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.
In an effort to understand the magical status of N=32 and N=34 at the very neutron rich edge, experiments have been carried out in the Titanium isotopes up to A=56. The measured staggering of the B(E2)'s is not reproduced by the shell model calculations using the best effective interactions. We argue that this may be related to the choice of the isovector effective charge and to the value of the N=34 neutron gap.
Amongst iron regime nuclei, $β$-decay rates on titanium isotopes are considered to be important during the late phases of evolution of massive stars. The key $β$-decay isotopes during presupernova evolution were searched from available literature and a microscopic calculation of the decay rates were performed using the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. As per earlier simulation results electron capture and $β$-decay on certain isotopes of titanium are considered to be important for the presupernova evolution of massive stars. Earlier the stellar electron…
Weak interaction rates on titanium isotopes are important during the late phases of evolution of massive stars. A search was made for key titanium isotopes from available literature and a microscopic calculation of weak rates of these nuclei were performed using the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. Earlier the author presented the stellar electron capture rates on titanium isotopes. In this paper I present the neutrino and antineutrino energy loss rates due to capture and decay rates on isotopes of titanium in stellar environment. Accurate estimate of n…
Electron captures are amongst the most important weak interaction rates related to the dynamics of stellar core collapse. They play a key role in the gravitational collapse of the core of a massive star triggering the supernova explosion. Titanium isotopes are believed to have significant impact on controlling the lepton-to-baryon fraction in the late phases of evolution of core of massive stars. This work consists of the calculation of electron capture rates on titanium isotopes. The pn-QRPA theory is used to calculate electron capture rates in stellar matter. The electron capture rates are c…
The $N = 28$ shell gap in sulfur, argon, calcium and titanium isotopes is investigated in the framework of relativistic continuum Hartree-Bogoliubov (RCHB) theory. The evolutions of neutron shell gap, separation energy, single particle energy and pairing energy are analyzed, and it is found that $N = 28$ shell gap is quenched in sulfur isotopes but persists in argon, calcium and titanium isotopes. The evolution of $N = 28$ shell gap in $N = 28$ isotonic chain is discussed, and the erosion of $N = 28$ shell gap is understood with the evolution of potential with proton number.
A precision mass investigation of the neutron-rich titanium isotopes $^{51-55}$Ti was performed at TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). The range of the measurements covers the $N=32$ shell closure and the overall uncertainties of the $^{52-55}$Ti mass values were significantly reduced. Our results confirm the existence of a weak shell effect at $N=32$, establishing the abrupt onset of this shell closure. Our data were compared with state-of-the-art \textit{ab-initio} shell model calculations which, despite very successfully describing where the $N=32$ shell gap is strong,…
Recent mass measurements show a substantial weakening of the binding energy difference delta_{2p} (Z,N) = E(Z-2,N) - 2 E(Z,N) + E(Z+2,N) in the neutron-deficient Pb isotopes. As delta_{2p} is often attributed to the size of the proton magic gap, it might be speculated that the reduction in delta_{2p} is related to a weakening of the spherical Z=82 shell. We demonstrate that the observed trend is described quantitatively by self-consistent mean-field models in terms of deformed ground states of Hg and Po isotopes.
