have a complete description of the nucleon single-particle propagator that accounts for all elastic nucleon-scattering observables in a wide energy domain up to 200 MeV. The current nonlocal implementation of the DOM fulfills this requirement.

Woods-Saxon-Gaussian potential and alpha-cluster structures of alpha + closed shell nuclei**Supported by the National Natural Science Foundation of China (11535004, 11761161001, 11375086, 11120101005, 11175085, 11235001), the National Key R&D Program of China (2018YFA0404403, 2016YFE0129300) and the Science and Technology Development Fund of Macau (008/2017/AFJ)

The Woods-Saxon-Gaussian (WSG) potential is proposed as a new phenomenological potential to systematically describe the level scheme, electromagnetic transitions, and alpha-decay half-lives of the alpha-cluster structures in various alpha + closed shell nuclei. It modifies the original Woods–Saxon (WS) potential with a shifted Gaussian factor centered at the nuclear surface. The free parameters in the WSG potential are determined by reproducing the correct level scheme of 212Po=208Pb+α. It is found that the resulting WSG potential matches the M3Y double-folding potential at the surface region and makes corrections to the inner part of the cluster-core potential. It was also determined that the WSG potential, with nearly identical parameters to that of 212Po (except for a rescaled radius), could also be used to describe alpha-cluster structures in 20Ne=16O+α and 44Ti=40Ca+α. In all three cases, the calculated values of the level schemes, electromagnetic transitions, and alpha-decay half-lives agree with the experimental data, which indicates that the WSG potential could indeed capture many important features of the alpha-cluster structures in alpha + closed shell nuclei. This study is a useful complement to the existing cluster-core potentials in literature. The Gaussian form factor centered at the nuclear surface might also help to improve our understanding of the alpha-cluster formation, which occurs in the same general region.

Combining symmetry breaking and restoration with configuration interaction: Extension to z -signature symmetry in the case of the Lipkin model

Background: Ab initio many-body methods whose numerical cost scales polynomially with the number of particles have been developed over the past fifteen years to tackle closed-shell mid-mass nuclei. Open-shell nuclei have been further addressed by implementing variants based on the concept of spontaneous symmetry breaking (and restoration). Purpose: In order to access the spectroscopy of open-shell nuclei more systematically while controlling the numerical cost, we design a novel many-body method that combines the merit of breaking and restoring symmetries with those brought about by low-rank individual excitations. Methods: The recently proposed truncated configuration-interaction method based on optimized symmetry-broken and -restored states is extended to the z-signature symmetry associated with a discrete subgroup of SU(2). The highly-truncated N-body Hilbert subspace within which the Hamiltonian is diagonalized is spanned by a z-signature broken and restored Slater determinant vacuum and associated low-rank excitations. Results: The proposed method provides an excellent reproduction of the ground-state energy and of low-lying excitation energies of various z-signatures and total angular momenta. In doing so, the successive benefits of (i) breaking the symmetry, (ii) restoring the symmetry, (iii) including low-rank particle-hole excitations and (iv) optimizing the amount by which the underlying vacuum breaks the symmetry are illustrated. Conclusions: The numerical cost of the newly designed variational method is polynomial with respect to the system size. The present study confirms the results obtained previously for the attractive pairing Hamiltonian in connection with the breaking and restoration of U(1) global gauge symmetry. These two studies constitute a strong motivation to apply this method to realistic nuclear Hamiltonians.

Microscopic optical potential obtained from energy-density-functional approach for neutron–nucleus elastic scattering

Nucleon–nucleus (NA) optical potentials are microscopically generated from a fully self-consistent framework of the particle-vibration coupling (PVC), in which the nucleon–nucleon (NN) effective interaction of the Skyrme type is consistently used to describe the Hartree–Fock (HF) mean-field, the small amplitude collective motions of the target, and the particle-collective states coupling. For the first time, a systematic calculation of low-energy NA elastic scattering off a series of doubly closed-shell nuclei is carried out without ad hoc adjusted parameters. Angular distributions obtained using the present optical potentials are in good agreement with the experimental data. This will be a major step forward in the applications of the Skyrme energy-density-functional theory to build up the global microscopic optical potentials, which are expected to be a powerful tool for the study of unstable (exotic) nuclei at low-incident nucleon energies.

