Neutron-rich Sr Research Articles

Single-Particle and Collective Structures in Neutron-Rich Sr Isotopes

Neutron-rich Sr nuclei around N=60 exhibit a sudden shape transition from a spherical ground state to strongly prolate-deformed. Recently, much new insight into the structure of Sr isotopes in this region has been gained through experimental studies of the excited levels, transition strengths, and spectroscopic factors. In this work, a “classic” shell model description of strontium isotopes from N=50 to N=58 is provided, using a natural valence space outside the 78Ni core. Both even–even and even–odd isotopes are addressed. In particular, spectroscopic factors are computed to shed more light on the structure of low-energy excitations and their evolution along the Sr chain. The origin of deformation at N=60 is mentioned in the context of the present and previous shell model and Monte Carlo shell model calculations.

Single-particle structure in neutron-rich Sr isotopes approaching the N=60 shape transition

Background: Neutron-rich nuclei around neutron number N=60 show a dramatic shape transition from spherical ground states to prolate deformation in Sr98 and heavier nuclei. Purpose: The purpose of this study is to investigate the single-particle structure approaching the shape transitional region. Method: The level structures of neutron-rich Sr93,94,95 were studied via the H2(Sr94,95,96,t) one-neutron stripping reactions at TRIUMF using a beam energy of 5.5 AMeV. γ-rays emitted from excited states and recoiling charged particles were detected by using the TIGRESS and SHARC arrays, respectively. States were identified by gating on the excitation energy and, if possible, the coincident γ radiation. Results: Triton angular distributions for the reactions populating states in ejectile nuclei Sr93,94,95 were compared with distorted wave Born approximation calculations to assign and revise spin and parity quantum numbers and extract spectroscopic factors. The results were compared with shell-model calculations and the reverse (d,p) reactions and good agreement was obtained. Conclusions: The results for the H2(Sr94,t)Sr93 and H2(Sr95,t)Sr94 reactions are in good agreement with shell-model calculations. A two-level mixing analysis for the 0+ states in Sr94 suggest strong mixing of two shapes. For the H2(Sr96,t)Sr95 reaction the agreement with the shell-model is less good. The configuration of the ground state of Sr96 is already more complex than predicted, and therefore indications for the shape transition can already be observed before N=60.9 MoreReceived 14 January 2020Accepted 17 August 2020DOI:https://doi.org/10.1103/PhysRevC.102.024335©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDirect reactionsSpectroscopic factors & electromagnetic momentsTransfer reactionsProperties90 ≤ A ≤ 149TechniquesRadioactive beamsNuclear Physics

Single-particle structure of neutron-rich Sr isotopes via H2(Sr94,95,96, p) reactions

Background: The region around neutron number N=60 in the neutron-rich Sr and Zr nuclei is one of the most dramatic examples of a ground-state shape transition from (near) spherical below N=60 to strongly deformed shapes in the heavier isotopes. Purpose: The single-particle structure of Sr95-97 approaching the ground-state shape transition at Sr98 has been investigated via single-neutron transfer reactions using the (d,p) reaction in inverse kinematics. These reactions selectively populate states with a large overlap of the projectile ground state coupled to a neutron in a single-particle orbital. Method: Radioactive Sr94,95,96 nuclei with energies of 5.5 AMeV were used to bombard a CD2, where D denotes H2, target. Recoiling light charged particles and γ rays were detected using a quasi-4π silicon strip detector array and a 12-element Ge array. The excitation energy of states populated was reconstructed employing the missing mass method combined with γ-ray tagging and differential cross sections for final states were extracted. Results: A reaction model analysis of the angular distributions allowed for firm spin assignments to be made for the low-lying 352, 556, and 681 keV excited states in Sr95 and a constraint has been placed on the spin of the higher-lying 1666 keV state. Angular distributions have been extracted for ten states populated in the H2(Sr95,p)Sr96 reaction, and constraints have been provided for the spins and parities of several final states. Additionally, the 0, 167, and 522 keV states in Sr97 were populated through the H2(Sr96,p) reaction. Spectroscopic factors for all three reactions were extracted. Conclusions: Results are compared to shell-model calculations in several model spaces and the structure of low-lying states in Sr94 and Sr95 is well described. The spectroscopic strength of the 0+ and 2+ states in Sr96 is significantly more fragmented than predicted. The spectroscopic factors for the H2(Sr96,p)Sr97 reaction suggest that the two lowest-lying excited states have significant overlap with the weakly deformed ground state of Sr96, but the ground state of Sr97 has a different structure.

Shape evolution in Kr, Zr, and Sr isotopic chains in covariant density functional theory

The relativistic-Hartree-Bogoliubov formalism using density-dependent zero and finite range $\mathit{NN}$ interactions, and separable pairing, is applied to the Kr isotopes ($Z=36$) and $N=34--64$ isotopes, neutron-rich Sr($Z=38$) and Zr($Z=40$) nuclei with neutron numbers $N=48--70$. A systematic search of triaxial ground state and the phenomena of unusual structural change and the coexistence of shape for $^{70\ensuremath{-}100}\mathrm{Kr}$, and at $N=58$ in the $^{86\ensuremath{-}108}\mathrm{Sr}$ and $^{88\ensuremath{-}110}\mathrm{Zr}$ isotopes are done. A reasonable agreement is found with the available experimental data and with the macro-microscopic finite range droplet model. The findings are also in good agreement with the self-consistent Hartree-Fock-Bogoliubov calculations based on the interaction Gogny-D1S force, and with relativistic calculations.

