Subshell Closure Research Articles

Sub-shell closure and shape coexistence in the transitional nucleus Zr 98

Sub-shell closure and shape coexistence in the transitional nucleus Zr 98

Evolution of single-particle structure of silicon isotopes

New data on proton and neutron single-particle energies $E_{nlj}$ of Si isotopes with neutron number $N$ from 12 to 28 as well as occupation probabilities $N_{nlj}$ of single particle states of stable isotopes $^{28,30}$Si near the Fermi energy were obtained by the joint evaluation of the stripping and pick-up reaction data and excited state decay schemes of neighboring nuclei. The evaluated data indicate following features of single-particle structure evolution: persistence of $Z = 14$ subshell closure with $N$ increase, the new magicity of the number $N = 16$, and the conservation of the magic properties of the number $N = 20$ in Si isotopic chain. The features were described by the dispersive optical model. The calculation also predicts the weakening of $N = 28$ shell closure and demonstrates evolution of bubble-like structure of the proton density distributions in neutron-rich Si isotopes.

Nuclear shapes: Quest for triaxiality in 86Ge and the shape of 98Zr

The region of neutron-rich nuclei above the N = 50 magic neutron shell closure encompasses a rich variety of nuclear structure, especially shapeevolutionary phenomena. This can be attributed to the complexity of sub-shell closures, their appearance and disappearance in the region, such as the N = 56 sub shell or Z = 40 for protons. Structural effects reach from a shape phase transition in the Zr isotopes, over shape coexistence between spherical, prolate, and oblate shapes, to possibly rigid triaxial deformation. Recent experiments in this region and their main physics viewpoints are summarized.

Alpha decay properties of the semi-magic nucleus 219Np

The semi-magic nucleus 219Np was produced in the fusion reaction 187Re(36Ar, 4n)219Np at the gas-filled recoil separator SHANS (Spectrometer for Heavy Atoms and Nuclear Structure). A fast electronics system based on waveform digitizers was used in the data acquisition and the sampled pulses were processed by digital algorithms. The reaction products were identified using spatial and time correlations between the implants and subsequent α decays. According to the observed α-decay chain, an energy of Eα=9039(40) keV and a half-life of T1/2=0.15−0.07+0.72 ms were determined for 219Np. The deduced proton binding energy of 219Np fits well into the systematics, which gives another evidence of that there is no sub-shell closure at Z=92. The influence of the N=126 shell closure on the stability of Np isotopes is discussed within the framework of α-decay reduced widths.

Structure of Sc55 and development of the N=34 subshell closure

The low-lying structure of $^{55}$Sc has been investigated using in-beam $\gamma$-ray spectroscopy with the $^{9}$Be($^{56}$Ti,$^{55}$Sc+$\gamma$)$X$ one-proton removal and $^{9}$Be($^{55}$Sc,$^{55}$Sc+$\gamma$)$X$ inelastic-scattering reactions at the RIKEN Radioactive Isotope Beam Factory. Transitions with energies of 572(4), 695(5), 1539(10), 1730(20), 1854(27), 2091(19), 2452(26), and 3241(39) keV are reported, and a level scheme has been constructed using $\gamma\gamma$ coincidence relationships and $\gamma$-ray relative intensities. The results are compared to large-scale shell-model calculations in the $sd$-$pf$ model space, which account for positive-parity states from proton-hole cross-shell excitations, and to it ab initio shell-model calculations from the in-medium similarity renormalization group that includes three-nucleon forces explicitly. The results of proton-removal reaction theory with the eikonal model approach were adopted to aid identification of positive-parity states in the level scheme; experimental counterparts of theoretical $1/2^{+}_{1}$ and $3/2^{+}_{1}$ states are suggested from measured decay patterns. The energy of the first $3/2^{-}$ state, which is sensitive to the neutron shell gap at the Fermi surface, was determined. The result indicates a rapid weakening of the $N=34$ subshell closure in $pf$-shell nuclei at $Z>20$, even when only a single proton occupies the $\pi f_{7/2}$ orbital.

