Simultaneous investigation of the $\mathbf{T=1~ (J^{\pi}=0^+)}$ and $\mathbf{T=0 ~ (J^{\pi}=9^+)}$ $\beta$ decays in $^{70}$Br

TL;DR

This study investigates the $eta$ decay of $^{70}$Br, measuring half-lives of its isomers, identifying new gamma-ray transitions, and proposing new excited states in $^{70}$Se, supported by shell-model calculations.

Contribution

It provides precise half-life measurements for $^{70}$Br isomers, reports new gamma-ray transitions, and proposes new excited states in $^{70}$Se with shell-model interpretation.

Findings

Half-life of $^{70}$Br $J^{ u}=9^+$ isomer: 2157 ms

Half-life of $^{70}$Br $J^{ u}=0^+$ ground state: 78.42 ms

Identification of four new gamma-ray transitions and two new excited states in $^{70}$Se

Abstract

The $\beta$ decay of the odd-odd nucleus $^{70}$Br has been investigated with the BigRIPS and EURICA setups at the Radioactive Ion Beam Factory (RIBF) of the RIKEN Nishina Center. The $T=0$ ($J^{\pi}=9^+$) and $T=1$ ($J^{\pi}=0^+$) isomers have both been produced in in-flight fragmentation of $^{78}$Kr with ratios of 41.6(8)\% and 58.4(8)\%, respectively. A half-life of $t_{1/2}=2157^{+53}_{-49}$ ms has been measured for the $J^{\pi}=9^+$ isomer from $\gamma$-ray time decay analysis. Based on this result, we provide a new value of the half-life for the $J^{\pi}=0^+$ ground state of $^{70}$Br, $t_{1/2}=78.42\pm0.51$ ms, which is slightly more precise, and in excellent agreement, with the best measurement reported hitherto in the literature. For this decay, we provide the first estimate of the total branching fraction decaying through the $2^+_1$ state in the daughter nucleus $^{70}$Se, $R(2^+_1)=1.3\pm1.1\%$. We also report four new low-intensity $\gamma$-ray transitions at 661, 1103, 1561, and 1749 keV following the $\beta$ decay of the $J^{\pi}=9^+$ isomer. Based on their coincidence relationships, we tentatively propose two new excited states at 3945 and 4752 keV in $^{70}$Se with most probable spins and parities of $J^{\pi}=(6^+)$ and $(8^+)$, respectively. The observed structure is interpreted with the help of shell-model calculations, which predict a complex interplay between oblate and prolate configurations at low excitation energies.

Tables

Table 1. Table 1: Error contributions to the half-life determination of the T = 1 ​ ( J π = 0 + ) 𝑇 1 superscript 𝐽 𝜋 superscript 0 T=1~{}(J^{\pi}=0^{+}) ground state of 70 Br. The total uncertainty is given in the last row.

Source	Contribution (ms)
bin	0.10
starting time of fit	0.14
fit range	0.0013
half-life 70Br isomer	0.16
half-life 70Se	0.002
half-life 70As	0.002
background	0.10
$\beta$ threshold	0.11
Statistical	0.43
Total	0.51

Table 2. Table 2: Determination of ℱ ​ t ℱ 𝑡 \mathcal{F}t values for the superallowed decay of 70 Br. First line, using the Q E ​ C subscript 𝑄 𝐸 𝐶 Q_{EC} from Davids ( 1980 ); Hardy and Towner ( 2015 ) , the f 𝑓 f value quoted in Hardy and Towner ( 2015 ) and the experimental t 1 / 2 subscript 𝑡 1 2 t_{1/2} and R 𝑅 R determined in this work. Second line, using the Q E ​ C subscript 𝑄 𝐸 𝐶 Q_{EC} value from Savory et al. ( 2009 ); Wang et al. ( 2017 ) and the f 𝑓 f value determined using the LOGFT code available in the NNDC website NNDC . Transition-dependent radiative and nuclear corrections are taken from Ref. Hardy and Towner ( 2015 ) , δ R ′ = 1.49 % subscript superscript 𝛿 ′ 𝑅 percent 1.49 \delta^{\prime}_{R}=1.49\% and δ C − δ N ​ S = 1.78 ± 0.25 % subscript 𝛿 𝐶 subscript 𝛿 𝑁 𝑆 plus-or-minus 1.78 percent 0.25 \delta_{C}-\delta_{NS}=1.78\pm 0.25\% .