Zeeman splitting in structure and composition of ultramagnetized spherical nuclei

Properties and mass distribution of ultramagnetized atomic nuclei that arise in heavy-ion collisions, magnetar crusts, during Type II supernova explosions and neutron star mergers are analyzed. For magnetic field strength range 0.1–10 teratesla the Zeeman effect leads to linear nuclear magnetic response with susceptibility parameter exceeding significantly nuclear g-factor. Respectively, binding energies increase for open shell and decrease for closed shell nuclei. Noticeable enhancement in a yield of corresponding explosive nucleosynthesis products with antimagic numbers corroborate with observational results.

Chiral NNLOsat descriptions of nuclear multipole resonances within the random-phase approximation

We study nuclear multipole resonances in the framework of the random phase approximation using the chiral potential NNLO$_{\text{sat}}$. This potential includes two- and three-body terms that has been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main foci have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, $^4$He, $^{16,22,24}$O, and $^{40,48}$Ca. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential $V_{\text{low-}k}$, based on the N$^3$LO two-body potential by Entem and Machleidt [Phys. Rev. \textbf{C68}, 041001 (2011)]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLO$_{\text{sat}}$ can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the $V_{\text{low-}k}$ potential that simultaneously describe the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich $^{22,24}$O show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that $^{22}$O and $^{24}$O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. The first component of this functional is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. A second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. We obtain a set of microscopically-constrained functionals for local chiral potentials from leading-order up to next-to-next-to-leading order with and without three-body forces and contributions from $\Delta$ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei and the fission barrier of $^{240}$Pu. Quantitatively, they perform noticeable better than the more phenomenological Skyrme functionals. The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies. This result is especially promising since all the fits have been performed at the single reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction have not been taken into account yet.

Interplay of quasiparticle-vibration coupling and pairing correlations on β-decay half-lives

The nuclear β-decay half-lives of Ni and Sn isotopes, around the closed shell nuclei 78Ni and 132Sn, are investigated by computing the distribution of the Gamow–Teller strength using the Quasiparticle Random Phase Approximation (QRPA) with quasiparticle-vibration coupling (QPVC), based on ground-state properties obtained by Hartree–Fock–Bogoliubov (HFB) calculations. We employ the effective interaction SkM⁎ and a zero-range effective pairing force. The half-lives are strongly reduced by including the QPVC. We study in detail the effects of isovector (IV) and isoscalar (IS) pairing. Increasing the IV strength tends to increase the lifetime for nuclei in the proximity of, but lighter than, the closed-shell ones in QRPA calculations, while the effect is significantly reduced by taking into account the QPVC. On the contrary, the IS pairing mainly plays a role for nuclei after the shell closure. Increasing its strength decreases the half-lives, and the effect at QRPA and QRPA+QPVC level is comparable. The effect of IS pairing is particularly pronounced in the case of the Sn isotopes, where it turns out to be instrumental to obtain good agreement with experimental data.

Doubly magic nuclei from lattice QCD forces at MPS=469MeV/c2

We perform ab initio self-consistent Green's function calculations of the closed shell nuclei $^{\rm 4}$He, $^{\rm 16}$O and $^{\rm 40}$Ca, based on two-nucleon potentials derived from Lattice QCD simulations, in the flavor SU(3) limit and at the pseudo-scalar meson mass of 469~MeV/c$^{\rm 2}$. The nucleon-nucleon interaction is obtained using the HAL QCD method and its short-distance repulsion is treated by means of ladder resummations outside the model space. Our results show that this approach diagonalises ultraviolet degrees of freedom correctly. Therefore, ground state energies can be obtained from infrared extrapolations even for the relatively hard potentials of HAL QCD. Comparing to previous Brueckner Hartree-Fock calculations, the total binding energies are sensibly improved by the full account of many-body correlations. The results suggest an interesting possible behaviour in which nuclei are unbound at very large pion masses and islands of stability appear at first around the traditional doubly-magic numbers when the pion mass is lowered toward its physical value. The calculated one-nucleon spectral distributions are qualitatively close to those of real nuclei even for the pseudo-scalar meson mass considered here.

