$\beta$ decay of the exotic $T_z=-2$ nuclei ${}^{48}\mathrm{Fe},{}^{52}\mathrm{Ni}$, and ${}^{56}\mathrm{Zn}$

The results of a study of the $\beta$ decays of three proton-rich nuclei with $T_z=-2$, namely ${}^{48}\mathrm{Fe},{}^{52}\mathrm{Ni}$, and ${}^{56}\mathrm{Zn}$, produced in an experiment carried out at GANIL, are reported. In all three cases we have extracted the half-lives and the total $\beta$-delayed proton emission branching ratios. We have measured the individual $\beta$-delayed protons and $\beta$-delayed $\gamma$ rays and the branching ratios of the corresponding levels. Decay schemes have been determined for the three nuclei, and new energy levels are identified in the daughter nuclei. Competition between $\beta$-delayed protons and $\gamma$ rays is observed in the de-excitation of the $T=2$ isobaric analog states in all three cases. Absolute Fermi and Gamow-Teller transition strengths have been determined. The mass excesses of the nuclei under study have been deduced. In addition, we discuss in detail the data analysis taking as a test case ${}^{56}\mathrm{Zn}$, where the exotic $\beta$-delayed $\gamma$-proton decay has been observed.

Figure 1

$\mathrm{\Delta }E$ vs ToF identification plot for the dataset optimized to implant ${}^{56}\mathrm{Zn}$ close to the middle of the DSSSD. The positions of the ${}^{48}\mathrm{Fe},{}^{52}\mathrm{Ni}$, and ${}^{56}\mathrm{Zn}$ implants are shown.

Figure 2

$\mathrm{\Delta }E$ vs ToF identification plot for the dataset optimized for ${}^{48}\mathrm{Fe}$. The positions of ${}^{48}\mathrm{Fe}$ and ${}^{52}\mathrm{Ni}$ are shown.

Figure 3

Spectrum of the time correlations between each decay event and all of the ${}^{56}\mathrm{Zn}$ implants (see text).

Figure 4

Spectrum of the time correlations between each proton decay (DSSSD energy $>0.8$ MeV) and all ${}^{56}\mathrm{Zn}$ implants.

Figure 5

Spectrum of the time correlations between each decay event and all the ${}^{56}\mathrm{Zn}$ implants. The [0, 1] s and [$-40,-10$] s gates are indicated by the red-dashed and blue-dotted regions, respectively.

Figure 6

DSSSD charged-particle spectra for decay events correlated with ${}^{56}\mathrm{Zn}$ implants. The spectrum (a) corresponds to time correlations from 0 to 1 s (red-dashed zone in Fig. 5) and contains both true and random correlations. The background spectrum (b) is created for time correlations from $-40$ to $-10$ s (blue-dotted zone in Fig. 5), normalized by the time interval used and contains only randoms. Peaks from the ${}^{53}\mathrm{Ni}$ contaminant ($T_{1/2}=55.2\left(7\right)$ ms) [8] are seen between 1 and 2.5 MeV. The removal of the randoms is achieved in spectrum (c), obtained by subtracting the spectrum (b) from (a).

Figure 7

(a) Monte Carlo simulations of $\beta \text{−}p$ events with $E_p=1.1$ MeV and a $\beta$ end-point energy of 11.2 MeV. The peak is fitted by a Gaussian function having an exponential high-energy tail. (b) DSSSD charged-particle spectrum for decay events correlated with ${}^{56}\mathrm{Zn}$ implants. The line shape of (a) was used for the fit shown here in dashed red.

Figure 8

Calibration of the efficiency for $\gamma$ detection. Data points from the ${}^{60}\mathrm{Co},{}^{137}\mathrm{Cs},{}^{133}\mathrm{Ba}$, and ${}^{207}\mathrm{Bi}$ sources are shown, together with a fit by the function from Ref. [19].

