$T_z=-1\to 0$ $\beta$ decays of ${}^{54}\mathrm{Ni},{}^{50}\mathrm{Fe},{}^{46}\mathrm{Cr}$, and ${}^{42}\mathrm{Ti}$ and comparison with mirror $({}^3\mathrm{He},t)$ measurements

We have studied the $\beta$ decay of the $T_z=-1,f_{7/2}$ shell nuclei ${}^{54}\mathrm{Ni},{}^{50}\mathrm{Fe},{}^{46}\mathrm{Cr}$, and ${}^{42}\mathrm{Ti}$ produced in fragmentation reactions. The proton separation energies in the daughter $T_z=0$ nuclei are relatively large $(\approx 4$–5 MeV) so studies of the $\gamma$ rays are essential. The experiments were performed at GSI as part of the Stopped-beam campaign with the RISING setup consisting of 15 Euroball Cluster Ge detectors. From the newly obtained high precision $\beta$-decay half-lives, excitation energies, and $\beta$ branching ratios, we were able to extract Fermi and Gamow-Teller transition strengths in these $\beta$ decays. With these improved results it was possible to compare in detail the Gamow-Teller (GT) transition strengths observed in beta decay including a sensitivity limit with the strengths of the $T_z=+1$ to $T_z=0$ transitions derived from high resolution $\left({}^3\mathrm{He},t\right)$ reactions on the mirror target nuclei at RCNP, Osaka. The accumulated $B$(GT) strength obtained from both experiments looks very similar although the charge exchange reaction provides information on a broader energy range. Using the “merged analysis” one can obtain a full picture of the $B$(GT) over the full $Q_{\beta }$ range. Looking at the individual transitions some differences are observed, especially for the weak transitions. Their possible origins are discussed.

Figure 1

The schematic layout of the FRS separator and the various detectors used for the identification of the ions. In the lower part of the figure, a schematic layout of the RISING setup including the arrangement of the six DSSSDs is shown.

Figure 2

Identification plot for the reaction fragments separated and identified up to SCI41 in the ${}^{54}\mathrm{Ni}$ run. $Z^{*}$ and $A/Q^{*}$ are adjusted to give the correct $Z$ and $A/Q$ for ${}^{54}\mathrm{Ni}$. Small differences from the correct $Z$ and $A/Q$ may exist for the other nuclear species.

Figure 3

Identification plots of the reaction fragments separated and identified, including the implantation condition in detector M2, for the four measurements. The window to select the desired implant is shown for each case. $Z^{*}$ and $A/Q^{*}$ are the correct $Z$ and $A/Q$ for the desired nuclei in each case; small differences from the correct $Z$ and $A/Q$ may exist for the other nuclear species.

Figure 4

Sum of all aligned but not calibrated M2 DSSSD Y-Strip signals for implantation events in the ${}^{54}\mathrm{Ni}$ measurement. The vertical lines show the selected implantation energy range in arbitrary units (a.u.).

Figure 5

Sum of all aligned but not calibrated M2 DSSSD Y-Strip signals for decay events in the ${}^{54}\mathrm{Ni}$ measurement. The red lines (color online) show the selected $\beta$-decay energy range.

Figure 6

Experimental and simulated $\gamma$ efficiencies using add-back. The experimental values for ${}^{60}\mathrm{Co},{}^{133}\mathrm{Ba},{}^{137}\mathrm{Cs},{}^{152}\mathrm{Eu}$, and ${}^{226}\mathrm{Ra}$ are shown as triangles and circles. The simulated efficiencies are shown as squares. Both experimental and simulated values were fitted using $ln\left[\epsilon \left(E_{\gamma }\right)\right]={\sum }_{k=0}^5{p}_k(ln{\left(E_{\gamma }\right)}^k$ [16], where $\epsilon \left(E_{\gamma }\right)$ is the $\gamma$ efficiency at energy $E_{\gamma }$ and $p_k$ values are the fitting parameters for the RISING Ge array $\mathrm{[}{p}_0$ = 50.31(4), $p_1$ = $-43.38$(1), $p_2$ = 14.42(1), $p_3$ = $-2.350$(1), $p_4$ = 18.74(1)$\times 10{}^{-2}$, and $p_6$ = $-58.84$(3)$\times 10{}^{-4}$]. The resulting efficiency curve is shown by the solid line.

