Neutron Orbitals Research Articles

Investigation of quasi-particle structure of proton-hole indium nuclei

The present work focuses on the successful application of the Projected Shell Model (PSM) in studying the yrast bands of neutron-rich odd-mass 111-119In nuclei. For these isotopes, the band structures have been analyzed in terms of quasi-particles configurations. The phenomenon of rotational alignment and back bending in moment of inertia is also studied in the present work. The intrinsic structure of 111-119In nuclei in the present study has also been described as arising due to an interplay between proton and neutron orbitals belonging to 1- and 3-qp configurations. Besides this, the reduced transition probabilities, B(E2) and B(M1) , are also obtained from the PSM wave functions.

Neutron-hole states in 131Sn and spin-orbit splitting in neutron-rich nuclei

In atomic nuclei, the spin-orbit interaction originates from the coupling of the orbital motion of a nucleon with its intrinsic spin. Recent experimental and theoretical works have suggested a weakening of the spin-orbit interaction in neutron-rich nuclei far from stability. To study this phenomenon, we have investigated the spin-orbit energy splittings of single-hole and single-particle valence neutron orbits of 132Sn. The spectroscopic strength of single-hole states in 131Sn was determined from the measured differential cross sections of the tritons from the neutron-removing 132Sn(d, t)131Sn reaction, which was studied in inverse kinematics at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. The spectroscopic factors of the lowest 3/2+, 1/2+ and 5/2+ states were found to be consistent with their maximal values of (2j+1), confirming the robust N=82 shell closure at 132Sn. We compared the spin-orbit splitting of neutron single-hole states in 131Sn to those of single-particle states in 133Sn determined in a recent measurement of the 132Sn(d, p)133Sn reaction. We found a significant reduction of the energy splitting of the weakly bound 3p orbits compared to the well-bound 2d orbits, and that all the observed energy splittings can be reproduced remarkably well by calculations using a one-body spin-orbit interaction and a Woods–Saxon potential of standard radius and diffuseness. The observed reduction of spin-orbit splitting can be explained by the extended radial wavefunctions of the weakly bound orbits, without invoking a weakening of the spin-orbit strength.

Investigation of nonlinear isoscalar–isovector coupling in a relativistic mean-field model by elastic magnetic electron scattering

In this paper, we study the sensitivity of single valence neutron properties and elastic magnetic form factors to three different relativistic mean-field (RMF) parameter sets: NL3, FSUGold, and IU-FSU. To perform our calculation, seven odd-A nuclei having single valence neutron on top of a magic neutron core: Be7, O17, Ca41, Ni57, Zr91, Ba139, and Pb209 are considered as model nuclei. The wave-function of the outer most neutron orbit, matter density, valence neutron density, and magnetic form factors are numerically calculated. It is shown that there are significant differences between the magnetic form factors in the mediate- and high-momentum transfer regions when calculate with different parameter sets. Such separation is more evident with larger nuclear mass and isospin asymmetry. By fitting to the experimental data, the spectroscopic factors for O17 and Ca41 are obtained. From the fitting, we infer that including the isoscalar–isovector meson self-coupling can give a better performance of the RMF calculation.

Low-energy quadrupole states in neutron-rich tin nuclei

We present a study on the isoscalar quadrupole strength in tin nuclei, focusing mainly on the low-energy region. The calculations are performed using the Skyrme type energy density functionals within the fully self-consistent quasiparticle random phase approximation, allowing for a good description of the experimental data for the first 2$^+$ state and the isoscalar giant quadrupole resonance. It is found that the first $2^+$ state and the low-energy quadrupole states between 3 and 6 MeV display an opposite behavior with increasing neutron number. While the strength of the first $2^+$ state decreases, some excited states start to accumulate between 3 and 6 MeV, and increase their strength with increasing neutron number. This low-energy region between 3 and 6 MeV is quite sensitive to the changes in the shell structure with increasing neutron number. In particular, between $^{116}$Sn and $^{132}$Sn, the filling of the neutron orbitals with large values of $j$, has an important impact on the low-energy region. Our analysis shows that the low-energy states have a non-collective character, except the first 2$^+$ state. In addition, the states in the low-energy region above 5 MeV display an interesting pattern: with the increase of the neutron number, their strength increases and their nature changes, namely they switch from proton excitations to neutron-dominated one. We conclude that the low-energy quadrupole states between 3 and 6 MeV can provide information about the shell evolution in open-shell nuclei.

