Relativistic Coulomb excitation of ${}^{88}\mathrm{Kr}$

To investigate the systematics of mixed-symmetry states in $N=52$ isotones, a relativistic Coulomb excitation experiment was performed during the PreSPEC campaign at the GSI Helmholtzzentrum für Schwerionenforschung to determine $E2$ transition strengths to $2^{+}$ states of the radioactive nucleus ${}^{88}\text{Kr}$. Absolute transition rates could be measured towards the first and third $2^{+}$ states. For the latter a mixed-symmetry character is suggested on the basis of the indication for a strong $M1$ transition to the fully symmetric $2_1{}^{+}$ state, extending the knowledge of the $N=52$ isotones below $Z=40$. A comparison with the proton-neutron interacting boson model and shell-model predictions is made and supports the assignment.

Figure 1

Partial level scheme of ${}^{88}\text{Kr}$ illustrating the lowest lying $2^{+}$ states and the known transitions between them. The thickness of the arrows expresses the branching ratios of the transitions adopted from Ref. [21]. Transitions that remained unobserved in this work are drawn with dashed grey lines. Energy labels are in keV.

Figure 2

FRS particle identification plot for the ${}^{88}\text{Kr}$ setting.

Figure 3

Doppler-corrected $\gamma$-ray energy spectra for ${}^{88}\text{Kr}$ for the (a) inner and (b) outer ring of germanium detectors in the PreSPEC setup. The spectra are drawn with their statistical errors. Fits to the observed transitions and the $1\sigma$ observation limit in case of the $2_3^{+}\to 2_1^{+}$ in the inner ring and a background function are indicated with the red (gray) line (see text for details).

Figure 4

Observed intensities with their statistical uncertainties (data points) and calculated angular distributions for the $2_1^{+}\to 0_1^{+}$ with pure $E2$ character (dashed line) and the $2_3^{+}\to 2_1^{+}$ (solid line) transitions. The angular range of the inner and outer rings of germanium detectors are marked with gray color. A $1\sigma$ observation limit is indicated for the $2_3^{+}\to 2_1^{+}$ in the inner ring.

Figure 5

(a) Excitation energies, (b) reduced $B\left(E2\right)$, and (c) $B\left(M1\right)$ transition strengths from the $2_1^{+}$ and $2_{ms}^{+}$ states in $N=52$ isotones [13, 14, 15, 16, 28, 29] together with the newly determined values for ${}^{88}\text{Kr}$ in red. Additionally shown are the results from shell-model calculations using the SDI [17] (green lines) and from new calculations based on the work of Ref. [30] (red lines).