Figure 7

“Good correlations” (in black) between beta and implantation events happening in the same pixel $\left(i,j\right)$ as a function of correlation time. “Wrong correlations” (in green) between beta events happening in pixel $\left(i,j\right)$, and implantations happening in the opposite pixel $\left(j,i\right)$ (for $i\ne j)$. The “Wrong correlation” background was normalized to the “Good correlations” data. As can be seen in the figure both spectra overlap perfectly. The 13-s period of the oscillating background is related to the 10 s ON and 3 s OFF spill structure of the primary beam from the SIS18 synchrotron.

Figure 8

The figure shows the implantation-$\beta$ correlations for (a) ${}^{54}\mathrm{Ni}$, (b) ${}^{50}\mathrm{Fe}$, (c) ${}^{46}\mathrm{Cr}$, and (d) ${}^{42}\mathrm{Ti}$ with the background from the random correlations subtracted (see text for details). The fits to the decay curves obtained were made with two components namely the decay of initial $T_z=-1$ nuclei and the growth and decay of $T_z=0$ daughter nuclei. As a result the half-lives of the $T_z=-1$ nuclei were obtained (see text).

Figure 9

The $\gamma$ spectrum obtained in the add-back mode for the ${}^{54}\mathrm{Ni}$ FRS setting in coincidence with $\beta$ particles, but without any condition on the implanted nuclei. The identified $\gamma$ lines in the ${}^{54}\mathrm{Co}$ daughter nucleus from the decay of the ${}^{54}\mathrm{Ni}$ mother nucleus are marked with the symbol $♣$. Gamma lines in the spectrum are also identified that correspond to neutron capture in Ge and Al (*), the summing of two gammas $\left(\Sigma \right)$, and $\gamma$ rays from the decay of other nuclei implanted in the M2 DSSSD such as ${}^{53}\mathrm{Mn}$ $(\otimes$, from ${}^{53}\mathrm{Fe}{\beta }^{+}$ decay [26]), ${}^{50}\mathrm{Cr}$ $(\oplus$, from ${}^{50}\mathrm{Mn}{\beta }^{+}$ decay [27]), ${}^{52}\mathrm{Fe}$ $(\aleph$, from ${}^{52}\mathrm{Co}{\beta }^{+}$ decay [28] or ${}^{53}\mathrm{Co}$ $p$ decay [29]), ${}^{53}\mathrm{Fe}$ $(\nabla$, from ${}^{53}\mathrm{Co}{\beta }^{+}$ decay [30]), and ${}^{52}\mathrm{Cr}$ $(\square$, from ${}^{52m}\mathrm{Mn}{\beta }^{+}$ decay [31]).

Figure 10

The $\gamma$ spectrum obtained in the add-back mode for the ${}^{50}\mathrm{Fe}$ FRS setting in coincidence with $\beta$ particles, but without any condition on the implanted nuclei. The identified $\gamma$ lines in the ${}^{50}\mathrm{Mn}$ daughter nucleus from the decay of the ${}^{50}\mathrm{Fe}$ mother nucleus are marked with the symbol $♣$. Gamma lines in the spectra are also identified that correspond to neutron capture in Ge and Al (*), the summing of two gammas $\left(\Sigma \right)$, and $\gamma$ rays from the decay of other nuclei implanted in the M2 DSSSD such as ${}^{49}V$ $(\aleph$, from ${}^{49}\mathrm{Cr}\hspace{0.5em}{\beta }^{+}$ decay [32]), ${}^{50}\mathrm{Cr}$ $(\oplus$, from ${}^{50m}\mathrm{Mn}\hspace{0.5em}{\beta }^{+}$ decay [27]), ${}^{48}\mathrm{Cr}$ $(\nabla$, from ${}^{48}\mathrm{Mn}\hspace{0.5em}{\beta }^{+}$ decay [33]), ${}^{44}\mathrm{Ca}$ $(\circledR$, from ${}^{44}\mathrm{Sc}\hspace{0.5em}{\beta }^{+}$ decay [34]), and ${}^{52}\mathrm{Cr}$ $(\square$, from ${}^{52m}\mathrm{Mn}\hspace{0.5em}{\beta }^{+}$ decay [31]).

