Subshell Closure Research Articles

Tensor and pairing interactions within the quark-meson coupling energy-density functional

In the latest version of the QMC model, QMC$\pi$-III-T, the density functional is improved to include the tensor component quadratic in the spin-current and a pairing interaction derived in the QMC framework. Traditional pairing strengths are expressed in terms of the QMC parameters and the parameters of the model optimised. A variety of nuclear observables are calculated with the final set of parameters. The inclusion of the tensor component improves the predictions for ground-state bulk properties, while it has a small effect on the single-particle spectra. Further, its effect on the deformation of selected nuclei is found to improve the energies of doubly-magic nuclei at sphericity. Changes in the energy curves along the Zr chain with increasing deformation are investigated in detail. The new pairing functional is also applied to the study of neutron shell gaps, where it leads to improved predictions for subshell closures in the superheavy region.

Charge Radius of the Short-Lived ^{68}Ni and Correlation with the Dipole Polarizability.

We present the first laser spectroscopic measurement of the neutron-rich nucleus ^{68}Ni at the N=40 subshell closure and extract its nuclear charge radius. Since this is the only short-lived isotope for which the dipole polarizability α_{D} has been measured, the combination of these observables provides a benchmark for nuclear structure theory. We compare them to novel coupled-cluster calculations based on different chiral two- and three-nucleon interactions, for which a strong correlation between the charge radius and dipole polarizability is observed, similar to the stable nucleus ^{48}Ca. Three-particle-three-hole correlations in coupled-cluster theory substantially improve the description of the experimental data, which allows to constrain the neutron radius and neutron skin of ^{68}Ni.

On the robustness of sub-shell closures: A high angular momentum analysis of the titanium isotopes

The potential sub-shell closures N=32 and N=34 are analyzed at high spins in the titanium isotopes within the generalized beyond mean field theory considering triaxial deformations and the angular frequency as generator coordinates together with the particle number and the angular momentum conservation. A good description of bulk properties, high angular momenta spectra and transition probabilities is obtained. The outcome at high spin in these nuclei is consistent with the magic number character of N=32 but not of N=34.

Investigation of the level structure of 90Nb nucleus using the shell model

Abstract Shell model calculations have been carried out for 90Nb nucleus with the model space in which the valence protons occupy the f5/2, p3/2, p1/2, and g9/2 orbitals and the valence neutrons occupy the p1/2, g9/2, d5/2, and g7/2 orbitals. According to the calculated results, the negative parity is from the contribution of the proton of the f5/2, p3/2, and p1/2 orbits. The moderate spin states of 90Nb are mainly due to the excitation of protons from the f5/2 and p3/2 orbits to the p1/2 and g9/2 orbits across the Z = 38 subshell closure, and the high spin states arise from the excitation of a single neutron from the g9/2 orbit into the d5/2 orbit across the N = 50 shell closure.

High-resolution study of Er166 with the ( p, t ) reaction

Excited states in the deformed nucleus $^{166}\mathrm{Er}$ have been studied with high-energy resolution in the ($p,t$) reaction, with the Munich Q3D spectrograph. 143 states have been observed up to 4 MeV excitation, and spin and parity has been proposed for about 100 states, based on a DWBA analysis of their angular distributions, out of which 11 are excited ${0}^{+}$ states, and 39 ${2}^{+}$ states. The excitation pattern of these states (especially the ${0}^{+}$ ones) in $^{166}\mathrm{Er}$ is compared to that in $^{168}\mathrm{Er}$. Calculations were carried out with the $spdf$-IBM model, which gives a reasonable agreement with the observed number of ${0}^{+}$ states in $^{166}\mathrm{Er}$ and their excitation in the ($p,t$) reaction. The $2n$-transfer intensity pattern for the ${0}^{+}$ states in the $^{166}\mathrm{Er}(t,p)^{168}\mathrm{Er}$ reaction is also reasonably predicted. However, the $spdf$-IBM calculations do not explain the differences between $^{166}\mathrm{Er}$ and $^{168}\mathrm{Er}$, in the ($p,t$) transfer distribution of the ${0}^{+}$ states. The understanding of these differences, which appear to be related to a structure change at the $N=98$ deformed subshell closure, remains as an important issue of future, more elaborated model calculations.