Shape coexistence in neutron-rich strontium isotopes at N = 60

The structure of neutron-rich Sr nuclei was investigated by low-energy Coulomb excitation of radioactive beams at the REX-ISOLDE facility, CERN, with the MINIBALL spectrometer. The results support the scenario of a shape transition at N = 60, giving rise to the coexistence of a highly deformed prolate and a spherical configuration in 98Sr with low configuration mixing. They are discussed in the context of systematics of quadrupole moments and transition probabilities in the N = 60 region.

Recoil distance method lifetime measurement of the 21+ state in Sr94 and implications for the structure of neutron-rich Sr isotopes

A high precision lifetime measurement of the ${2}_{1}^{+}$ state in $^{94}\mathrm{Sr}$ was performed at TRIUMF's ISAC-II facility by coupling the recoil distance method implemented via the TIGRESS integrated plunger with unsafe Coulomb excitation in inverse kinematics. Due to limited statistics imposed by the use of a radioactive $^{94}\mathrm{Sr}$ beam, a likelihood ratio ${\ensuremath{\chi}}^{2}$ method was derived and used to compare experimental data to Geant4 simulations. The $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ value extracted from the lifetime measurement of $7.{80}_{\ensuremath{-}0.40}^{+0.50}\text{(stat.)}\ifmmode\pm\else\textpm\fi{}0.07\text{(sys.)}$ ps is approximately 25% larger than previously reported while the relative error has been reduced by a factor of approximately 8. A baseline deformation has been established for Sr isotopes with $N\ensuremath{\le}58$ which is a necessary condition for the quantum phase transition interpretation of the onset of deformation in this region. A comparison to existing theoretical models is presented.

Quasiparticle-phonon coupling plus rotor model for low-lying states of the neutron-rich Sr, Zr, Mo and Ru isotopes

Quasiparticle-phonon coupling plus rotor model for low-lying states of the neutron-rich Sr, Zr, Mo and Ru isotopes

$\gamma $ Spectroscopy of Neutron-rich Nuclei with $A\approx 100$ Produced by Cluster Transfer Reactions at REX-ISOLDE

In this work, we present an exploratory experiment performed at REX-ISOLDE to investigate neutron-rich Sr, Y and Zr nuclei around mass A = 100 by cluster transfer reactions of radioactive 98Rb/98Sr beams on a 7Li target. The goal of the experiment is to test the potential of clustertransfer mechanism to study the low-lying structure of neutron-rich nuclei, performing, as a first case, a -spectroscopy study of the structure in deformed nuclei beyond N = 60 populated, so far, only via β decay and spontaneous fission experiments.

AN INVESTIGATION OF THE NUCLEAR STRUCTURES OF EVEN–EVEN NEUTRON-RICH Sr, Zr AND Mo ISOTOPES

Binding energies and their differences are investigated to evaluate the two-neutron separation energies (S2n), the two-proton separation energies (S2p) and the average proton–neutron interaction strengths (δVpn) of neutron-rich Sr , Zr and Mo isotopes in the mass region A = 86–110, including even–even nuclei. Calculations were performed using the Hartree–Fock–Bogoliubov (HFB) method with different Skyrme force parametrizations. The obtained results are discussed and compared with the results of experimental and relativistic mean-field theory (RMFT).

Onset of collectivity in neutron-rich Sr and Kr isotopes: Prompt spectroscopy after Coulomb excitation at REX-ISOLDE, CERN

A rapid onset of quadrupole deformation is known to occur around the neutron number 60 in the neutron-rich Zr and Sr isotopes. This shape change has made the neutron-rich A = 100 region an active area of experimental and theoretical studies for many decades now. We report in this contribution new experimental results in the neutron rich 96,98 Sr investigated by safe Coulomb excitation of radioactive beams at the REX-ISOLDE facility, CERN. Reduced transition probabilities and spectroscopic quadrupole moments have been extracted from the differential Coulomb excitation cross section supporting the scenario of shape coexistence/change at N = 60. Future perspectives are presented including the recent experimental campaign performed at ILL-Grenoble.

Lifetime measurements and nuclear deformation in theA≈100region

The EUROGAM-2 array has been used to study $\ensuremath{\gamma}$ rays emitted following the spontaneous fission of a ${}^{248}$Cm source. Analysis of Doppler-broadened lineshapes corresponding to transitions from excited rotational states in neutron-rich Sr, Zr, Mo, Ru, and Pd fission fragments has enabled measurements of state lifetimes in these nuclei at nuclear spins of $I\ensuremath{\sim}10$. Extracted transition quadrupole moments are compared with various recent theoretical approaches, as well as with measurements at lower spin, and an interpretation of the data is made within the context of prolate-oblate shape competition in this region.