Fast-timing spectroscopy at ISOLDE

The advanced time-delayed (t) method has been used at ISOLDE since the relocation of the facility from the synchrocyclotron to the CERN proton synchrotron booster, a quarter of a century ago. The method was designed for precision measurements with low-intensity beams, achieving good efficiency and excellent time resolution with a compact setup. Over this time the technique has evolved to cope with the challenge of measuring lifetimes of complex level schemes of increasingly exotic nuclei populated in β decay. The ISOLDE facility provides unsurpassed opportunities to study many regions of the nuclide chart. The physics case encompasses topics of interest across the nuclide chart, including the evolution of shell structure around neutron shell and subshell closures such as N = 20, N = 40 and N = 50, shape coexistence, and octupole correlations in heavy nuclei. The recently commissioned ISOLDE decay station provides enhanced capabilities that will be fully exploited with the increased beam intensities available at the upcoming HIE-ISOLDE facility.

Generalized seniority states and isomers in tin isotopes

Isomeric studies in neutron-rich nuclei are a powerful tool for exploring structure at the nuclear extremes. In this paper we discuss the systematic features of the excitation energies and transition probabilities of Sn isotopes in the region N = 50–82 and present their basic understanding in terms of generalized seniority. We further use generalized seniority as a probe to explore the neutron-rich seniority isomers in 134–138Sn, and to validate the neutron single-particle energies beyond N = 82. We show that these isomers behave as generalized seniority isomers, where the so-called anomalous behavior of the isomer in 136Sn may be naturally explained. We support these results by shell model calculations, where the latest neutron single-particle energies of the N = 82–126 region have been used, and the i13/2 neutron single-particle energy has been suitably modified in the renormalized charge-dependent Bonn interaction. This entails a possible new subshell closure at N = 112 due to the suggested higher location of the i13/2 neutron orbital, also consistent with the choice of orbitals in the generalized seniority scheme. However, a small reduction in the f7/2 two-body matrix elements is still required in the shell model calculations to consistently reproduce the experimental level energies as well as the transition probabilities in 134–138Sn isotopes.

α-cluster breaking effects on cluster structures in12C

To clarify the effects of α-cluster breaking on 3α cluster structures in12C, we investigate12C using a hybrid model that combines the Brink-Bloch cluster model with the p3/2 subshell closure wave function. We have found that α-cluster breaking significantly changes the cluster structures of 0+ states through orthogonality to lower states. As a result of the structure changes of 0+ states, the band assignment for the state is changed. The state is likely to be the band-head of the state instead of the state because the present calculation reproduces experimental data of the low-lying states well with α-cluster breaking. We have found that this band can be considered a linear chain-like band from the analysis of the intrinsic structures.

Nuclear structure investigations of 84Sr and 86Sr using γ-ray spectroscopic methods

To investigate the low-spin structure of 84Sr and 86Sr, two fusion-evaporation experiments using the (p,2n) reaction have been performed. The data have been evaluated in terms of γ-ray spectroscopy, i.e. the level scheme was built up, branching intensities were determined, nuclear state spin and parity assignments were made after γγ angular correlation analyses. The previously known level scheme information was extended. In addition, lifetimes were determined by means of the Doppler Shift Attenuation Method (DSAM). In 86Sr, a new method for lifetime determinations, the Spectral Difference Method (SDM), was applied for the first time. In cases where all necessary input variables were known, reduced transition strengths were calculated with Monte Carlo simulated probability density functions. It is stressed that linear error propagation for the calculated errors of reduced transition strengths is not universally applicable. As both nuclei lie in the vicinity of the N=50 neutron shell closure and on a possible proton subshell closure of the 2p3/2 orbital at Z=38, Nuclear Shell Model calculations for 84Sr, 86Sr, and 88Sr have been performed in the truncated (2p3/2, 1f5/2, 2p1/2, 1g9/2) model space for protons and neutrons with the empirical JUN45 residual interaction. The comparison between experimental results and theoretical predictions show a large degree of consistency.