Nuclear masses ranging from O to Ti isotopes are systematically investigated with relativistic continuum Hartree-Bogoliubov (RCHB) theory, which can provide a proper treatment of pairing correlations in the presence of the continuum. From O to Ti isotopes, there are 402 nuclei predicted to be bound by the density functional PC-PK1. For the 234 nuclei with mass measured, the root mean square (rms) deviation is 2.23 MeV. It is found that the proton drip-lines predicted with various mass models are roughly the same and basically agree with the observation. The neutron drip-lines predicted, howeve…
The coupling of single-particle motion and of vibrations in $^{11}_4$Be produces dressed neutrons which spend only a fraction of the time in pure single-particle states, and which weighting differently from the bare neutrons, lead to parity inversion. The interaction of the two least bound neutrons in the ground state of $^{12}_4$Be mediated by the $v_{14}$ Argonne nucleon-nucleon potential and by the exchange of the phonon cloud, give rise to a strongly correlated state, where the neutrons spend more than half of the time in (s$^2$+d$^2$)-configurations, resulting in a breaking of the N=8 she…
In this paper, we investigate features of the ground state of some nuclei far from the stability for isotope chains with proton numbers Z=18 and 20. Our aim is to predict the eventual existence of magic numbers in these exotic nuclei. For this purpose, we use two methods: the non relativistic Hartree-Fock-Bogoliubov (HFB) approach based on SLy4 Skyrme functional and the relativistic (so-called covariant) density functional theory (CDFT) by using the DD-ME2 force parametrization. We compare our results with the available experimental data and with the predictions of other models such as Finite …
The Gamow-Teller (GT) transition is inarguably one of the most important nuclear weak transitions of the spin-isosopin $στ$ type. It has many applications in nuclear and astrophysics. These include, but are not limited to, r-process $β$-decays, stellar electron captures, neutrino cooling rates, neutrino absorption and inelastic scattering on nuclei. The quasiparticle random phase approximation (QRPA) is an efficient way to generate GT strength distribution. In order to better understand both theoretical systematics and uncertainties, we compare the GT strength distributions, centroid and width…
The low-lying level structures of $^{26}{\rm Ne}$, $^{28}{\rm Ne}$ and $^{30}{\rm Ne}$ which are related to the breaking of the N=20 shell closure have been studied by the framework of the deformed-basis antisymmetrized molecular dynamics plus generator coordinate method using Gogny D1S force. The properties of the many-particle and many-hole states are discussed as well as that of the ground band. We predict that the negative-parity states in which neutrons are promoted into $pf$-orbit from $sd$ orbit have the small excitation energy in the cases of $^{28}{\rm Ne}$ and $^{30}{\rm Ne}$ which, …
We have performed microscopic distorted-wave Born approximation (DWBA) calculations of differential cross sections for the two reactions 136Sn(p,t)134Sn and 134Sn(t,p)136Sn, which are within reach of near-future experiments with radioactive ion beams. We have described the initial and final nuclear states in terms of the shell model, employing a realistic low-momentum two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential that has already proved quite successful in describing the available low-energy energy spectrum of 134Sn. We discuss the main features of the predi…
Based on the realistic nuclear force of the high-precision CD-Bonn potential, we have performed comprehensive calculations for neutron-rich calcium isotopes using the Gamow shell model (GSM) which includes resonance and continuum. The realistic GSM calculations produce well binding energies, one- and two-neutron separation energies, predicting that $^{57}$Ca is the heaviest bound odd isotope and $^{70}$Ca is the dripline nucleus. Resonant states are predicted, which provides useful information for future experiments on particle emissions in neutron-rich calcium isotopes. Shell evolutions in th…