Neutron knockout from 68,70Ni ground and isomeric states.

Neutron-rich isotopes are an important source of new information on nuclear physics. Specifically, the spin-isospin components in the nucleon-nucleon (NN) interaction, e.g., the proton-neutron tensor force, are expected to modify shell structure in exotic nuclei. These potential changes in the intrinsic shell structure are of fundamental interest. The study of the excitation energy of states corresponding to specific configurations in even-even isotopes, together with the single-particle character of the first excited states of odd-A, neutron-rich Ni isotopes, probes the evolution of the neutron orbitals around the Fermi surface as a function of the neutron number a step forward in the understanding of the region and the nature of the NN interaction at large N/Z ratios.In an experiment carried out at the National Superconducting Cyclotron Laboratory [1], new spectroscopic information was obtained for 68Ni and the distribution of single-particle strengths in 67,69Ni was characterized by means of single-neutron knockout from 68,70Ni secondary beams. The spectroscopic strengths, deduced from the measured partial cross sections to the individual states tagged by their de-exciting gamma rays, is used to identify and quantify configurations that involve neutron excitations across the N = 40 harmonic oscillator shell closure. The de-excitation γ rays were measured with the GRETINA tracking array [2].The results challenge the validity of the most current shell-model Hamiltonians and effective interactions, highlighting shortcomings that cannot yet be explained. These results suggest that our understanding of the low-energy states in such nuclei is not complete and requires further investigation.

Isomers and shell evolution in neutron-rich nuclei below the doubly magic nucleus 132Sn

The level structures of the very neutron-rich nuclei 128Pd82 and 126Pd80 have been investigated for the first time. A new isomer with a half-life of 5.8(8) μs in 128Pd is proposed to have a spin and parity of 8+ and is associated with a maximally aligned configuration arising from the g9/2Pd proton subshell with seniority υ = 2. The level sequence below the 8+ isomer is similar to that in the N = 82 isotone 130Cd, but the electric quadrupole transition that depopulates the 8+ isomer is more hindered in 128Pd than in 130Cd, as expected in the seniority scheme for a semi-magic, spherical nucleus. For 126Pd, three new isomers with Jπ = (5-), (7-), and (10+) have been identified with half-lives of 0.33(4) μs, 0.44(3) μs, and 23.0(8) ms, respectively. The smaller energy difference between the 10+ and 7- isomers in 126Pd than in the heavier N = 80 isotones can be interpreted as being ascribed to the monopole shift of the h11/2 neutron orbit. The nature of the N = 82 shell closure scrutinized with these characteristic isomers is discussed.

Reinvestigation of the excited states in the proton emitter Lu151 : Particle-hole excitations across the N=Z=64 subshell

The excited states of the proton emitter Lu151 were reinvestigated in a recoil-decay tagging experiment at the Accelerator Laboratory of the University of Jyväskylä (JYFL). The level scheme built on the ground state of Lu151 was updated with five new γ-ray transitions. Large-scale shell model calculations were carried out in the model space consisting of the neutron and proton orbitals 0g7/2, 1d5/2, 1d3/2, 2s1/2, and 0h11/2 with the optimized monopole interaction in order to interpret the experimental level scheme of Lu151. It is found that the excitation energies of states above the 27/2− and 23/2+ isomeric levels in Lu151 can be sensitive to excitations from g7/2 and d5/2 to single-particle orbitals above N=Z=64.Received 11 October 2017DOI:https://doi.org/10.1103/PhysRevC.96.064307©2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectromagnetic transitionsEnergy levels & level densitiesLow & intermediate energy heavy-ion reactionsNuclear spin & parityNuclear structure & decaysProton emissionShell modelProperties150 ≤ A ≤ 189Nuclear Physics