Quest of shape coexistence in Zr isotopes

The mass region with A~100 and Z~40 is known to experience a sudden onset of deformation. The presence of the subshell closure $Z=40$ makes feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region. The aim of this work is to describe excitation energies, transition rates, radii, and two-neutron separation energies for the even-even 94-110Zr nuclei and, moreover, to obtain information about wave functions and deformation. The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2p-2h excitations. On one hand, the parameters appearing in the Hamiltonian and in the E2 transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes. Spectra, transition rates, radii, $\rho^2(E0)$, and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too. The importance of shape coexistence has been shown to correctly describe the A~100 mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of 94-98Zr and its deformed nature for 100-110Zr isotopes. The sudden onset of deformation in 100Zr is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes.

Reinvestigation of the high-spin level structure of Nb92 : Excitations across the Z=38 and N=50 closed shells

High-spin states in $^{92}\mathrm{Nb}$ have been investigated by using in-beam $\ensuremath{\gamma}$ ray spectroscopy with the $^{82}\mathrm{Se}(^{14}\mathrm{N},4\mathrm{n})^{92}\mathrm{Nb}$ reaction at a beam energy of 54 MeV. The positive-parity decay sequences above the previously known state ${13}^{+}$ have been extended to ${I}^{\ensuremath{\pi}}\ensuremath{\ge}({20}^{+})$ by adding nineteen new $\ensuremath{\gamma}$ rays. The level structures in $^{92}\mathrm{Nb}$ have been interpreted in terms of the shell model calculations performed in the configuration space $\ensuremath{\pi}(1{f}_{5/2},2{p}_{3/2},2{p}_{1/2},1{g}_{9/2})$ for the protons and $\ensuremath{\nu}(2{p}_{1/2},1{g}_{9/2},1{g}_{7/2},2{d}_{5/2})$ for the neutrons. The calculated results show that the inclusion of proton core excitation relative to the $Z=38$ subshell closure and neutron particle-hole excitation for the $N=50$ shell closure are essential to adequately describe the experimental high-spin states at $I\ensuremath{\approx}(18--20)\ensuremath{\hbar}$ with excitation energies above 8.5 MeV.

Two-Neutron Correlations in a Borromean $$\varvec{^{20}\mathrm{C}+n+n}$$ System: Sensitivity of Unbound Subsystems

The structure of $^{22}$C plays a vital role in the new physics at subshell closure of $N=16$ in the neutron-rich region. We study the two-neutron correlations in the ground state of the weakly-bound Borromean nucleus $^{22}$C sitting at the edge of the neutron-drip line and its sensitivity to ${\rm core}$-$n$ potential. For the present study, we employ a three-body (${\rm core}+n+n$) structure model designed for describing the Borromean system by explicit coupling of unbound continuum states of the subsystem (${\rm core}+n$). We use a density-independent contact-delta interaction to describe the neutron-neutron interaction and its strength is varied to fix the binding energy. Along with the ground-state properties of $^{22}$C, we investigate its electric-dipole and monopole responses, discussing the contribution of various configurations. Our results indicate more configuration mixing as compared to the previous studies in the ground state of $^{22}$C. However, they strongly depend upon the choice of the $^{20}{\rm C}$-$n$ potential as well as the binding energy of $^{22}$C, which call for new precise measurements for the low-lying continuum structure of the binary system ($^{20}{\rm C}+n$) and the mass of $^{22}$C. These measurements will be essential to understand the Borromean three-body system $^{22}$C with more accuracy.

