Lifetimes of low-lying excited states in ${}_{36}{}^{86}\mathrm{Kr}_{50}$

Background: The evolution of nuclear magic numbers at extremes of isospin is a topic at the forefront of contemporary nuclear physics. $N=50$ is a prime example, with increasing experimental data coming to light on potentially doubly magic ${}^{100}\mathrm{Sn}$ and ${}^{78}\mathrm{Ni}$ at the proton-rich and proton-deficient extremes, respectively; however, experimental discrepancies exist in the data for less exotic systems.

Purpose: In ${}^{86}\mathrm{Kr}$ the $B(E2;2_1^{+}\to 0_1^{+})$ value—a key indicator of shell evolution—has been experimentally determined by two different methodologies, with the results deviating by $3\sigma$. Here, we report on a new high-precision measurement of this value, as well as the first measured lifetimes and hence transition strengths for the $2_2^{+}$ and $3_{\left(2\right)}^{-}$ states in the nucleus.

Methods: The Doppler-shift attenuation method was implemented using the TRIUMF-ISAC $\gamma$-ray escape-suppressed spectrometer (TIGRESS) $\gamma$-ray spectrometer and the TIGRESS integrated plunger device. High-statistics Monte Carlo simulations were utilized to extract lifetimes in accordance with state-of-the-art methodologies.

Results: Lifetimes of $\tau \left(2_1^{+}\right)=336\pm 4\text{(stat.)}\pm 20\text{(sys.)}$ fs, $\tau \left(2_2^{+}\right)=263\pm 9\text{(stat.)}\pm 19\text{(sys.)}$ fs, and $\tau \left(3_{\left(2\right)}^{-}\right)=73\pm 6\text{(stat.)}\pm 32\text{(sys.)}$ fs were extracted. This yields a transition strength for the first-excited state of $B(E2;2_1^{+}\to 0_1^{+})=259\pm 3\text{(stat.)}\pm 16\text{(sys.)}$ $e^2$ ${\mathrm{fm}}^4$.

Conclusions: The measured lifetime disagrees with the previous Doppler-shift attenuation method measurement by more than $3\sigma$, while agreeing well with a previous value extracted from Coulomb excitation. The newly extracted $B(E2;2_1^{+}\to 0_1^{+})$ value indicates a more significant reduction in the $N=50$ isotones approaching $Z=40$.

Figure 1

The particle identification (PID) parameter determined from wave-form fitting plotted against the energy in the CsI(Tl) detectors with the major loci indicated.

Figure 2

Black: Add-back $\gamma$-ray spectrum. Blue: Requiring a good time coincidence with a CsI(Tl) event and an RF beam bucket. Red: Requiring the coincident CsI(Tl) event that has a PID parameter consistent with the carbon detection. The $\gamma$-ray peaks arising from the decays of states of interest are indicated. Note that $\gamma$ rays originating from the $3^{-}$ state are not resolvable from those from the $2_1^{+}$ state in this figure.

Figure 3

Reduced level scheme indicating the states of interest in the present work. Dashed transitions indicate $\gamma$ rays that were not observed but for which feeding contributions were incorporated into the line-shape analysis.

Figure 4

Simulated line shape (filled) plotted along with the experimental data (data points) for rings 1, 2, 5, and 6 [panels (a)–(d), respectively] for a simulated lifetime, $\tau \left(2_2^{+}\right)=260$ fs.

Figure 5

${\chi }^2$ plotted against the simulated lifetime of the $2_2^{+}$ state for all four sensitive rings (see Fig. 4). As indicated, the ${\chi }^2$ minimum is found to correspond to $\tau =263$(9) fs. Once systematic uncertainties are incorporated the final value becomes $\tau =263$(9) (19) fs.

Figure 6

The ${\chi }^2$ surface fitted to the minimized ${\chi }^2$ values (red circles) used to determine the lifetime minima for the overlapping $2_1^{+}$ and $3_{\left(2\right)}^{-}$ line shapes.

Figure 7

Top: The ${\chi }^2$ surface as determined from the fit shown in Fig. 6 in the region of ${\chi }_{\text{min}}^2$. Bottom: The ${\chi }^2\le {\chi }_{\text{min}}^2+1$ region from which the minimum and associated statistical uncertainties were determined.

Figure 8

Fitted line shape (thick solid, red line) corresponding to the minimized ${\chi }^2$ overlayed on the experimental data (black points) for the six rings in TIGRESS. Also shown are the primary contributions to the line shape arising from direct population of the $2_1^{+}$ state (thin solid, red line), population via the $4_1^{+}$ state (dotted, red line) and via the $3_{\left(2\right)}^{-}$ state (dashed, red line). Details of the parameters varied in the fits are provided in the text. Rings 3 and 4 were insensitive to the state lifetimes and were not included in the ${\chi }^2$ surface shown in Fig. 6.

Figure 9

Line shapes for a $2_1^{+}$ state lifetime of 450 fs [Ref. [13]: $\tau \left(2_1^{+}\right)=440\left(25\right)$ fs] for the downstream- and upstream-most rings. A $3_{\left(2\right)}^{-}$ state lifetime of $\tau \left(3_{\left(2\right)}^{-}\right)=10$ fs is used, corresponding to the approximate ${\chi }^2$ minimum in Fig. 6 at $\tau \left(2_1^{+}\right)=450$ fs. The poorer quality of the fit for both the $2_1^{+}$ and $3^{-}$ components is clear in comparison to that of Fig. 8.

Figure 10

$B(E2;2_1^{+}\to 0_1^{+})$ value systematics for the $N=50$ isotones. The uncertainties on the present result are dominated by systematics (dashed lines) but agree well with previous Coulomb-excitation data. The evaluated data range is indicated by the shaded band. Experimental data were taken from Refs. [13, 14, 15, 16, 17, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43]. Also shown is the $B(E2;2_1^{+}\to 0_1^{+})$ value predicted for ${}^{78}\mathrm{Ni}$ in Ref. [6].