Parity-doublet structure in the La9057147 nucleus

Excited states in $^{147}\mathrm{La}$, populated in spontaneous fission of $^{252}\mathrm{Cf}$, have been reinvestigated by means of $\ensuremath{\gamma}$-ray spectroscopy, using high-fold $\ensuremath{\gamma}$-ray coincidences measured with the Gammasphere array of Ge detectors. The 229.5-keV level, which has been assigned spin parity $9/{2}^{\ensuremath{-}}$ in a recent evaluation, is shown to have spin parity $11/{2}^{\ensuremath{-}}$. Consequently, the ground state has spin parity $5/{2}^{+}$. Excited levels in $^{147}\mathrm{La}$ have been arranged into a parity-doublet structure, showing that at medium excitation energy the $^{147}\mathrm{La}$ nucleus may have octupole deformation. The $B(E1)$ rates in $^{147}\mathrm{La}$, which are factor of four lower than in $^{145}\mathrm{La}$, suggest that the electric dipole moment in $^{147}\mathrm{La}$ is depressed by an extra mechanism, probably connected with the population of particular neutron orbitals.

Emergence of low-energy monopole strength in the neutron-rich calcium isotopes

The isoscalar monopole response of neutron-rich nuclei is sensitive to both the incompressibility coefficient of symmetric nuclear matter and the density dependence of the symmetry energy. The main goal of this paper is to explore the emergence, evolution, and origin of low energy monopole strength along the even-even calcium isotopes: from 40Ca to 60Ca. The distribution of isoscalar monopole strength is computed in a relativistic random phase approximation (RPA) using three effective interactions that have been calibrated to the properties of finite nuclei and neutron stars. A non-spectral approach is adopted that allows for an exact treatment of the continuum without any reliance on discretization. For the stable calcium isotopes, no evidence of low-energy monopole strength is observed, even as the 1f7/2 neutron orbital is being filled and the neutron-skin thickness progressively grows. Further, in contrast to experimental findings, a mild softening of the monopole response with increasing mass number is predicted. Beyond 48Ca, a significant amount of low-energy monopole strength emerges as soon as the weak-binding neutron orbitals (2p and 1f5/2) become populated. The emergence and evolution of low-energy strength is identified with transitions from these weakly-bound states into the continuum. Moreover, given that models with a soft symmetry energy tend to reach the neutron-drip line earlier than their stiffer counterparts, we identify an inverse correlation between the neutron-skin thickness and the inverse energy weighted sum.

Covalent Binding with Neutrons on the Femto-scale

In light nuclei we have well defined clusters, nuclei with closed shells, which serve as centers for binary molecules with covalent binding by valence neutrons. Single neutron orbitals in light neutron-excess nuclei have well defined shell model quantum numbers. With the combination of two clusters and their neutron valence states, molecular two-center orbitals are defined; in the two-center shell model we can place valence neutrons in a large variety of molecular two-center states, and the formation of Dimers becomes possible. The corresponding rotational bands point with their large moments of inertia and the Coriolis decoupling effect (for K = 1/2 bands) to the internal molecular orbital structure in these states. On the basis of these the neutron rich isotopes allow the formation of a large variety molecular structures on the nuclear scale. An extended Ikeda diagram can be drawn for these cases. Molecular bands in Be and Ne-isotopes are discussed as text-book examples.

