Single-particle structure of neutron-rich Sr isotopes via ${}^2\mathrm{H}({}^{94,95,96}\mathrm{Sr},\hspace{0.17em}p)$ 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 ${}^{95–97}\mathrm{Sr}$ approaching the ground-state shape transition at ${}^{98}\mathrm{Sr}$ 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 ${}^{94,95,96}\mathrm{Sr}$ nuclei with energies of 5.5 $A\mathrm{MeV}$ were used to bombard a ${\mathrm{CD}}_2$, where D denotes ${}^2\mathrm{H}$, target. Recoiling light charged particles and $\gamma$ rays were detected using a quasi-$4\pi$ 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 $\gamma$-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 ${}^{95}\mathrm{Sr}$ 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 ${}^2\mathrm{H}({}^{95}\mathrm{Sr},p){}^{96}\mathrm{Sr}$ reaction, and constraints have been provided for the spins and parities of several final states. Additionally, the 0, 167, and 522 keV states in ${}^{97}\mathrm{Sr}$ were populated through the ${}^2\mathrm{H}({}^{96}\mathrm{Sr},p)$ 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 ${}^{94}\mathrm{Sr}$ and ${}^{95}\mathrm{Sr}$ is well described. The spectroscopic strength of the $0^{+}$ and $2^{+}$ states in ${}^{96}\mathrm{Sr}$ is significantly more fragmented than predicted. The spectroscopic factors for the ${}^2\mathrm{H}({}^{96}\mathrm{Sr},p){}^{97}\mathrm{Sr}$ reaction suggest that the two lowest-lying excited states have significant overlap with the weakly deformed ground state of ${}^{96}\mathrm{Sr}$, but the ground state of ${}^{97}\mathrm{Sr}$ has a different structure.

Figure 1

Kinematics plot for ${}^{95}\mathrm{Sr}$ incident on the ${\mathrm{CD}}_2$ target, compared to calculated kinematics lines drawn for elastic scattering (black, dotted lines) and ($d,p$) transfer at 0, 2, 4, and 6 MeV excitation energy (red). In addition to uniquely identified particle in the DBOX, elastic scattered protons and deuterons are shown below the identification threshold of about 5000 keV identified by their kinematic $E\left({\theta }_{\text{lab}}\right)$ relation. The inset shows the particle identification plot for the DBOX section (see text), which was used to distinguish between protons and deuterons.

Figure 2

Comparison of ${}^2\mathrm{H}({}^{94,95,96}\mathrm{Sr},d)$ angular distribution data to DWBA calculations using the optimized optical potential that is given in Table 2. The inset shows the comparison of the $p({}^{94,95,96}\mathrm{Sr},p)$ data to the global potential PP-76 [45] (see text).

Figure 3

Excitation energy versus $\gamma$-ray energy matrix (top) and projected $\gamma$-ray spectrum (bottom) for ${}^{95}\mathrm{Sr}$ states populated via ${}^2\mathrm{H}({}^{94}\mathrm{Sr},p)$.

Figure 4

Level scheme for ${}^{95}\mathrm{Sr}$ states that were populated through ${}^2\mathrm{H}({}^{94}\mathrm{Sr},p)$. The 204 keV $\gamma$ ray was not observed due to the 21.9(5) ns [3, 49] half-life of the 556 keV state (more details in the text).

Figure 5

Excitation energy spectrum extracted from the recoiling proton energies and angles at a center of mass angle ${\theta }_{\text{cm}}={30}^{\circ }$. The continuous green line shows the constrained three-peak fit of the 0, 352, and 681 keV ${}^{95}\mathrm{Sr}$ states. The dashed line represents the continuous background.

Figure 6

(a)–(c) Comparison of the reaction model calculations to the angular distributions for the 0, 352 and 681 keV states in ${}^{95}\mathrm{Sr}$. The experimental data has been obtained from the constrained three-peak fit (Fig. 5). The solid lines are the best-fitting reaction model calculations using the DWBA (blue) and ADWA (green) methods. (d) Comparison of the two methods to extract the angular distribution for the 352 keV state (see text).

Figure 7

Excitation energy versus $\gamma$-ray energy matrix (top) and projected $\gamma$-ray spectrum (bottom) for ${}^{96}\mathrm{Sr}$ states populated via the ${}^2\mathrm{H}({}^{95}\mathrm{Sr},p)$ reaction.

Figure 8

Level scheme of states in ${}^{96}\mathrm{Sr}$ that were populated in the ${}^2\mathrm{H}({}^{95}\mathrm{Sr},p)$ reaction. The newly observed level at 3506 keV is indicated by a star.

Figure 9

Angular distributions for $\mathrm{\Delta }\ell =0$ states in ${}^{96}\mathrm{Sr}$. The experimental data is presented alongside the fitted DWBA (blue) and ADWA (green) calculations, respectively.

Figure 10

Angular distributions for $\mathrm{\Delta }\ell =2$ states in ${}^{96}\mathrm{Sr}$. The experimental data is presented alongside the fitted DWBA (blue) and ADWA (green) calculations, respectively.

Figure 11

Angular distributions for $\mathrm{\Delta }\ell =4$ states in ${}^{96}\mathrm{Sr}$. The experimental data is presented alongside the fitted DWBA (blue) and ADWA (green) calculations, respectively. Potential contamination of the 2120 keV state angular distribution by the neighboring 2113 keV state has been neglected (see text).

Figure 12

Projected $\gamma$-ray spectrum for ${}^{97}\mathrm{Sr}$ states populated via the ${}^2\mathrm{H}({}^{96}\mathrm{Sr},p)$ reaction. A cut on excitation energies below 1 MeV has been applied.

Figure 13

Level scheme for ${}^{97}\mathrm{Sr}$ states that were populated through ${}^2\mathrm{H}({}^{96}\mathrm{Sr},p)$.

Figure 14

Excitation energy spectrum extracted from the recoiling proton energies and angles at a center of mass angles ${\theta }_{\text{cm}}=22,26$, and ${30}^{\circ }$. The continuous green line shows the constrained three-peak fit of the 0, 167, and 522 keV states. The dashed line represents the continuous background.

Figure 15

Fit of the reaction model calculations to the experimental data for the 167 and 522 keV states in ${}^{97}\mathrm{Sr}$. The solid lines are the best-fitting reaction model calculations using the DWBA (blue) and ADWA (green) methods. The fitting was restricted to the forward angles (${\theta }_{\text{cm}}<{40}^{\circ }$). For the 167 keV state the angular distribution extracted by gating on the 167 keV $\gamma$-ray transition and the excitation energy is also shown.

Figure 16

Comparison of experimental (expt) spectroscopic factors ($C^{2}S$) to those from shell model calculations carried out in model spaces (a), (b), and (c), see text. States are labeled by the neutron single-particle orbital populated in the transfer reaction.

Figure 17

Comparison of experimental (expt) spectroscopic factors ($C^{2}S$) for ${}^2\mathrm{H}({}^{94}\mathrm{Sr},p){}^{95}\mathrm{Sr}$ to shell model calculations that were carried out in model spaces (a), (b), and (c), see text. States are labeled by their spin and parity as well as the orbital populated in the transfer reaction. Open symbols label the $1^{+}$ states populated by transfer to the $2s_{1/2}$ orbital, as well as transfer to the $1d_{5/2}$ orbital for $J^{\pi }=2,3^{+}$. Only states with $C^{2}S>0.01$ are shown. For experiment $J^{\pi }=2^{+}$ has been assumed for the 2084, 2576, and 3506 keV.