Recent upgrades of the multiple-reflection time-of-flight mass spectrometer at TITAN, TRIUMF

A multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) has been installed and integrated into the TITAN experiment at TRIUMF. The MR-TOF-MS extends the capabilities and improves the performance of the TITAN experiment, for instance it provides fast isobar separation, short measurement cycles, yield measurements and broad-band beam diagnosis, and enhanced rate capabilities and dynamic range. Thereby, even more exotic nuclides become accessible at TITAN for experiments. Such improved capabilities of TITAN have been used in first experiments to investigate the sub-shell closure of neutron-rich nuclides at N = 32 and the r-process nucleo-synthesis for masses at A ∼ 85. The vacuum system, electronics and data-acquisition hardware and software have been recently upgraded. For the first time an isomeric state has been measured with TITAN′s MR-TOF-MS, 84mRb (excitation energy: 464 keV). The accurate measurement of excitation energies of low-lying isomeric states is possible due to the high mass resolving power of TITAN′s MR-TOF-MS and a specialized data-analysis procedure.

Masses of neutron-rich Sc52–54 and Ti54,56 nuclides: The N=32 subshell closure in scandium

Isochronous mass spectrometry has been applied in the storage ring CSRe to measure the masses of the neutron-rich $^{\operatorname{52-54}}$Sc and $^{54,56}$Ti nuclei. The new mass excess values $ME$($^{52}$Sc) $=$ $-40525(65)$ keV, $ME$($^{53}$Sc) $=$ $-38910(80)$ keV, and $ME$($^{54}$Sc) $=$ $-34485(360)$ keV, deviate from the Atomic Mass Evaluation 2012 by 2.3$\sigma$, 2.8$\sigma$, and 1.7$\sigma$, respectively. These large deviations significantly change the systematics of the two-neutron separation energies of scandium isotopes. The empirical shell gap extracted from our new experimental results shows a significant subshell closure at $N = 32$ in scandium, with a similar magnitude as in calcium. Moreover, we present $ab$ $initio$ calculations using the valence-space in-medium similarity renormalization group based on two- and three-nucleon interactions from chiral effective field theory. The theoretical results confirm the existence of a substantial $N = 32$ shell gap in Sc and Ca with a decreasing trend towards lighter isotones, thus providing a consistent picture of the evolution of the $N = 32$ magic number from the $pf$ into the $sd$ shell.

How Robust is the N=34 Subshell Closure? First Spectroscopy of ^{52}Ar.

The first γ-ray spectroscopy of ^{52}Ar, with the neutron number N=34, was measured using the ^{53}K(p,2p) one-proton removal reaction at ∼210 MeV/u at the RIBF facility. The 2_{1}^{+} excitation energy is found at 1656(18)keV, the highest among the Ar isotopes with N>20. This result is the first experimental signature of the persistence of the N=34 subshell closure beyond ^{54}Ca, i.e., below the magic proton number Z=20. Shell-model calculations with phenomenological and chiral-effective-field-theory interactions both reproduce the measured 2_{1}^{+} systematics of neutron-rich Ar isotopes, and support a N=34 subshell closure in ^{52}Ar.

Sub-shell closure and shape coexistence in the transitional nucleus Zr98

As zirconium gains neutrons, its nucleus morphs in shape---changing from a soccer ball to an American football---and researchers have found the exact moment of the transition.

Symmetrical level schemes of the even–even Sm[formula omitted] and Yb[formula omitted] nuclei up to 10+ in the yrast bands

For the first time, we show here that three isotopes of the Sm isotopic chain almost overlay with three isotopes of the Yb isotopic chain in terms of experimental observables within the NπNν scheme. A recent systematic work by Sayğı on reduced transitional probabilities in pseudo-mirror nuclei revealed that nuclei having particle–hole symmetry tend to manifest alike experimental structures. The NπNν quantity is an indicator of the symmetry and depends on valence nucleon (or holes) number from the nearest closed shell by considering the subshell closures, which simplifies the systematics of excitation energies and related B(E2; L+→(L−2)+) values of excited states in nuclei placed in the different mass regions of nuclear chart. In the light of available data, the experimental observables in the group of 136Sm–160Yb, 134Sm–162Yb and 132Sm–164Yb nuclei have been analyzed in a vertical and horizontal perspectives and the ratio of reduced transition probabilities of the first excited states compared with existing theoretical predictions. The data brought to light that the structure of each group reflects identical yrast bands up to 10+.