Abrupt shape transition at neutron number N=60 : B(E2) values in Sr94,96,98 from fast γ−γ timing

Lifetimes of low-lying yrast states in neutron-rich 94,96,98Sr have been measured by Germanium-gated γ−γ fast timing with LaBr3(Ce) detectors using the EXILL&FATIMA spectrometer at the Institut Laue-Langevin. Sr fission products were generated using cold-neutron-induced fission of 235U and stopped almost instantaneously within the thick target. The experimental B(E2) values are compared with results of Monte Carlo shell-model calculations made without truncation on the occupation numbers of the orbits spanned by eight proton and eight neutron orbits and show good agreement. Similarly to the Zr isotopes, the abrupt shape transition in the Sr isotopes near neutron number N=60 is identified as being caused by many-proton excitations to its g9/2 orbit.

Shell structure of 107,109Ag nuclei and spin–parities nuclei in which the 1 g9/2 orbit is being filled

Occupation numbers and energies of proton and neutron orbits in the isotopes 107Ag and 109Ag were obtained on the basis of data on nucleon-stripping and nucleon-pickup reactions. A special data-analysis method reducing systematic and statistical uncertainties was applied in relevant calculations. It is shown that, in this region, the spin–parity of nuclei is determined by shells, pairing, and polarization. The schemes of proton and neutron (sub)orbits were constructed. These schemes explain the ground-state spin–parities of N, Z = 39–49 nuclei.

Direct Evidence for Octupole Deformation in ^{146}Ba and the Origin of Large E1 Moment Variations in Reflection-Asymmetric Nuclei.

Despite the more than 1 order of magnitude difference between the measured dipole moments in ^{144}Ba and ^{146}Ba, the octupole correlations in ^{146}Ba are found to be as strong as those in ^{144}Ba with a similarly large value of B(E3;3^{-}→0^{+}) determined as 48(+21-29) W.u. The new results not only establish unambiguously the presence of a region of octupole deformation centered on these neutron-rich Ba isotopes, but also manifest the dependence of the electric dipole moments on the occupancy of different neutron orbitals in nuclei with enhanced octupole strength, as revealed by fully microscopic calculations.

Quantum Phase Transition in the Shape of Zr isotopes.

The rapid shape change in Zr isotopes near neutron number N=60 is identified to be caused by type II shell evolution associated with massive proton excitations to its 0g_{9/2} orbit, and is shown to be a quantum phase transition. MonteCarlo shell-model calculations are carried out for Zr isotopes of N=50-70 with many configurations spanned by eight proton orbits and eight neutron orbits. Energy levels and B(E2) values are obtained within a single framework in good agreement with experiment, depicting various shapes in going from N=50 to 70. The novel coexistence of prolate and triaxial shapes is suggested.

Ordering of the0d5/2and1s1/2proton levels in light nuclei

A survey of the available single-proton data in $A\leq17$ nuclei, along with calculations using a Woods-Saxon potential, show that the ordering of the $0d_{5/2}$ and $1s_{1/2}$ proton orbitals are determined primarily by the proximity of the $s$-state proton energy to the Coulomb barrier. This is analogous to the dependence of the corresponding neutron orbitals in proximity to the neutron threshold, that was previously discussed.

Electromagnetic Properties of the I π = 11/2− isomers in the cadmium isotopes: What can we learn from them?

The electromagnetic features of the 11/2− isomers in the odd-mass Cd isotopes are shown to exhibit an an anomaly near N = 70. We report shell-model calculations of these isotopes aimed at describing these properties. We find a sudden phase change in the hexadecapole component of the wave functions precisely at N = 70, which gives rise to different linear relations between the Q and μ values before and after N = 70, as needed to reproduce the experimental data. The particle-hole transformation properties associated with a strong subshell closure at N = 70 followed by fairly close-lying neutron orbitals from N = 70 − 82 is suggested as a possible explanation for this phase change.