New short-lived isotope 223Np and the absence of the Z = 92 subshell closure near N = 126

The N=130 short-lived isotope 223Np was produced as evaporation residue (ER) in the fusion reaction 40Ar + 187Re at the gas-filled recoil separator Spectrometer for Heavy Atom and Nuclear Structure (SHANS). It was identified through temporal and spatial correlations with α decays of 215Ac and/or 211Fr, the third and fourth members of the α-decay chain starting from 223Np. The pileup signals of ER(223Np)–α(223Np)–α(219Pa) were resolved by using the digital pulse processing technique. An α decay with half-life of T1/2=2.15(52100) μs and energy of Eα=9477(44)keV was attributed to 223Np. Spin and parity of 9/2− were tentatively proposed for the ground state of 223Np by combining the reduced α-decay width and large-scale shell-model calculations. This assignment together with the proton separation energy disprove the existence of a Z=92 subshell closure.

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.

Identification of highly deformed even–even nuclei in the neutron- and proton-rich regions of the nuclear chart from the B(E2)↑ and E2 predictions in the generalized differential equation model

We identify here the possible occurrence of large deformations in the neutron- and proton-rich ([Formula: see text]-rich and [Formula: see text]-rich) regions of the nuclear chart from extensive predictions of the values of the reduced quadrupole transition probability [Formula: see text] for the transition from the ground state to the first [Formula: see text] state and the corresponding excitation energy [Formula: see text] of even–even nuclei in the recently developed generalized differential equation (GDE) model exclusively meant for these physical quantities. This is made possible from our analysis of the predicted values of these two physical quantities and the corresponding deformation parameters derived from them such as the quadrupole deformation [Formula: see text], the ratio of [Formula: see text] to the Weisskopf single-particle [Formula: see text] and the intrinsic electric quadrupole moment [Formula: see text], calculated for a large number of both known as well as hitherto unknown even–even isotopes of oxygen to fermium (0 to FM; [Formula: see text]–100). Our critical analysis of the resulting data convincingly support possible existence of large collectivity for the nuclides [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], whose values of [Formula: see text] are found to exceed 0.3 and even 0.4 in some cases. Our findings of large deformations in the exotic [Formula: see text]-rich regions support the existence of another “island of inversion” in the heavy-mass region possibly caused by breaking of the [Formula: see text] subshell closure.

Direct mass measurements of neutron-rich 86Kr projectile fragments and the persistence of neutron magic number N=32 in Sc isotopes**Supported by 973 Program of China (2013CB834401), the NSFC (U1232208, U1432125, 11205205, 11035007) and the Helmholtz-CAS Joint Research Group (HCJRG-108)

In this paper, we present direct mass measurements of neutron-rich 86Kr projectile fragments conducted at the HIRFL-CSR facility in Lanzhou by employing the Isochronous Mass Spectrometry (IMS) method. The new mass excesses of 52–54Sc nuclides are determined to be −40492(82), −38928(114), −34654(540) keV, which show a significant increase of binding energy compared to the reported ones in the Atomic Mass Evaluation 2012 (AME12). In particular, 53Sc and 54Sc are more bound by 0.8 MeV and 1.0 MeV, respectively. The behavior of the two neutron separation energy with neutron numbers indicates a strong sub-shell closure at neutron number N=32 in Sc isotopes.

Evidence for Increased neutron and proton excitations between 51 − 63Mn

The hyperfine structures of the odd-even 51−63Mn atoms (N=26−38) were measured using bunched beam collinear laser spectroscopy at ISOLDE, CERN. The extracted spins and magnetic dipole moments have been compared to large-scale shell-model calculations using different model spaces and effective interactions. In the case of 61,63Mn, the results show the increasing importance of neutron excitations across the N=40 subshell closure, and of proton excitations across the Z=28 shell gap. These measurements provide the first direct proof that proton and neutron excitations across shell gaps are playing an important role in the ground state wave functions of the neutron-rich Mn isotopes.