The shell structure of even-even isotopes in Si, S, Ar and Ca has been analysed. The theoretical calculations of shell closure parameter $D_{n} (N)$ and the differential variation of the two-neutron separation energy $dS_{2n} (Z, N )$ are carried out within the framework of Hartree-Fock-Bogoliubov theory. Calculations are carried out for different skyrme forces and their sensitivity has been tested. Same nuclides are studied by employing the relativistic mean field aproach based on meson exchange and point coupling models. Theoretically calculated estimates are in good agreement with the recen…
We discuss the mechanism causing the `kink' in the charge radius isotope shift at the N=126 shell closure. The occupation of the 1$i_{11/2}$ neutron orbital is the decisive factor for reproducing the experimentally observed kink. We investigate whether this orbital is occupied or not by different Skyrme effective interactions as neutrons are added above the shell closure. Our results demonstrate that several factors can cause an appreciable occupation of the 1$i_{11/2}$ neutron orbital, including the magnitude of the spin-orbit field, and the isoscalar effective mass of the Skyrme interaction.…
We have employed RMF+BCS (relativistic mean-field plus BCS) approach to study behaviour of pf shell with the help of ground state properties of even-even nuclei. Our present investigations include separation energies , deformations, single particle energies, wavefunction, potential as well etc density distribution. As per recent experiments showing neutron magicity at N = 32 for Ca isotopes, our results with mass dependent pairing indicate a shell closure at N = 32 in Ca isotopes and a more strong shell closure at N = 34 in proton deficient 48Si because of reorganization of neutron pf shell. I…
The recently confirmed neutron-shell closure at N = 32 has been investigated for the first time below the magic proton number Z = 20 with mass measurements of the exotic isotopes 52,53K, the latter being the shortest-lived nuclide investigated at the online mass spectrometer ISOLTRAP. The resulting two-neutron separation energies reveal a 3 MeV shell gap at N = 32, slightly lower than for 52Ca, highlighting the doubly-magic nature of this nuclide. Skyrme-Hartree-Fock-Boguliubov and ab initio Gorkov-Green function calculations are challenged by the new measurements but reproduce qualitatively t…
Recent experimental results obtained using $β$ decay and isomer spectroscopy indicate an unusual behaviour of the energies of the first excited 2$^{+}$ states in neutron-rich Cd isotopes approaching the N=82 shell closure. To explain the unexpected trend, changes of the nuclear structure far-off stability have been suggested, namely a quenching of the N=82 shell gap already in $^{130}$Cd, only two proton holes away from doubly magic $^{132}$Sn. We study the behaviour of the 2$^+$ energies in the Cd isotopes from N=50 to N=82, i.e. across the entire span of a major neutron shell using modern be…
We probe the $N=82$ nuclear shell closure by mass measurements of neutron-rich cadmium isotopes with the ISOLTRAP spectrometer at ISOLDE-CERN. The new mass of $^{132}$Cd offers the first value of the $N=82$, two-neutron shell gap below $Z=50$ and confirms the phenomenon of mutually enhanced magicity at $^{132}$Sn. Using the recently implemented phase-imaging ion-cyclotron-resonance method, the ordering of the low-lying isomers in $^{129}$Cd and their energies are determined. The new experimental findings are used to test large-scale shell-model, mean-field and beyond-mean-field calculations, a…
Monopole shift in the proton states in odd neutron rich F isotopes has been studied with neutron number changing from N = 10 to 20 for three different interactions. The variation of monopole shift point out towards appearance of shell closure at N = 14 and N = 16 and its disappearance at N = 20. Low lying states of odd F isotopes have also been calculated in the limited configuration space of {\it sd} shells for these interactions.
We have studied neutron-rich calcium isotopes in terms of the shell model employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the potential is renormalized by way of the V-low-k approach. The calculated results are in very good agreement with the available experimental data, thus supporting our predictions for the hitherto unknown spectra of 53-56Ca nuclei. In this context, the possible existence of an N=34 shell closure is discussed.