Precision Mass Measurements on Neutron-Rich Rare-Earth Isotopes at JYFLTRAP: Reduced Neutron Pairing and Implications for r-Process Calculations.

The rare-earth peak in the r-process abundance pattern depends sensitively on both the astrophysical conditions and subtle changes in nuclear structure in the region. This work takes an important step towards elucidating the nuclear structure and reducing the uncertainties in r-process calculations via precise atomic mass measurements at the JYFLTRAP double Penning trap. ^{158}Nd, ^{160}Pm, ^{162}Sm, and ^{164-166}Gd have been measured for the first time, and the precisions for ^{156}Nd, ^{158}Pm, ^{162,163}Eu, ^{163}Gd, and ^{164}Tb have been improved considerably. Nuclear structure has been probed via two-neutron separation energies S_{2n} and neutron pairing energy metrics D_{n}. The data do not support the existence of a subshell closure at N=100. Neutron pairing has been found to be weaker than predicted by theoretical mass models. The impact on the calculated r-process abundances has been studied. Substantial changes resulting in a smoother abundance distribution and a better agreement with the solar r-process abundances are observed.

α particle preformation and shell effect for heavy and superheavy nuclei**Supported by National Natural Science Foundation of China (11675066, 11475050), Fundamental Research Funds for the Central Universities (lzujbky-2017- ot04) and Feitian Scholar Project of Gansu Province

The α particle preformation factor is extracted within a generalized liquid drop model for Z = 84 - 92 isotopes and N = 126, 128, 152, 162, 176, 184 isotones. The calculated results show clearly that the shell effects play a key role in α particle preformation. The closer the proton and neutron numbers are to the magic numbers, the more difficult the formation of the α cluster inside the mother nucleus is. The preformation factors of the isotopes reflect that N = 126 is a magic number for Po, Rn, Ra, and Th isotopes, but for U isotopes the weakening of the influence of the N = 126 shell closure is evident. The trend of the factors for N = 126 and N = 128 isotones also support this conclusion. We extend the calculations for N = 152, 162, 176, 184 isotones to explore the magic numbers for heavy and superheavy nuclei, which are probably present near Z = 108 to N = 152, 162 isotones and Z = 116 to N = 176, 184 isotones. The results also show that another subshell closure may exist after Z = 124 in the superheavy nuclei. This is useful for future experiments.

Relativistic Brueckner-Hartree-Fock theory for neutron drops

Neutron drops confined in an external field are studied in the framework of relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. The ground state energies and radii of neutron drops with even numbers from $N = 4$ to $N=50$ are calculated and compared with results obtained from other nonrelativistic \textit{ab initio} calculations and from relativistic density functional theory. Special attention has been paid to the magic numbers and to the sub-shell closures. The single-particle energies are investigated and the monopole effect of the tensor force on the evolutions of the spin-orbit and the pseudospin-orbit splittings is discussed. The results provide interesting insight of neutron rich systems and can form an important guide for future density functionals.

Evidence for prevalent Z = 6 magic number in neutron-rich carbon isotopes

The nuclear shell structure, which originates in the nearly independent motion of nucleons in an average potential, provides an important guide for our understanding of nuclear structure and the underlying nuclear forces. Its most remarkable fingerprint is the existence of the so-called magic numbers of protons and neutrons associated with extra stability. Although the introduction of a phenomenological spin–orbit (SO) coupling force in 1949 helped in explaining the magic numbers, its origins are still open questions. Here, we present experimental evidence for the smallest SO-originated magic number (subshell closure) at the proton number six in 13–20C obtained from systematic analysis of point-proton distribution radii, electromagnetic transition rates and atomic masses of light nuclei. Performing ab initio calculations on 14,15C, we show that the observed proton distribution radii and subshell closure can be explained by the state-of-the-art nuclear theory with chiral nucleon–nucleon and three-nucleon forces, which are rooted in the quantum chromodynamics.