Low-Lying Structure of (50)Ar and the N=32 Subshell Closure.

The low-lying structure of the neutron-rich nucleus (50)Ar has been investigated at the Radioactive Isotope Beam Factory using in-beam γ-ray spectroscopy with (9)Be((54)Ca,(50)Ar+γ)X, (9)Be((55)Sc,(50)Ar+γ)X, and (9)Be((56)Ti,(50)Ar+γ)X multinucleon removal reactions at ∼220 MeV/u. A γ-ray peak at 1178(18) keV is reported and assigned as the transition from the first 2(+) state to the 0(+) ground state. A weaker, tentative line at 1582(38) keV is suggested as the 4(1)(+)→2(1)(+) transition. The experimental results are compared to large-scale shell-model calculations performed in the sdpf model space using the SDPF-MU effective interaction with modifications based on recent experimental data for exotic calcium and potassium isotopes. The modified Hamiltonian provides a satisfactory description of the new experimental results for (50)Ar and, more generally, reproduces the energy systematics of low-lying states in neutron-rich Ar isotopes rather well. The shell-model calculations indicate that the N=32 subshell gap in (50)Ar is similar in magnitude to those in (52)Ca and (54)Ti and, notably, predict an N=34 subshell closure in (52)Ar that is larger than the one recently reported in (54)Ca.

Evolution of quadrupole collectivity inN=80isotones toward theZ=64subshell gap: TheB(E2;21+→01+)value ofSm142

It was shown that the evolution of the $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ values in $N$ = 80 isotones from Te to Nd is affected by the underlying subshell structure. This manifests itself in the observation of the local suppression of the $B(E2)$ value at $Z=58$ with respect to the neighboring nuclei $^{136}\mathrm{Ba}$ and $^{140}\mathrm{Nd}$. To investigate this shell sensitivity toward the $Z=64$ subshell gap, the $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ value of the unstable nucleus $^{142}\mathrm{Sm}$ was measured utilizing the projectile Coulomb excitation technique. The radioactive ion beam (RIB) experiment was performed at the REX-ISOLDE facility at CERN. The $B(E2)$ value of $32\phantom{\rule{0.16em}{0ex}}(4)\phantom{\rule{0.16em}{0ex}}\mathrm{W}.\mathrm{u}.$ reflects the impact of the $\ensuremath{\pi}(1{g}_{7/2}\phantom{\rule{0.16em}{0ex}}2{d}_{5/2})$ subshell closure at $Z=64$ with respect to a linear scaling of collectivity with valence proton number.

Probing collectivity in Zn isotopes with one particle or hole outside theN=40subshell closure

The nuclear structure of the odd-mass $^{69}\mathrm{Zn}$ and $^{71}\mathrm{Zn}$ isotopes, with one hole or one particle outside the $N=40$ subshell closure, has been investigated by measuring the lifetime of excited states using the recoil distance Doppler-shift method. The nuclei of interest were produced in a deep-inelastic reaction in inverse kinematics with a $^{238}\mathrm{U}$ beam impinging on a $^{70}\mathrm{Zn}$ target. Single-particle and collective states were found to coexist at low energy in $^{69}\mathrm{Zn}$ and $^{71}\mathrm{Zn}$.

Effects ofα-cluster breaking on3α-cluster structures inC12

To clarify the effects of $\alpha$-cluster breaking on 3$\alpha$ cluster structures in $^{12}$C, we investigate $^{12}$C using a hybrid model that combines the Brink-Bloch cluster model with the $p_{3/2}$ subshell closure wave function. We have found that $\alpha$-cluster breaking caused by spin-orbit force significantly changes cluster structures of excited $0^{+}$ states through orthogonality to lower states. Spatially developed cluster components of the $0^{+}_{2}$ state are reduced. The $0^{+}_{3}$ state changes from a vibration mode in the bending motion of three $\alpha$ clusters to a chain-like 3$\alpha$ structure having an open triangle configuration. As a result of these structure changes of $0^{+}$ states, the band assignment for the $2^{+}_{2}$ state is changed by the $\alpha$-cluster breaking effect. Namely, in model calculations without the $\alpha$-cluster breaking effect, the $0^{+}_{2}$ state is assigned to be the band-head of the $2^{+}_{2}$ state. However, when we incorporate $\alpha$-cluster breaking caused by the spin-orbit force, the $0^{+}_{3}$ state is regarded as the band-head of the $2^{+}_{2}$ state.