Shell Evolution and E2 Collectivity: New Spectroscopic Information

New spectroscopic information on electric quadrupole collectivity has recently been obtained. We report on our identification of a coexisting deformed structure in the quasi-doubly closed-shell nucleus 96Zr from our measurement of a corresponding absolute E2 intraband transition strength in electron scattering reactions and its small mixing matrix element with the spherical ground state structure. The even-mass zirconium isotopes exhibit a first order quantum shape phase transition between neutron numbers 58 and 60. We have used photon scattering reactions for a first measurement of the E2 decay strength of the nuclear 1+ scissors mode. Evidence for its 2+ rotational excitation and its extraordinarily large rotational moment of inertia are presented.

Systematic study of unfavored α -decay half-lives of closed-shell nuclei related to ground and isomeric states

In present work, the unfavored $\mathcal{\alpha}$ decay half-lives and $\mathcal{\alpha}$ preformation probabilities of closed shell nuclei related to ground and isomeric states around $Z=82$, $N=82$ and 126 shell closures are investigated by adopting two-potential approach from the perspective of valence nucleon (hole) and isospin asymmetry of the parent nucleus. The results indicate that $\mathcal{\alpha}$ preformation probability is linear dependence on $N_p N_n$ or $N_p N_n I$, the same as the case of favored $\mathcal{\alpha}$ decay in our previous work [X.-D. Sun \textit{et al.}, Phys. Rev. C 94, 024338 (2016)]. $N_p$, $N_n$, and $I$ represent the number of valence protons (holes), the number of valence neutrons (holes), and the isospin of the parent nucleus, respectively. Fitting the $\mathrm{\alpha}$ preformation probabilities data extracted from the differences between experimental data and calculated half-lives without a shell correction, we give two linear formulas of the $\mathcal{\alpha}$ preformation probabilities and the values of corresponding parameters. Based on the formulas and corresponding parameters, we calculate the $\mathrm{\alpha}$ decay half-lives for those nuclei. The calculated results can well reproduce the experimental data.

Charge distribution in the ternary fragmentation of 252Cf

We present here, for the first time, a study on ternary fragmentation charge distribution of 252Cf using the convolution integral method and the statistical theory. The charge distribution for all possible charge combinations of a ternary breakup are grouped as a bin containing different mass partitions. Different bins corresponding to various third fragments with mass numbers from $ A_3 = 16$ to 84 are identified with the available experimental masses. The corresponding potential energy surfaces are calculated using the three cluster model for the two arrangements $ A_1 + A_2 + A_3$ and $ A_1 + A_3 + A_2$ . The ternary fragmentation yield values are calculated for the ternary combination from each bin possessing minimum potential energy. The yields of the resulting ternary combinations as a function of the charge numbers of the three fragments are analyzed for both the arrangements. The calculations are carried out at different excitation energies of the parent nucleus. For each excitation energy the temperature of the three fragments are iteratively computed conserving the total energy. The distribution of fragment temperatures corresponding to different excitation energies for some fixed third fragments are discussed. The presence of the closed shell nucleus Sn in the favourable ternary fragmentation is highlighted.

Saturation with chiral interactions and consequences for finite nuclei

We explore the impact of nuclear matter saturation on the properties and systematics of finite nuclei across the nuclear chart. Using the ab initio in-medium similarity renormalization group (IM-SRG), we study ground-state energies and charge radii of closed-shell nuclei from $^4$He to $^{78}$Ni, based on a set of low-resolution two- and three-nucleon interactions that predict realistic saturation properties. We first investigate in detail the convergence properties of these Hamiltonians with respect to model-space truncations for both two- and three-body interactions. We find one particular interaction that reproduces well the ground-state energies of all closed-shell nuclei studied. As expected from their saturation points relative to this interaction, the other Hamiltonians underbind nuclei, but lead to a remarkably similar systematics of ground-state energies. Extending our calculations to complete isotopic chains in the $sd$ and $pf$ shells with the valence-space IM-SRG, the same interaction reproduces not only experimental ground states but two-neutron-separation energies and first excited $2^+$ states. We also calculate radii with the valence-space IM-SRG for the first time. Since this particular interaction saturates at too high density, charge radii are still too small compared with experiment. Except for this underprediction, the radii systematics is, however, well reproduced. Our results highlight the importance of nuclear matter as a theoretical benchmark for the development of next-generation chiral interactions.