Figure 11

The $\gamma$ spectrum obtained in the add-back mode for the ${}^{46}\mathrm{Cr}$ FRS setting in coincidence with $\beta$ particles, but without any condition on the implanted nuclei. The identified $\gamma$ lines in the ${}^{46}\mathrm{V}$ daughter nucleus from the decay of the ${}^{46}\mathrm{Cr}$ mother nucleus are marked with the symbol $♣$. Gamma lines in the spectra are also identified that correspond to neutron capture in Ge, Al, and Si (*), the summing of two gammas $\left(\Sigma \right)$, and $\gamma$ rays from the decay of other nuclei implanted in the M2 DSSSD such as ${}^{42}\mathrm{Ca}$ $(\oplus$, from ${}^{42m}\mathrm{Sc}\hspace{0.5em}{\beta }^{+}$ decay [35] and ${}^{42g}\mathrm{Sc}\hspace{0.5em}{\beta }^{+}$ decay [37]), ${}^{44}\mathrm{Ti}$ $(\aleph$, from ${}^{44g}\mathrm{V}\hspace{0.5em}{\beta }^{+}$ decay [28] or $\nabla$ from ${}^{44m}\mathrm{V}\hspace{0.5em}{\beta }^{+}$ decay [28]), ${}^{44}\mathrm{Ca}(\circledR$, from ${}^{44}\mathrm{Sc}\hspace{0.5em}{\beta }^{+}$ decay [34]), and ${}^{38}\mathrm{Ar}$ $(\square$, from ${}^{38}\mathrm{K}\hspace{0.5em}{\beta }^{+}$ decay [38]).

Figure 12

The $\gamma$ spectrum obtained in the add-back mode for the ${}^{42}\mathrm{Ti}$ FRS setting in coincidence with $\beta$ particles, but without any condition on the implanted nuclei. The identified $\gamma$ lines in the ${}^{42}\mathrm{Sc}$ daughter nucleus from the decay of the ${}^{42}\mathrm{Ti}$ mother nucleus are marked with the symbol $♣$. Gamma lines in the spectra are also identified that correspond to neutron capture in Ge and Al (*), the summing of two gammas $\left(\Sigma \right)$, and $\gamma$ rays from the decay of other nuclei implanted in the DSSSD such as ${}^{42}\mathrm{Ca}$ $(\oplus$, from ${}^{42m}\mathrm{Sc}{\beta }^{+}$ decay [35]), ${}^{38}\mathrm{Ar}$ $(\square$, from ${}^{38}\mathrm{K}{\beta }^{+}$ decay [38]), and ${}^{40}\mathrm{Ca}(\oslash$, from ${}^{40}\mathrm{Sc}{\beta }^{+}$ decay).

Figure 13

${}^{54}\mathrm{Ni}\beta$-decay scheme. All the values given in this figure originate from the present work except for the $Q_{\beta }$ value which is taken from [9] and the daughter half-life, taken from [7].

Figure 14

${}^{50}\mathrm{Fe}\beta$-decay scheme. All the values given in this figure originate from the present work except for the $Q_{\beta }$ value which is taken from [9] and the daughter half-life, taken from [7].

Figure 15

${}^{46}\mathrm{Cr}$ $\beta$-decay scheme. All the values given in this figure originate from the present work except for the $Q_{\beta }$ value which is taken from [9] and the daughter half-life, taken from [7].

Figure 16

${}^{42}\mathrm{Ti}\beta$-decay scheme. All the values given in this figure originate from the present work except for the $Q_{\beta }$ value which is taken from [21] and the daughter half-life, taken from [7].

Figure 17

The figure shows the implantation $\beta -\gamma$ correlations for ${}^{54}\mathrm{Ni}$ implants and the 937-keV $\gamma$ line, with the background of the random correlations subtracted. The fit to the decay curve was made with a single decay component.

Figure 18

Comparison of $B$(GT) values obtained in the present analysis (solid red triangles) and those from the $({}^3\mathrm{He},t)$, CE reactions (solid blue circles) as a function of excitation energy in the daughter nucleus. To derive the absolute $B$(GT) values from the CE reaction data, the “merged analysis” was used (see text). The dots show the sensitivity limit in the present experiment; for masses 54 and 50 the limit stops at the energy where proton decay is expected to dominate (see text).

Figure 19

Comparison of accumulated $B$(GT) values obtained in the present analysis (solid red triangles) and those from the $({}^3\mathrm{He},t)$, CE reactions (solid blue circles) as a function of excitation energy in the daughter nucleus. To derive the absolute accumulated $B$(GT) values from the data of CE reactions, the “merged analysis” was used (see text).