Nucleon pairing correlations and theαcluster preformation probability inside heavy and superheavy nuclei

The presence of paired or unpaired protons and neutrons in the open-shell radioactive \ensuremath{\alpha} emitter affects the preformation probability of the \ensuremath{\alpha} cluster inside it. The \ensuremath{\alpha}-preformation probability inside the $\mathrm{odd}(Z)\text{\ensuremath{-}}\mathrm{even}(N)$, $\mathrm{even}(Z)\text{\ensuremath{-}}\mathrm{odd}(N)$, and $\mathrm{odd}(Z)\text{\ensuremath{-}}\mathrm{odd}(N)$ \ensuremath{\alpha} emitters is investigated. The study is restricted to those decays with no angular momentum transfer to make a precise prediction about the mere pairing effect. The extended cluster model of \ensuremath{\alpha} decay and the WKB approximation are used by taking into account the deformation degrees of freedom to carry out the calculations for 105 parent nuclei in the mass region of $A=175--289.$ The $\ensuremath{\alpha}$ + daughter interaction potential is calculated by using the Hamiltonian energy-density approach in terms of the SLy4 Skyrme-like interaction, then it is implemented to find the average decay width over the different orientations. The half-life of the decay is then estimated and employed in turn to extract the \ensuremath{\alpha}-preformation probability by taking account of errors on both the released energy and the experimental half-life time. According to the present calculations, it is found that the \ensuremath{\alpha} cluster preformation probability inside the nuclei which have unpaired nucleons is less than it would be in the neighboring nuclei of the same shell and subshell closures but have no unpaired nucleons. In particular, the effect of the single unpaired neutron in the $\mathrm{even}(Z)\text{\ensuremath{-}}\mathrm{odd}(N)$ nuclei is slightly larger than that of the single unpaired proton in the $\mathrm{odd}(Z)\text{\ensuremath{-}}\mathrm{even}(N)$ ones. The effect of the unpaired nucleons appears more clearly in the $\mathrm{odd}(Z)\text{\ensuremath{-}}\mathrm{odd}(N)$ nuclei which have both an unpaired neutron and an unpaired proton. Based on the obtained results, an empirical pairing term is added to the empirical formula [J. Phys. G 40, 105102 (2013)] that relates the \ensuremath{\alpha} cluster preformation probability to the proton and neutron numbers outside the closed shells of the parent nucleus.

Spectroscopy ofGd153andGd157using the(p,dγ)reaction

Low-spin single quasineutron levels in $^{153}\mathrm{Gd}$ and $^{157}\mathrm{Gd}$ have been studied following the $^{154}\mathrm{Gd}$($p,d\ensuremath{-}\ensuremath{\gamma}$)$^{153}\mathrm{Gd}$ and $^{158}\mathrm{Gd}$($p,d\ensuremath{-}\ensuremath{\gamma}$)$^{157}\mathrm{Gd}$ reactions. A combined Si telescope and high-purity germanium array was utilized, allowing $d\text{\ensuremath{-}}\ensuremath{\gamma}$ and $d\text{\ensuremath{-}}\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence measurements. Almost all of the established low-excitation-energy, low-spin structures were confirmed in both $^{153}\mathrm{Gd}$ and $^{157}\mathrm{Gd}$. Several new levels and numerous new $\ensuremath{\gamma}$ rays are observed in both nuclei, particularly for ${E}_{x}\ensuremath{\ge}1$ MeV. Residual effects of a neutron subshell closure at $N=64$ are observed in the form of a large excitation energy gap in the single quasineutron level schemes.