We present a comprehensive study on the low-lying states of neutron-rich Er, Yb, Hf, and W isotopes across the $N=126$ shell with a multi-reference covariant density functional theory. Beyond mean-field effects from shape mixing and symmetry restoration on the observables that are relevant for understanding quadrupole collectivity and underlying shell structure are investigated. The general features of low-lying states in closed-shell nuclei are retained in these four isotopes around $N=126$, even though the shell gap is overall quenched by about 30\% with the beyond mean-field effects. These …
The variation of E(2+_1) of (134-140)Sn calculated with empirical SMPN interaction has striking similarity with that of experimental E(2+_1) of even-even (18-22)O and (42-48)Ca, showing clearly that N=84-88 spectra exhibit the effect of gradual filling up of ν(2f_{7/2}) orbital which finally culminates in a new shell closure at N=90. Realistic two-body interaction CWG does not show this feature. Spin-tensor decomposition of SMPN and CWG interactions and variation of their components with valence neutron number reveals that the origin of the shell closure at 140Sn lies in the three body effects…
Isotope shifts in the nuclear charge radius of even and odd calcium isotopes are calculated within the nuclear shell model. The model space includes all configurations of nucleons in the $2s, 1d_{3/2}, 1f_{7/2}, {\rm and} ~2p_{3/2}$ orbits. The shell model describes well the energies of the intruder states in Sc and Ca, as well as the energies of the low-lying $2^+$ and $3^-$ states in the even Ca isotopes. The characteristic features of the isotope shifts, the parabolic dependence on $A$ and the prominent odd-even staggering, are well reproduced by the model. These features are related to the…
We calculate the low-lying spectra of the zirconium isotopes Z=40 with neutron numbers from N=52 to N=60 using the 1p1/20g9/2 proton and 2s1d0g7/20h11/2 neutron sub-shells to define the model space. Effective proton-proton, neutron--neutron and proton-neutron interactions have been derived using 88Sr as closed core and employing perturbative many-body techniques. The starting point is the nucleon-nucleon potential derived from modern meson exchange models. The comprehensive shell-model calculation performed in this work provides a qualitative reproduction of essential properties such as the su…
We recently proposed a new method to calculate the standard nuclear matrix elements for neutrinoless double-$β$ decay ($0νββ$) of ${}^{48}$Ca going beyond the closure approximation. Here we extend this analysis to the important case of ${}^{82}$Se, which was chosen as the base isotope for the upcoming SuperNEMO experiment. We demonstrate that using a mixed method that considers information from closure and non-closure approaches, one can get excellent convergence properties for the nuclear matrix elements, which allows one to avoid unmanageable computational costs. We show that in contrast wit…
We derive and compute effective valence-space shell-model interactions from ab-initio coupled-cluster theory and apply them to open-shell and neutron-rich oxygen and carbon isotopes. Our shell-model interactions are based on nucleon-nucleon and three-nucleon forces from chiral effective-field theory. We compute the energies of ground and low-lying states, and find good agreement with experiment. In particular our calculations are consistent with the N=14, 16 shell closures in oxygen-22 and oxygen-24, while for carbon-20 the corresponding N=14 closure is weaker. We find good agreement between o…
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 mag…
We employ interactions from chiral effective field theory and compute the binding energies and low-lying excitations of calcium isotopes with the coupled-cluster method. Effects of three-nucleon forces are included phenomenologically as in-medium two-nucleon interactions, and the coupling to the particle continuum is taken into account using a Berggren basis. The computed ground-state energies and the low-lying 2+ states for the isotopes 42,48,50,52Ca are in good agreement with data, and we predict the excitation energy of the first 2+ state in 54Ca at 1.9 MeV, displaying only a weak sub-shell…
Combining laser spectroscopy in a Versatile Arc Discharge and Laser Ion Source, with Penning-trap mass spectrometry at the CERN-ISOLDE facility, this work reports on mean-square charge radii of neutron-rich mercury isotopes across the $N = 126$ shell closure, the electromagnetic moments of $^{207}$Hg and more precise mass values of $^{206-208}$Hg. The odd-even staggering (OES) of the mean square charge radii and the kink at $N = 126$ are analyzed within the framework of covariant density functional theory (CDFT), with comparisons between different functionals to investigate the dependence of t…