Rapid structural change in low-lying states of neutron-rich Sr and Zr isotopes

The rapid structural change in low-lying collective excitation states of neutron-rich Sr and Zr isotopes is tudied by solving a five-dimensional collective Hamiltonian with parameters determined by both relativistic mean-field and non-relativistic Skyrme-Hartree-Fock calculations using the PC-PK1 and SLy4 forces respectively. Pair correlations are treated in BCS method with either a separable pairing force or a density-dependent zero-range force. The isotope shifts, excitation energies, electric monopole and quadrupole transition strengths are calculated and compared with corresponding experimental data. The calculated results with both the PC-PK1 and SLy4 forces exhibit a picture of spherical-oblate-prolate shape transition in neutron-rich Sr and Zr isotopes. Compared with the experimental data, the PC-PK1 (or SLy4) force predicts a more moderate (or dramatic) change in most of the collective properties around N=60. The underlying microscopic mechanism responsible for the rapid transition is discussed.

Systematics of one-quasiparticle configurations in neutron-rich odd Sr, Zr, and Mo isotopes with the Gogny energy density functional

The systematics of one-quasiparticle configurations in neutron-rich Sr, Zr, and Mo odd isotopes is studied within the Hartree-Fock-Bogoliubov plus equal filling approximation method preserving both axial and time-reversal symmetries. Calculations based on the Gogny energy density functional with both the standard D1S parametrization and the new D1M incarnation of this functional are included in our analysis. The nuclear deformation and shape coexistence inherent to this mass region are shown to play a relevant role in the understanding of the spectroscopic features of the ground and low-lying one-quasineutron states.

Charge radii and structural evolution in Sr, Zr, and Mo isotopes

The evolution of the ground-state nuclear shapes in neutron-rich Sr, Zr, and Mo isotopes, including both even-even and odd-A nuclei, is studied within a self-consistent mean-field approximation based on the D1S–Gogny interaction. Neutron separation energies and charge radii are calculated and compared with available data. A correlation between a shape transition and a discontinuity in those observables is found microscopically. While in Sr and Zr isotopes the steep behavior observed in the isotopic dependence of the charge radii is a consequence of a sharp prolate–oblate transition, the smooth behavior found in Mo isotopes has its origin in an emergent region of triaxiality.

Microscopic study of low-lying yrast spectra and deformation systematics in neutron-rich 98–106Sr isotopes

Variation-after-projection (VAP) calculations in conjunction with Hartree-Bogoliubov (HB) ansatz have been carried out for A = 98–106 strontium isotopes. In this framework, the yrast spectra with J Π ≥ 10+, B(E2) transition probabilities, quadrupole deformation parameter and occupation numbers for various shell model orbits have been obtained. The results of the calculation for yrast spectra give an indication that it is important to include the hexadecapole-hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in Sr isotopes. Besides this, it is also found that the simultaneous polarization of p 3/2 and f 5/2 proton subshells is a significant factor in making a sizeable contribution to the deformation in neutron-rich Sr isotopes.

Identical transitions in the strongly deformed99Srand100Sr

The decay of the very neutron-rich nucleus ${}^{100}\mathrm{Rb}$ has been studied by \ensuremath{\gamma} spectroscopy of online mass-separated samples. Schemes for \ensuremath{\beta} decay to ${}^{100}\mathrm{Sr}$ and $\ensuremath{\beta}n$ decay to ${}^{99}\mathrm{Sr}$ are presented. New sets of transitions in ${}^{99}\mathrm{Sr}$ and ${}^{100}\mathrm{Sr}$ with identical energies are observed. All identical bands so far observed in neutron-rich Sr isotopes obey a simple energy rule valid for even-even, odd-even, and odd-odd bands.

Spin-Dependent Triaxial Deformation in Neutron-Rich Mo Isotopes.

The Eurogam-2 array has been used to study $\ensuremath{\gamma}$ rays emitted following the spontaneous fission of a $^{248}\mathrm{Cm}$ source. Analysis of Doppler-broadened line shapes corresponding to decays from excited rotational states in neutron-rich Sr, Zr, and Mo fission fragments has enabled the first measurements of state lifetimes in these nuclei at around $I=10$. The results are consistent with a predicted rotation-induced change in the triaxiality of the yrast states of the Mo isotopes that contrasts with the more stable behavior observed in the Zr and Sr nuclei.

Experimental indication of the onset of nuclear deformation in neutron-rich Sr isotopes at mass 98

A partial decay scheme for 0.1 sec 98Rb has been deduced from γ-singles, γ-multispectra ana γγ coincidence measurements taken at the OSTIS mass-separator system at the Institut Laue-Langevin. The low-lying levels of 98Sr follow the energy level systematics of the even- A N = 60 isotones. The onset of nuclear deformation in even- A neutron-rich Sr isotopes appears to occur at mass 98, as the first 2 + level energy drops from the nearly constant value of about 800 keV for masses 90–96 to 144 keV at mass 98. Energy level systematics indicate that a transition in the nuclear structures of the more neutron-rich nuclei near mass 100 occurs rather sharply at neutron number N = 60.