Fragments mass and charge distribution in the light particle accompanied fission of 252Cf

The ternary fission mass and charge distribution of 252Cf for different light third fragments (A3 = 4He, 10Be, 14C, 20O, 20Ne and 24Ne) are studied with the use of statistical theory of fission. Two different approaches are adopted to generate the possible ternary fragment combinations: in one case, the Z/A of the products is the same as 252Cf, in the other the finite-range droplet model (FRDM) data are used, creating all the possible combinations also with different Z/A. For the calculation of the nuclear level densities, single-particle level energies of FRDM are also used. When the lighter fragment A3 is 4He, our calculated mass and charge distribution results, at T = 1 MeV, show the larger yield for the deformed fragment combinations which is in line with the experimental observation. Interestingly, for various third fragments, our calculated results at T = 2 MeV indicate that the favorable ternary configuration contains closed shell nucleus either Pb or Sn as the heaviest fragment. In addition, we have compared our calculated ternary isotopic yields with the available experimental and theoretical data.

Ab initioexcited states from the in-medium similarity renormalization group

We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of $1$p$1$h excitations) becomes exact for a subset of eigenvalues. In the second approach, equations-of-motion (EOM) techniques are applied to the ground-state-decoupled IMSRG Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two-dimensions and the closed shell nuclei $^{16}$O and $^{22}$O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster (EOM-CC) calculations, which paves the way for more interesting applications of the EOM-IMSRG to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within 1-2 nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

Binary Fission fragmentation of 184 466,476X

Based on the statistical theory of fission, we discuss here the binary fission fragmentation of these giant nuclear systems formed in low energy U+U collisions. Here, the mass and charge distribution of fragments from the binary fission of thesesystems are studied at T= 1 and 2 MeV. From our results at T= 1 MeV, fragments in the near-asymmetric and near-symmetric regions pronounce higher yield values. However, at T= 2 MeV, our results are grossly different. Furthermore, the binary fragmentation with the largest yield consists of at least one closed shell nucleus. Different possible binary fission modes are presented to look for U+Ugiant nuclear systems.

Quark mean field model with pion and gluon corrections

The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pion and gluon into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pion and gluon on the nucleon structure are treated in second-order perturbation theory. For the nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, $m_q$, we determine three parameter sets about the coupling constants between mesons and quarks, named as QMF-NK1, QMF-NK2, and QMF-NK3 by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give satisfactory description on properties of nuclear matter and finite nuclei, meanwhile they can also predict the larger neutron star mass around $2.3M_\odot$ without the hyperon degrees of freedom.

Ab initionuclear many-body perturbation calculations in the Hartree-Fock basis

Starting from realistic nuclear forces, the chiral N$^3$LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, $^4$He and $^{16}$O. The two-body N$^3$LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the anti-symmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation propabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available and find good agreement. This supports the conclusion that our methods produce reasonably converged results with these interactions. We also compare our results with experimental data.

English

The simple local optical potential adopted in analyzing successfully elastic scattering data in the delta resonance region has been emphasized here. This is based on obtaining the same nature for the potential by extracting potential points from available  phase shifts at 114, 163, 240 and 340 MeV using inverse scattering theory within the framework of Klein-Gordon equation.  Luckily, and as expected, the obtained analytical potential form has also been used successfully in accounting for the experimental angular distributions at another nearby four energies, namely 170, 220, 230, and 270 MeV. At energies considered herein, the calculated reaction cross sections are in good agreement with available experimental ones, and are in spectral match with experimental ones. The nature of the real part of the potential showed a change from attractive to repulsive at about 200 MeV, and the imaginary part is dominated by the surface absorption term. In treating the pion-nucleus scattering problem, we found that there is no privacy for a doubly closed-shell self-conjugate target nucleus compared to another nucleus, at least  light bound nucleus, and for incident pion energies in the domain of the delta resonance region. Instead, it seems that the description of the scattering process is mainly attributed to the geometrical structure of the target nucleus. This is a first time corollary, and more investigations are needed. Key words: Pion-nucleus potential, elastic scattering, inverse scattering theory, high energy physics.