We compute the charge radii of even-mass neon and magnesium isotopes from neutron number N = 8 to the dripline. Our calculations are based on nucleon-nucleon and three-nucleon potentials from chiral effective field theory that include delta isobars. These potentials yield an accurate saturation point and symmetry energy of nuclear matter. We use the coupled-cluster method and start from an axially symmetric reference state. Binding energies and two-neutron separation energies largely agree with data and the dripline in neon is accurate. The computed charge radii have an estimated uncertainty o…
The angular momentum projected Generator Coordinate Method using the quadrupole moment as collective coordinate and the Gogny force as the effective interaction is used to describe the properties of the ground state and low-lying excited states of the neutron rich light nuclei 32,34,36Si. It is found that the ground state of the nucleus 34Si is spherical. However, this is not only due to the N=20 shell closure as the ground state of 34Si contains a significant amount of the intruder f7/2 neutron orbital. On the other hand, rather good agreement with experimental data for many observables is ob…
We have employed RMF+BCS (relativistic mean-field plus BCS) ap- proach to study behaviour of N = 16 shell closure with the help of ground state properties of even-even nuclei. Our present investigations include sin- gle particle energies, deformations, separation energies as well as pairing energies etc. As per recent experiments showing neutron magicity at N = 16 for O isotopes, our results indicate a strong shell closure at N = 16 in 22C and 24O. A large gap is found in between neutron 2s1/2 and 1d3/2 states for 22C and 24O. These results are also supported by a sharp increase in two neutron…
The mean-square charge radii of $^{207,208}$Hg ($Z=80, N=127,128$) have been studied for the first time and those of $^{202,203,206}$Hg ($N=122,123,126$) remeasured by the application of in-source resonance-ionization laser spectroscopy at ISOLDE (CERN). The characteristic \textit{kink} in the charge radii at the $N=126$ neutron shell closure has been revealed, providing the first information on its behavior below the $Z=82$ proton shell closure. A theoretical analysis has been performed within relativistic Hartree-Bogoliubov and non-relativistic Hartree-Fock-Bogoliubov approaches, considering…
The interaction cross sections for $^A Na + ^{12}C$ reaction are calculated using Glauber model. The continuum Hartree-Bogoliubov theory has been generalized to treat the odd particle system and take the continuum into account. The theory reproduces the experimental result quite well. The matter distributions from the proton drip line to the neutron drip line in Na isotopes have been systematically studied and presented. The relation between the shell effects and the halos has been examined. The tail of the matter distribution shows a strong dependence on the shell structure. The neutron N=28 …
The very simple product of the number of particles by the number of holes appearing in the expression of the reduced B(E2:0+->2+) transition probability of even-even nuclei obtained from the extension of the seniority scheme is used to analyze the experimental B(E2:0+->2+) values in the Cr up to Se isotopes. A new interpretation is given to the B(E2:0+->2+) measured in 68Ni and 70Zn. The B(E2:0+->2+) features of the even-even nuclei between Ni and Se with neutron number ranging from 28 up to 50 fit in with a global scenario involving p-n interaction. The evolution of the B(E2:0+->2+) curves pr…
Gamow-Teller (GT) strength distributions (B(GT)) in electron-capture (EC) daughters stemming from the parent ground state are computed with the shell-model in the full pf-shell space, with quasi-particle random-phase approximation (QRPA) in the formalism of Krumlinde and Möller and with an Approximate Method (AM) for assigning an effective B(GT). These are compared to data available from decay and charge-exchange (CE) experiments across titanium isotopes in the pf-shell from A=43 to A=62, the largest set available for any chain of isotopes in the pf-shell. The present study is the first to exa…
Low-energy dipole excitations have been investigated theoretically in N=50, several N=82 isotones and the Z=50 Sn isotopes. For this purpose a method incorporating both HFB and multi-phonon QPM theory is applied. A concentration of one-phonon dipole strength located below the neutron emission threshold has been calculated in these nuclei. The analysis of the corresponding neutron and proton dipole transition densities allows to assign a genuine pattern to the low-energy excitations and making them distinct from the conventional GDR modes. Analyzing also the QRPA wave functions of the states we…