Towards Superheavies: Spectroscopy of 94 < Z < 98, 150 < N < 154 Nuclei

The heaviest nuclei where excitations above the ground state can be studied lie near Z ~ 100. These nuclear structure studies are important testing grounds for theoretical models that aim to describe superheavy nuclei. To study the highest neutron orbitals (150 ≤ N ≤ 154), we have populated high angular momentum states in a series of Pu (Z = 94), Cm (Z = 96) and Cf (Z = 98) nuclei, via inelastic and transfer reactions, with heavy beams on long-lived radioactive actinide targets. Multiple collective excitation modes and structures were identified, and their configurations deduced. Quasiparticle alignments are mapped, with odd-A band structures helping identify specific orbital contributions via blocking arguments. Higher-order multipole shapes are observed to play a significant role in disentangling competing neutron and proton alignments. The N > 152 data provide new perspectives on physics beyond the N = 152 sub-shell gap.

Advanced density matrix renormalization group method for nuclear structure calculations

We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various concepts of quantum information theory. We first show how this new DMRG methodology could solve a previous $400$ KeV discrepancy in the ground state energy of $^{56}$Ni. We then report the first DMRG results in the $pf+g9/2$ shell model space for the ground $0^+$ and first $2^+$ states of $^{64}$Ge which are benchmarked with reference data obtained from Monte Carlo shell model. The corresponding correlation structure among the proton and neutron orbitals is determined in terms of the two-orbital mutual information. Based on such correlation graphs we propose several further algorithmic improvement possibilities that can be utilized in a new generation of tensor network based algorithms.

Search for the terminating27−state inNd140

In the search for the fully aligned ${27}^{\ensuremath{-}}$ state in $^{140}\mathrm{Nd}$ predicted by cranked Nilsson-Strutinsky calculations, new close-to-spherical high-spin states have been discovered. Both the close-to-spherical and the triaxial calculated states are in good agreement with the experimental results, supporting the existence of shape coexistence up to very high spins. Shell-model calculations using a newly developed effective interaction for the $50\ensuremath{\le}N,Z\ensuremath{\le}82$ mass region are in good agreement with the observed spherical states. The comparison between the experimental and calculated level energies allowed the relative energy to be established between several proton and neutron orbitals at high energy and spins.

Analytical continuation from bound to resonant states in the Dirac equation with quadrupole-deformed potentials

Background: Resonances with pronounced single-particle characteristics are crucial for quantitative descriptions of exotic nuclei near and beyond the drip lines, and often impact halo formation and nucleon decay processes. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold can lead to improved descriptions of exotic nuclei.Purpose: Develop a method to study single-particle resonant orbital structure in the Dirac equation with a quadrupole-deformed Woods-Saxon potential. Determine the structure evolution of bound and resonant levels with deformation in this scheme, and examine the impact on halo formation in loosely bound systems, with a focus on the recent halo candidate nucleus $^{37}\mathrm{Mg}$.Method: Analytical continuation of the coupling constant (ACCC) method is developed on the basis of the Dirac equation with a deformed Woods-Saxon potential. The scalar and vector terms in the deformed potential are determined by the energies of the valence neutron and nearby orbitals, which are extracted from a self-consistent relativistic Hartree-Bogoliubov (RHB) calculation with the PC-PK1 density functional.Results: We compare the energies and widths of resonant orbitals in the recent halo nucleus candidate $^{37}\mathrm{Mg}$ using the ACCC method based on the Dirac coupled-channel equations with those determined from the scattering phase shift (SPS) method. It is found that the results from the two methods agree well for narrow resonances, whereas the SPS method fails for broad resonances. Nilsson levels for bound and resonant orbitals from the ACCC method are calculated over a wide range of deformations and show some decisive hints of halo formation in $^{37}\mathrm{Mg}$.Conclusions: In our ACCC model for deformed potentials in the coupled-channel Dirac equations, the crossing of the configuration $1/2[321]$ and $5/2[312]$ orbitals at a deformation of approximately 0.5 enhances the probability to occupy the $1/2[321]$ orbital coming from $2{p}_{3/2}$ thereby explaining the recent observation of a $\mathit{p}$-wave one-neutron halo configuration in $^{37}\mathrm{Mg}$. The resonant $1/2[301]$ configuration plays a crucial role in halo formation in the magnesium isotopes beyond $A=40$ for a wide range of deformations larger than 0.2.