Sr Nuclei 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.

Shape Evolution in Ge, Se, Kr and Sr Nuclei within the Covariant Density Functional Theory

Published from 1956, the Bulgarian Journal of Physics accepts articles in the fields of: General and Mathematical Physics; Particle Physics and Field Theory; Atomic and Molecular Physics; Nuclear Physics; Fundamental Areas of Phenomenology; Theory of Relativity and Astrophysics; Condensed Matter, Statistical Physics; Cross-Disciplinary Physics; and Related Areas of Science and Technology.

Excitation of Isomeric States in the (\(\gamma , n\)) and (\(n, 2n\)) Reactions on \(^{86,88}\)Sr Nuclei

Excitation of Isomeric States in the (\(\gamma , n\)) and (\(n, 2n\)) Reactions on \(^{86,88}\)Sr Nuclei

Shell evolution in neutron-rich Ge, Se, Kr and Sr nuclei within RHB approach

The exotic even–even isotopic chains from [Formula: see text] to [Formula: see text] are investigated by means of the relativistic Hartree–Bogoliubov (RHB) approach with the explicit Density Dependent Meson-Exchange (DD-ME2) and Density-Dependent Point-Coupling (DD-PC1) models. The classic magic number [Formula: see text] is reproduced and the new number [Formula: see text] is predicted to be a robust shell closure by analysing several calculated quantities such as: two-neutron separation energies, two-neutron shell gap, neutron pairing energy, potential energy surface and neutron single particle energies. The obtained results are compared with the predictions of finite range droplet model (FRDM) and with the available experimental data. A reasonable and satisfactory agreement between the theoretical models and experiment is established.

Investigation of Nuclear Structures of Self-conjugate Zn, Ge, Se, Kr, Sr Nuclei

Nuclear structures of the atomic nuclei can be theoretically investigated by using nuclear shell model. Generally, a doubly closed-shell nucleus has been considered as inert core and the nucleons outside the core are taken into account in the calculation. It is assumed that the nucleons in the inert core do not move but each valance nucleon out of the core moves under an average potential created by the others. The self-conjugate (N=Z) moderate mass nuclei region is one of the region for the investigation of several phenomena because of the maximum spatial overlap of neutrons and protons. In this study, the nuclear structures of the moderate mass N=Z have been analyzed in the scope of the nuclear shell model by using KSHELL computer code. In the calculations, doubly magic 56Ni were taken as core and p3/2, f5/2 and p1/2 single particle orbits were used as valance orbits. Different two-body interactions have been taken into account. The results have been compared with each other and the available values existing in the literature.

Shell model description of the core excited level structure of $$^{89}$$Sr nucleus and systematic features of the $$N=51$$ odd-A isotones

Shell-model calculations are performed using NuShellX code in the model space $$\pi $$($$f_{5/2}$$, $$p_{3/2}$$, $$p_{1/2}$$, $$g_{9/2}$$) $$\otimes $$ $$\nu $$($$g_{9/2}$$, $$g_{7/2}$$, $$d_{5/2}$$, $$h_{11/2}$$), which probe the proton core excitation from the interior of $$Z=38$$ semiclosed shell and neutron core excitation from the interior of $$N=56$$ semiclosed shell for the level structure of $$^{89}$$Sr. Our calculations show that the excitation of a single $$d_{5/2}$$ neutron across $$N=56$$ semiclosed shell into the $$h_{11/2}$$ orbit should have great effects on the excited states of $$^{89}$$Sr. In addition, the systematic features of proton core excitation across $$Z=38$$ semiclosed shell into the $$g_{9/2}$$ orbit and neutron core excitation across $$N=56$$ semiclosed shell into the $$g_{7/2}$$, $$s_{1/2}$$, $$d_{3/2}$$, $$h_{11/2}$$ orbits in $$N=51$$ isotones are discussed.

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 and coexistence in neutron-deficient Kr, Rb, Sr and Zr nuclei

The potential energy surfaces of the isotopes of Kr, Rb, Sr and Zr and the isotones N=40 in the A∼80 region of the nuclear landscape display interesting shape variations with N and Z. The shape evolution and the possible shape coexistence are discussed within the cranked Nilsson-Strutinsky (CNS) framework for the isotopic and isotonic chains. The results indicate an oblate shell gap at Z=36 and 37 and a prolate shell gap at Z=38 and 40 with deformation ϵ2∼0.4. Our calculations show a well deformed prolate shell gap at N=40 so that it is determinant in the nuclear shape in this mass region.