Nuclear charge radii of $^{55,56}$Ni were measured by collinear laser spectroscopy. The obtained information completes the behavior of the charge radii at the shell closure of the doubly magic nucleus $^{56}$Ni. The trend of charge radii across the shell closures in calcium and nickel is surprisingly similar despite the fact that the $^{56}$Ni core is supposed to be much softer than the $^{48}$Ca core. The very low magnetic moment $μ(^{55}\mathrm{Ni})=-1.108(20)\,μ_N$ indicates the impact of M1 excitations between spin-orbit partners across the $N,Z=28$ shell gaps. Our charge-radii results are…
Neutron skin thickness and its volume and surface contributions in berkelium isotopes
School of Physics, Zhengzhou University（郑州大学物理学院）；State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与核技术国家重点实验室）；State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所重离子科学和技术国家重点实验室）
For the first time, the shell structure of open-shell nuclei is described in a fully self-consistent extension of the covariant energy density functional theory. The approach implies quasiparticle-vibration coupling for superfluid systems. One-body Dyson equation formulated in the doubled quasiparticle space of Dirac spinors is solved for nucleonic propagators in tin isotopes which represent the reference case: the obtained energies of the single-quasiparticle levels and their spectroscopic amplitudes are in agreement with data. The model is applied to describe the shell evolution in a chain o…
The $λ$ and $m_{ββ}$ mechanisms of neutrinoless double beta decay ($0νββ$) occur with light neutrino exchange via $W_L-W_R$, and $W_L-W_L$ mediation, respectively. In the present study, we calculate the nuclear matrix elements (NMEs) for the $m_{ββ}$ and $λ$ mechanisms of $0νββ$, which has origin in the left-right symmetric model with right-handed gauge boson at TeV scale. The NMEs are calculated for one of the $0νββ$ decaying isotope $^{48}$Ca in the interacting nuclear shell-model using the GXPF1A effective interaction of $pf$-shell. The NMEs are calculated in both closure and nonclosure app…
Isomeric studies in neutron-rich nuclei present a powerful tool to explore the structure at the nuclear extremes. We recently used the shell model calculations with Renormalized Charge Depen- dent Bonn (RCDB) effective interaction to calculate the properties of the $6^+$ seniority isomers in $^{134-138}$Sn in an attempt to resolve the anomalous B(E2) behavior of the $6^+$ isomer in $^{136}$Sn [Phys. Rev. C 91, 024321 (2015)]. We further explore these isomers by using the generalized seniority scheme for multi-j orbitals recently presented by us [Phys. Lett. B 753, 122 (2016)]; the B(E2) values…
Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton ($np$) correlations, is here applied for the first time to the study of odd-$Z$ copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3$^{*}$ parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across $N=50$ and $82$ shell cl…
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 $\sim$210 MeV/u at the RIBF facility. The 2$^{+}_{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 o…
We formulate the In-Medium Similarity Renormalization Group (IM-SRG) for open-shell nuclei using a multi-reference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multi-reference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of even oxygen isotopes with chiral NN and 3N Hamiltonians, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the Importance-Truncated No-Core Shell Model and the Coupled Cluster …
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 explain the nuclear magic numbers, its origins are still open questions. Here, we present experimental evidence for the smallest SO-originated ma…
Magicity, or shell closure, plays an important role in our understanding of complex nuclear phenomena. In this work, we employ one of the state-of-the-art density functional theories, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the density functional PC-PK1, to investigate the evolution of the $N=20,28,50$ shell closures in the $ 20 \leqslant Z \leqslant 30$ region. We show how these three conventional shell closures evolve from the proton drip line to the neutron drip line by studying the charge radii, two-neutron separation energies, two-neutron gaps, quadru…
DWBA analysis of the inelastic $^{30-40}$S$(p,p')$ and $^{18-22}$O$(p,p')$ scattering data measured in the inverse kinematics has been performed to determine the isoscalar ($δ_0$) and isovector ($δ_1$) deformation lengths of the 2$^+_1$ excitations in the Sulfur and Oxygen isotopes using a compact folding approach. A systematic $N$-dependence of $δ_0$ and $δ_1$ has been established which shows a link between $δ_1$ and the neutron-shell closure. Strong isovector deformations were found in several cases, e.g., the 2$^+_1$ state in $^{20}$O where $δ_1$ is nearly three times larger than $δ_0$. The…