$Q_{EC}$ (keV)	$t_{1/2}$ (s)	$f$	$R$ (%)	$P_{EC}$ (%)	$ft$ (s)	$ℱt$ (s)
$9970\pm 170$ Davids (1980)	$0.07842\pm 0.00051$	$38600\pm 3600$ Hardy and Towner (2015)	$97.94\pm 1.75$	0,173	$3096\pm 293$	$3086\pm 293$
$10504\pm 15$ Savory et al. (2009)	$0.07842\pm 0.00051$	$50979\pm 385$ NNDC	$97.94\pm 1.75$	0,133	$4087\pm 83$	$4078\pm 83$

Equations

$$\mathcal{F}t\equiv ft(1+{\delta }_R^{{}^{\prime }})(1+{\delta }_{NS}-{\delta }_C)=\frac{K}{2G_V^2(1+{\Delta }_R^V)}$$

$$\text{centering}{N}_{\gamma }(\Delta t_2)=N_0^{\beta }\cdot F(\Delta t_2,9^{+})\cdot R^m\cdot {\epsilon }_{\gamma }\cdot I_{\gamma }^{T=0}(2_1^{+})\text{@add@centering}$$

$$\text{centering}\begin{array}{r}{N}_{\gamma }(\Delta t_1)=N_0^{\beta }\cdot F(\Delta t_1,9^{+})\cdot R^m\cdot {\epsilon }_{\gamma }\cdot I_{\gamma }^{T=0}(2_1^{+})\\ +N_0^{\beta }\cdot F(\Delta t_1,0^{+})\cdot (1-R^m)\cdot {\epsilon }_{\gamma }\cdot I_{\gamma }^{T=1}(2_1^{+})\end{array}\text{@add@centering}$$

$$t=\frac{t_{1/2}}{R}(1+P_{EC})$$

Full text

I Introduction

One of the core concepts of the electroweak standard model is the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix which is used to describe the quark weak-interaction eigenstates in terms of the quark mass eigenstates Hardy and Towner (2013). Hitherto, superallowed $\beta$ transitions between $J^{\pi}=0^{+}$, $T=1$ analog states have provided the most precise value of the largest matrix element, the up-down term $V_{ud}$. $V_{ud}$ can be extracted from the ratio between $G_{V}$, the vector coupling constant for a semileptonic decay, and $G_{F}$, the weak-interaction constant for a pure leptonic decay. The Conserved Vector Current (CVC) hypothesis postulates that $G_{V}$ is a universal constant independent of the nuclear medium. This means that the strength or $ft$ value of the superallowed Fermi transitions, which are only mediated by the vector current, is the same for nuclei with identical isospin. As a result, a mean $ft$ value can be used to determine $V_{ud}$ Hardy and Towner (2015).

Experimental $ft$ values are obtained from the total transition energy $Q_{EC}$ (required for the calculation of $f$), the half-life of the parent state, and the branching ratio of the superallowed Fermi transition (both required for the calculation of $t$). In practice, small corrections accounting for radiative and isospin symmetry-breaking effects are incorporated as discussed in Ref. Hardy and Towner (2015), resulting in a “corrected” $\mathcal{F}t$ value given by

[TABLE]

where $K$ is a constant, $\delta_{C}$ is the isospin symmetry-breaking correction, $\Delta^{V}_{R}$ is the transition-independent part of the radiative correction, and $\delta^{{}^{\prime}}_{R}$ and $\delta_{NS}$ are the transition dependent parts of the radiative correction Hardy and Towner (2015).

Up to now, 14 superallowed $\beta$ decays have been measured with enough precision to test the CVC hypothesis, resulting in a world-average corrected $\mathcal{F}t=3072.27\pm 0.72$ s Hardy and Towner (2015). The superallowed $\beta$ decay of 70Br has been excluded from this compilation due to conflicting experimental values for the $Q_{EC}$ decay energy Davids (1980); Savory et al. (2009). On top of this, the currently adopted half-life is only known to a precision of $\sim 10$ parts in a thousand and the superallowed $0^{+}\rightarrow 0^{+}$ branching ratio has not been measured yet Hardy and Towner (2015). This decay, combined with the relatively recent results on 62Ga Finlay et al. (2008) and 74Rb Dunlop et al. (2013), is an excellent testing ground for theoretical modeling due to the increased role of the charge-dependent corrections in nuclei with A $\geq$ 62 Hardy and Towner (2002).