Description of Energy Levels for 84,86,96,98Sr Isotopes

The positive ground-state band (GSB) of 84,86,96,98Sr has been calculated using the Bohr–Mottelson (BM) model, interacting vector boson model (IVBM), and interacting boson model (IBM-1), while the negative-parity band (NPB) of 84,86,96,98Sr has been calculated using the BM model and IVBM. IBM-1 has been used to calculate the energy of the gamma and beta bands. To determine the properties of the ground-state band, the ratio (r(I +2)/I) and the E-GOScurve (Eγ/I) have been plotted as a function of the spin (I). The potential energy surface (PES) has been calculated using IBM-1. The contour plots of the PESs show that 84,86,96Sr nuclei have vibrational properties and 98Sr has rotational characteristics.

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.

Magnetic rotation phenomenon in the dipole ( $\Delta I = 1$ Δ I = 1 ) bands of transitional strontium (Sr) isotopes near N=50 shell closure

The lifetime measurements were done for the transitions of the dipole ( $\Delta I=1$ ) bands in 85,86Sr nuclei using the Doppler Shift Attenuation Method (DSAM). The high-spin states in these nuclei were populated in the 76Ge(13C, 4n)85Sr and 76Ge(13C, 3n)86Sr reactions. The B(M1) transition rates have been obtained for the states of two positive-parity dipole ( $\Delta I=1$ ) bands in the 85Sr nucleus and one positive-parity dipole ( $\Delta I=1$ ) band in the 86 Sr nucleus. The present results on the transition rates are important to know whether these dipole ( $\Delta I=1$ ) bands have the signatures of Magnetic Rotation (MR). In order to investigate their magnetic character, the experimental results have been compared with the calculations within the framework of hybrid Tilted-Axis-Cranking (TAC) model. On the basis of the TAC calculations, band 2 of the 85Sr nucleus is assigned the $\pi (g_{9/2})^{2}\otimes \nu (g_{9/2})^{-1}$ configuration and shows the MR character, while for band 3, the $\pi [(g_{9/2})^{2} (f_{5/2})^{2}]\otimes \nu (g_{9/2})^{-1}$ configuration is suggested. In the case of 86Sr nucleus, band 3 has the $\pi (g_{9/2})^{2}\otimes \nu (g_{9/2})^{-2}$ configuration below the spin $I^{\pi} = 16^{+}$ and above this spin the $\pi [(g_{9/2})^{2} (f_{5/2})^{1} (p_{1/2}/p_{3/2})^{1}] \otimes \nu (g_{9/2})^{-2}$ configuration plays an important role. The experimental B(M1) transition rates show a decreasing trend with the increase in spin and are comparable with the TAC calculations before the $I^{\pi} = 16^{+}$ .

Low-energy Coulomb excitation of Sr96,98 beams

The structure of neutron-rich 96,98Sr nuclei was investigated by low-energy safe Coulomb excitation of radioactive beams at the REX-ISOLDE facility, CERN, with the MINIBALL spectrometer. A rich set of transitional and diagonal E2 matrix elements, including those for non-yrast structures, has been extracted from the differential Coulomb-excitation cross sections. 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, and are compared to predictions from several theoretical calculations. The experimental data suggest a significant contribution of the triaxal degree of freedom in the ground state of both isotopes. In addition, experimental information on low-lying states in 98Rb has been obtained.

Structural evolution inA≈100nuclei within the mapped interacting boson model based on the Gogny energy density functional

The structure of even-even neutron-rich Ru, Mo, Zr and Sr nuclei in the $A\approx 100$ mass region is studied within the interacting boson model (IBM) with microscopic input from the self-consistent mean-field approximation based on the Gogny-D1M energy density functional. The deformation energy surface in the quadrupole deformation space $(\beta,\gamma)$, computed within the constrained Hartree-Fock-Bogoliubov framework, is mapped onto the expectation value of the appropriately chosen IBM Hamiltonian with configuration mixing in the boson condensate state. The mapped IBM Hamiltonian is used to study the spectroscopic properties of $^{98-114}$Ru, $^{96-112}$Mo, $^{94-110}$Zr and $^{92-108}$Sr. Several cases of $\gamma$-soft behavior are predicted in Ru and Mo nuclei while a pronounced coexistence between strongly-prolate and weakly-oblate deformed shapes is found for Zr and Sr nuclei. The method describes well the evolution of experimental yrast and non-yrast states as well as selected $B$(E2) transition probabilities.