Nuclear structure and decay modes of Ra isotopes within an axially deformed relativistic mean field model**Supported by Project No. SR/FTP/PS-106/2013, SERB, DST, Govt. of India

We examine the structural properties and half-life decay of Ra isotopes within the axially deformed Relativistic Mean-Field (RMF) theory with NL3 force parameters. We work out the binding energy (BE), RMS radii, two-neutron separation energies (S2n), and some other observables. The results are in good agreement with the finite-range droplet model (FRDM) and experimental results. Considering the possibility of neutron magic number, the α-decay and cluster decay half-lives of Ra isotopes are calculated systematically using the Q-values obtained from the RMF formalism. These decay half-life calculations are carried out by taking three different empirical formulae. The calculated decay half-lives are found to be highly sensitive to the choice of Q-values. Possible shell or sub-shell closures are found at daughter nuclei with N = 128 and N = 126 when alpha and 8Be, 12C, 18O respectively are emitted from Ra isotopes. Though the cluster radioactivity is affected by the shell closure of parent and daughter, a long half-life indicates the stability of the parent, and a small parent half-life indicates that the shell stability of the daughter against decay.

Probing the N = 14 subshell closure: g factor of the [formula omitted] state

The first-excited state g factor of 26Mg has been measured relative to the g factor of the Mg24(21+) state using the high-velocity transient-field technique, giving g=+0.86±0.10. This new measurement is in strong disagreement with the currently adopted value, but in agreement with the sd-shell model using the USDB interaction. The newly measured g factor, along with E(21+) and B(E2) systematics, signal the closure of the νd5/2 subshell at N=14. The possibility that precise g-factor measurements may indicate the onset of neutron pf admixtures in first-excited state even–even magnesium isotopes below 32Mg is discussed and the importance of precise excited-state g-factor measurements on sd shell nuclei with N≠Z to test shell-model wavefunctions is noted.

Quasifree ( p,pN ) scattering of light neutron-rich nuclei near N=14

Background: For many years, quasifree scattering reactions in direct kinematics have been extensively used to study the structure of stable nuclei, demonstrating the potential of this approach. The (RB)-B-3 collaboration has performed a pilot experiment to study quasifree scattering reactions in inverse kinematics for a stable C-12 beam. The results from that experiment constitute the first quasifree scattering results in inverse and complete kinematics. This technique has lately been extended to exotic beams to investigate the evolution of shell structure, which has attracted much interest due to changes in shell structure if the number of protons or neutrons is varied. Purpose: In this work we investigate for the first time the quasifree scattering reactions (p, pn) and (p, 2p) simultaneously for the same projectile in inverse and complete kinematics for radioactive beams with the aim to study the evolution of single-particle properties from N = 14 to N = 15. Method: The structure of the projectiles O-23, O-22, and N-21 has been studied simultaneously via (p, pn) and (p, 2p) quasifree knockout reactions in complete inverse kinematics, allowing the investigation of proton and neutron structure at the same time. The experimental data were collected at the (RB)-B-3-LAND setup at GSI at beam energies of around 400 MeV/u. Two key observables have been studied to shed light on the structure of those nuclei: the inclusive cross sections and the corresponding momentum distributions. Conclusions: The knockout reactions (p, pn) and (p, 2p) with radioactive beams in inverse kinematics have provided important and complementary information for the study of shell evolution and structure. For the (p, pn) channels, indications of a change in the structure of these nuclei moving from N = 14 to N = 15 have been observed, i.e., from the 0d(5/2) shell to the 1s(1/2). This supports previous observations of a subshell closure at N = 14 for neutron-rich oxygen isotopes and its weakening for the nitrogen isotopes.