Transition from collectivity to single-particle degrees of freedom from magnetic moment measurements on ${}_{38}^{82}\text{Sr}$${}_{44}$ and ${}_{38}^{90}\text{Sr}$${}_{52}$

Background: The ${}_{38}^{88}\text{Sr}$ and ${}_{40}^{90}\text{Zr}$ nuclei have been utilized as closed cores for large-scale shell-model calculations in the $28\le Z\le 50$ region around the $N=50$ shell. Measurements of magnetic moments for nuclei in this region would provide microscopic information about the use of ${}^{88}$Sr and ${}^{90}$Zr as stable closed-core nuclei. While the $g$ factors of the 2${}_1^{+}$ states in the stable Sr isotopes have been previously measured, experimental $g$ factors for the radioactive ${}^{82,90}$Sr have not been obtained to date.

Purpose: The purpose was to measure the $g$ factors of the 2${}_1^{+}$ and 4${}_1^{+}$ states in the unstable ${}^{82}$Sr and ${}^{90}$Sr nuclei in order to extend the systematics along the Sr isotopic chain. A comparison of the structure of the $N=52$ isotopes ${}^{90}$Sr and ${}^{92}$Zr will shed light on the relative robustness of proton subshell closures at $Z=38$ and $Z=40$.

Methods: The pickup reaction of $\alpha$ particles in inverse kinematics together with the transient field technique were applied to beams of ${}^{78}$Kr and ${}^{86}$Kr at the Cyclotron Institute of Texas A&M University.

Results: The values $g{(}^{82}\mathrm{Sr};2_1^{+})=+0.44\left(19\right)$, $g{(}^{82}\mathrm{Sr};4_1^{+})=+0.53\left(39\right)$, $g{(}^{90}\mathrm{Sr};2_1^{+})=-0.12\left(11\right)$, and $g{(}^{90}\mathrm{Sr};4_1^{+})=-0.02\left(17\right)$ were measured for the first time. Simultaneously, the $g$ factors of the low-lying states in the Coulomb-excited beam projectiles were remeasured. The $g\left(4_1^{+}\right)$ = +1.03(14) in ${}^{86}$Kr was also measured for the first time.

Conclusions: For ${}^{82}$Sr both $g$ factors are in agreement with the collective value $Z/A$ expected for nuclei in the middle of a major shell. The $g$ factors in ${}^{90}$Sr are negative but smaller than in the isotone ${}^{92}$Zr. The results also indicate that ${}^{88}$Sr is a proton-soft core nucleus and perhaps even softer than ${}^{90}$Zr.

Figure 1

The $g\left(2_1^{+}\right)$ factors of isotopic chains on both sides of the closed neutron shell $N=50$. The Z/A line represents an average value for the given range of nuclei.

Figure 2

Experimental setup. Four clover HPGe $\gamma$ detectors and a circular (300 mm${}^2$) PIPS Canberra silicon surface-barrier particle detector were located symmetrically around the target. Clovers 2 and 3 were placed in the forward hemisphere at $\pm {67}^{\circ }$, while clovers 1 and 4 occupied the backward angles at $\pm {113}^{\circ }$, all at a distance of 120 mm from the target. The particle detector was positioned 20 mm downstream of the target at 0${}^{\circ }$ to the beam direction and spanned an opening angle of $\pm {24}^{\circ }$. Inset: The multilayered target design.

Figure 3

Particle spectra and overlaid spectra of particles in coincidence with $\gamma$ transitions in ${}^{90}$Sr and ${}^{82}$Sr at the three beam energies. The lightly shaded areas show $\Delta E$ spectra of $\alpha$ particles. At the lower beam energies the spectra of the Coulomb-scattered carbon ions and $\alpha$ particles overlap more and more. The “cusps” in the spectra are artifacts due to the finite thickness of the particle detector.

Figure 4

Random-subtracted $\gamma$-ray spectra in coincidence with forward-scattered carbon particles recorded in a clover segment at $\theta ={121}^{\circ }$. The ${}^{87}$Rb lines in the ${}^{86}$Kr spectrum arise from the proton pickup reaction ${}^{12}$C(${}^{86}$Kr,${}^{11}$B)${}^{87}$Rb, where ${}^{11}$B is indistinguishable from ${}^{12}$C in the particle spectrum.

Figure 5

Random-subtracted $\gamma$-ray spectra in coincidence with the double $\alpha$ peak in the particle spectra showing the transitions in ${}^{82}$Sr and ${}^{90}$Sr. ${}^{92}$Zr is populated in the ${}^{12}$C(${}^{86}$Kr,$\alpha$2n)${}^{92}$Zr reaction.

Figure 6

Angular correlations for Coulomb excitation and $\alpha$ transfer derived from precession data in clover segments. The $\alpha$-transfer data for ${}^{90}$Sr also include data for clover detectors positioned at 50${}^{\circ }$, 80${}^{\circ }$, 100${}^{\circ }$, and 130${}^{\circ }$.

Figure 7

Energy dependence of the yields for Coulomb excitation and $\alpha$ transfer with ${}^{86}$Kr beams.

Figure 8

Corresponding particle yields for the main reaction channels obtained with the 3.0-MeV/$u$ ${}^{86}$Kr beam. The graph for ${}^{86}$Kr $2_1^{+}$ is scaled down by a factor of 6.

Figure 9

Comparison of the $g$ factors in the Zr and extended Sr isotopic chains. The new results ($N=44,52$) are highlighted. Missing error bars are smaller than the symbol size.