Decay mechanism and lifetime of ${}^{67}\mathrm{Kr}$

The lifetime of the recently discovered $2p$ emitter ${}^{67}\mathrm{Kr}$ was found to be considerably below the lower limit predicted theoretically. This communication addresses this issue. Different separation energy systematics are analyzed and different mechanisms for $2p$ emission are evaluated. We find that the most plausible reason for this disagreement is the decay mechanism of ${}^{67}\mathrm{Kr}$, which is not “true $2p$” emission but rather “transitional dynamics” on the borderline between true $2p$ and sequential $2p$ decay mechanisms. If this is correct, this imposes stringent limits of $E_r=1.35$–1.42 MeV on the ground-state energy of ${}^{66}\mathrm{Br}$ relative to the ${}^{65}\mathrm{Se}-p$ threshold.

Figure 1

Lifetime of ${}^{67}\mathrm{Kr}$ as a function of the $p$-wave ground-state resonance energy $E_r$ in ${}^{66}\mathrm{Br}$ for fixed energy $E_T=1.69$ MeV. (a) IDDM model. Solid black and dashed red curves correspond to different assumed weights of the $\left[p^2\right]$ configuration. Solid gray curves correspond to the solid black curve with $\pm 0.2$ fm modified channel radius $r_{\text{cp}}$. The blue dotted line shows the two-body $R$-matrix estimate of the decay width into the ${}^{66}\mathrm{Br}+p$ channel with energy $E_T-E_r$. (b) Dashed lines show three-body model results for P3 and P5 potentials producing different configuration mixing. Solid lines show the extrapolation of three-body results from large $E_r$ values (where they are converged) by IDDM curves. The referred publications are [1] for [Goigoux 2016] and [2] for [Grigorenko 2003].

Figure 2

Systematics of $N$ and $2N$ separation energies ($S_N^{\left(A\right)}$ and $S_{2N}^{\left(A\right)}$, respectively) for krypton isobar and mirror isotone members with mass number $A$. The isotone values are provided with constant offsets (in MeV) for visual comparison. Thick gray lines marked as [Ormand 1997] show systematics predictions from Ref. [19].

Figure 3

Systematics of odd-even staggering energies $E_{\text{OES}}$ for krypton isobar and mirror isotone. Dotted ellipsis show the expected uncertainty for ${}^{67}\mathrm{Kr}$ due to the TES.

Figure 4

Systematics of charge radii for krypton and selenium isobars. Solid arrows extrapolate rising and falling trends along the isotopic chains which could be expected based on data on other nuclei. Gray rectangle shows expected uncertainty for ${}^{65}\mathrm{Se}$. The dashed arrows translate it into ${}^{67}\mathrm{Kr}$ charge radius uncertainty by using an independent particle model, which seems consistent with analogous extrapolation for the krypton isobaric chain.

Figure 5

Convergence of the three-body lifetime calculations as a function of the hyperspherical basis size $K_{max}$. Potential P2 [Grigorenko 2003] is the one used in [2].

Figure 6

Lifetime of ${}^{67}\mathrm{Kr}$ as a function of $2p$ decay energy $E_T$ for several $E_r$ values. The three-body model with realistic structure (P5 potential) and IDDM extrapolation were used. The results of the three-body calculations with pure $\left[l^2\right]$ configurations from [2] are shown by thick gray curves. The pink cross marked as [Goigoux 2016] shows the experimental value [1] with error bars.

Figure 7

Energy correlations between the ${}^{65}\mathrm{Se}$ core and one of the protons in $2p$ decay of ${}^{67}\mathrm{Kr}$ with $E_T=1.69$ MeV. Calculations by IDDM with different $E_r$ values in the core-$p$ subsystem ${}^{66}\mathrm{Br}$ illustrate true $2p$ decay mechanism ($E_r=2$ MeV) and the region of transitional decay dynamics ($E_r=1375$–1400 keV). The curves are normalized to unity maximum value of the $\varepsilon \sim 0.5$ peak. The estimated width of the ${}^{66}\mathrm{Br}$ g.s. is very small, therefore we convolve sequential decay peaks with Gaussians of 150 keV FWHM for the sake of visual comparison. Centroids of the low-$\varepsilon$ sequential decay peaks are indicated by the vertical dashed lines.