β-Decay half-lives and nuclear structure of exotic proton-rich waiting point nuclei under rp-process conditions

We investigate even–even nuclei in the A∼70 mass region within the framework of the proton–neutron quasi-particle random phase approximation (pn-QRPA) and the interacting boson model-1 (IBM-1). Our work includes calculation of the energy spectra and the potential energy surfaces V(β,γ) of Zn, Ge, Se, Kr and Sr nuclei with the same proton and neutron number, N=Z. The parametrization of the IBM-1 Hamiltonian was performed for the calculation of the energy levels in the ground state bands. Geometric shape of the nuclei was predicted by plotting the potential energy surfaces V(β,γ) obtained from the IBM-1 Hamiltonian in the classical limit. The pn-QRPA model was later used to compute half-lives of the neutron-deficient nuclei which were found to be in very good agreement with the measured ones. The pn-QRPA model was also used to calculate the Gamow–Teller strength distributions and was found to be in decent agreement with the measured data. We further calculate the electron capture and positron decay rates for these N=Z waiting point (WP) nuclei in the stellar environment employing the pn-QRPA model. For the rp-process conditions, our total weak rates are within a factor two compared with the Skyrme HF+BCS+QRPA calculation. All calculated electron capture rates are comparable to the competing positron decay rates under rp-process conditions. Our study confirms the finding that electron capture rates form an integral part of the weak rates under rp-process conditions and should not be neglected in the nuclear network calculations.

Magnetic moment measurements – extending isotopic chains beyond the stable elements

The magnetic moments in many isotopic chains have been systematically measured using the transient field technique on beams of separated isotopes excited in inverse kinematics. Such experiments have provided insight into how the structure of nuclei evolves by successively adding nucleons. Since naturally occurring isotopic chains are relatively short, efforts are underway to make unstable isotopes available. In limited cases the use of an a-particle transfer to beam projectiles has been successfully employed in measurements on unstable nuclei. In this investigation beams of 78Kr and 86Kr were used to measure magnetic moments of excited states in the unstable 82 Sr and 90 Sr nuclei utilizing the transfer of an α particle from 12 C nuclei in the target.

$\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.

Structure of the Sr-Zr isotopes near and at the magicN=50shell fromg-factor and lifetime measurements in4088Zr and84,86,3888Sr

Background: The evolution of and interplay between single-particle and collective excitations in the 40 $\ensuremath{\leqslant}N\ensuremath{\leqslant}$ 50 range for ${}_{38}$Sr and ${}_{40}$Zr isotopes have been studied.Purpose: Measurement of the $g$ factor of the 2${}_{1}^{+}$ and 4${}_{1}^{+}$ states in radioactive ${}^{88}$Zr while simultaneously remeasuring the $g({2}_{1}^{+})$ factors in the Sr isotopes and extention of the measurements to higher energy states in the Sr isotopes. Lifetimes of states in these nuclei are determined.Methods: The transient field technique in inverse kinematics and line-shape analysis using the Doppler-shift attenuation method are applied. The ${}^{88}$Zr nuclei were produced by the transfer of an $\ensuremath{\alpha}$ particle from the ${}^{12}$C nuclei of the target to ${}^{84}$Sr nuclei in the beam. The excited states in the stable ${}^{84}$Sr isotopes were simultaneously populated via Coulomb excitation by ${}^{12}$C in the same target. Coulomb excitation measurements on ${}^{86,88}$Sr were carried out with the same apparatus.Results: The resulting $g$ factors and $B(E2)$ values of these nuclei reveal similarities between the two chains of Zr and Sr isotopes. Large-scale shell-model calculations were performed within the ${p}_{3/2},{f}_{5/2},{p}_{1/2},{g}_{9/2}$ orbital space for both protons and neutrons and yielded results in agreement with the experimental data.Conclusions: In this paper the magnetic moments and lifetimes of several low-lying states in ${}^{88}$Zr and ${}^{84.86,88}$Sr have been measured and compared to large-scale shell-model calculations.

Calculation of single-particle energies in the 38 96 Sr nucleus within the mean field model with the dispersive optical potential

Evaluated and experimental neutron single-particle energies of the 88, 94, 96Sr and 90, 96, 98Zr nuclei near the Fermi energy are compared. A possibility of formation of a considerable particle-hole gap in the 94, 96Sr typical of traditional magic nuclei is investigated. Agreement is obtained between the single-particle energies calculated within the mean field model with the dispersive optical potential and the evaluated energies for the 94, 96Sr nuclei.

Evolution of the yrast-band structure in 76 Sr nuclei within microscopic theory

A new viewpoint is proposed for understanding the quantum phase transition from a higher-ordered excitation model to other lower-ordered one, which suggests that a nucleus populated at high-momentum state decouples firstly to the yrast-band with the E2-trasitions mode, and then to the coexist region, wherein the structure-energy is released, the change in the nucleon coupling intensity ensues, finally the basic state of the lower-ordered excitation model is reconstructed, the evolution of basic states structure is accomplished. Therefore this is a smooth and calm transition. Using an example of the 76 Sr nucleus, the problem is discussed carefully.