Figure 9

$\gamma$-ray spectra for decay events correlated with ${}^{56}\mathrm{Zn}$ implants. The spectrum (a) corresponds to time correlations from 0 to 1 s (red-dashed zone in Fig. 5) and contains both true and random correlations. The background spectrum (b) is created for time correlations in the blue-dotted zone in Fig. 5, normalized by the time interval used and contains only randoms. The removal of the randoms is achieved by subtracting the spectrum (b) from (a) and it is shown in the spectrum (c). In addition to the 511-keV $\gamma$ line associated with the annihilation of the positrons emitted in the decay of ${}^{56}\mathrm{Zn}$, a peak belonging to the daughter ${}^{56}\mathrm{Cu}$ is seen at 1835 keV [7].

Figure 10

Spectrum of the time correlations between all the ${}^{48}\mathrm{Fe}$ implants and each proton decay (DSSSD energy $E_p>$ 0.94 MeV, with the additional condition $E_p\notin [1.85,2.23]$ MeV to remove the ${}^{49}\mathrm{Fe}$ contaminant).

Figure 11

(a) DSSSD charged-particle spectrum for decay events correlated with ${}^{48}\mathrm{Fe}$ implants. (b) Fit of the peaks related to the proton emission following the $\beta$ decay of ${}^{48}\mathrm{Fe}$. Peaks are labeled according to the corresponding excitation energies in the $\beta$-daughter ${}^{48}\mathrm{Mn}$. The peak labeled as ${}^{49}\mathrm{Fe}$ (in blue) is due to a residual contamination from this isotope.

Figure 12

$\gamma$-ray spectrum for decays correlated with ${}^{48}\mathrm{Fe}$.

Figure 13

DSSSD charged-particle spectrum correlated with ${}^{48}\mathrm{Fe}$ implants. The black-empty histogram is the full DSSSD spectrum. The dashed-red histogram is gated on the $\gamma$ line at 98 keV and scaled up to account for the $\gamma$ efficiency.

Figure 14

Decay scheme of ${}^{48}\mathrm{Fe}$ deduced from the present experiment. Explanations on the dashed levels at 3.619 and 4.299 MeV are given in the text.

Figure 15

Spectrum of the time correlations between each proton decay (DSSSD energy $>0.98$ MeV) and all ${}^{52}\mathrm{Ni}$ implants.

Figure 16

(a) DSSSD charged-particle spectrum for decay events correlated with ${}^{52}\mathrm{Ni}$ implants. (b) Fit of the peaks related to the proton emission following the $\beta$ decay of ${}^{52}\mathrm{Ni}$. Peaks are labeled according to the corresponding excitation energies in the $\beta$-daughter ${}^{52}\mathrm{Co}$.

Figure 17

$\gamma$-ray spectrum for decay events correlated with ${}^{52}\mathrm{Ni}$ implants. (a) High-amplification spectrum showing the $\gamma$ line at 141 keV. (b) Low-amplification spectrum showing the $\gamma$ line at 2407 keV.

Figure 18

Decay scheme of ${}^{52}\mathrm{Ni}$ deduced from the present experiment. The energy of the $2^{+}$ level is assumed from the mirror ${}^{52}\mathrm{Mn}$. The dashed $1^{+}$ state has been observed in ${}^{52}\mathrm{Mn}$.

Figure 19

$\gamma$-ray spectrum for decay events correlated with ${}^{56}\mathrm{Zn}$ implants in coincidence with protons from the levels at (a) 1.691, (b) 2.661, and (c) 1.391 MeV.

Figure 20

Decay scheme of ${}^{56}\mathrm{Zn}$ deduced from the results of the present experiment. The dashed lines represent transitions corresponding to those observed in the mirror ${}^{56}\mathrm{Co}$ nucleus.

Figure 21

Mass excesses of the $T_z=-2$ nuclei ${}^{48}\mathrm{Fe},{}^{52}\mathrm{Ni}$, and ${}^{56}\mathrm{Zn}$. The difference is shown between the values we obtain from the IMME (red circles) and values from the systematics 2003 AME [30] (blue triangles) and 2012 AME [26] (green squares). The data points belonging to each nucleus are slightly displaced to show the error bars better.