In addition to the CVC motivation, the nuclei in this mass region are of particular interest because their properties change rapidly with the addition or subtraction of one nucleon. The resulting scenario of nuclear shape evolution is intricate and challenges state-of-the-art nuclear models, which have to cope with the development of spherical, oblate, and prolate shapes stabilized by the occupation of the deformation-driving orbital $g_{9/2}$ Hasegawa et al. (2007); Möller et al. (2009); Zhi-Jun et al. (2015). Moreover different shape minima may compete simultaneously at low spins and excitation energies in a single nucleus, leading to the occurrence of shape coexistence. This phenomenon, widely studied in recent years (see Ref. Heyde and Wood (2011) for a review), may help us to understand the microscopic mechanisms enhancing quantum many-body correlations in exotic nuclei Otsuka and Tsunoda (2016); Kremer et al. (2016); Morales et al. (2017).

Experimentally, the picture of shape-related phenomena in the Se (Z=34) isotopic chain is more ambiguous than for the heavier Kr (Z=36) isotopes Gade et al. (2005); Clément et al. (2007); Poirier et al. (2004); Briz et al. (2015); Görgen et al. (2005); Iwasaki et al. (2014). It has been shown that the ground states of the even-even 74-82Se are prolate-deformed Lecomte et al. (1977, 1978). However, for the lighter 68,70,72Se isotopes, there is evidence for oblate-deformed ground states Fischer et al. (2000); Ljungvall et al. (2008); McCutchan et al. (2011), but this has been called into question by other studies Hurst et al. (2007); Obertelli et al. (2009). Theoretically, a number of microscopic approaches support an oblate ground-state shape that evolves rapidly into a prolate collective rotation for spin $J\geqslant 6$ Mylaeus et al. (1989); Petrovici et al. (2003); Kaneko et al. (2004); Ljungvall et al. (2008); Hinohara et al. (2009); Kaneko et al. (2015); Petrovici (2015). This is consistent with the measured moments of inertia (see, for instance, Fig. 1 of Ref. McCutchan et al. (2011)). There are discrepancies, though, in the value of the spin at which the phase-shape transition occurs. This is due to the differences found between models in the predicted shape minima and configuration mixing, which lead to different shape-coexistence pictures. Hence, further experimental information on the competing shapes is important to completely understand the rapid shape changes in the $A\sim 70$ mass region.

It is worth also noting that most of these nuclei are on the pathway of the rp-process of stellar nucleosynthesis Wallace and Woosley (1981); Schatz et al. (2001); Savory et al. (2009) and some of them, as 68Se and 72Kr, are important waiting-points defining the time scale of the process. Here, shape coexistence and mixing are crucial to determine the shape of the $\beta$-strength distribution and, hence, the stellar $\beta$-decay rates.

In the present article we report on a $\beta$-decay study of the odd-odd self-conjugate nucleus 70Br. The experiment was performed at the RIKEN Nishina Center using the BigRIPS spectrometer and the EURICA $\beta$-decay station Nishimura (2012). The results are of relevance in terms of deriving an additional $\mathcal{F}t$ value for the CVC test and extending our knowledge of the structure of 70Se. We present here an improved measurement of the half-life of the $T=1$ ($J^{\pi}=0^{+}$) ground state of 70Br and, for the first time, an estimate of the total branching fraction to the $2^{+}_{1}$ state in the daughter nucleus 70Se.

In previous half-life measurements, 70Br nuclei were produced in fragmentation and fusion-evaporation reactions Alburger (1978); Burch et al. (1988); López Jiménez et al. (2002); Rogers et al. (2014), which are optimal tools for the population of isomeric states. Though the $T=0~{}(J^{\pi}=9^{+})$ $\beta$-decaying isomer was already known by the time most of these works were published Vosicki et al. (1981), its contribution to the measured decay curve has hitherto been neglected. Therefore, this is the first work in which both the $T=1~{}(J^{\pi}=0^{+})$ and $T=0~{}(J^{\pi}=9^{+})$ $\beta$ decays of 70Br were investigated simultaneously.

The paper is organized as follows. In Sec. II the experimental apparatus is presented. Section III describes the correlations defined to obtain the $\beta$-decay information. Next we present the results for the $T=0~{}(J^{\pi}=9^{+})$ (Sec. IV) and $T=1~{}(J^{\pi}=0^{+})$ (Sec. V) states of 70Br. A discussion of these results, including a comparison with shell-model calculations, is provided in Sec. VI. Finally, we present a brief summary and conclusions in Sec. VII.

II The experimental setup

70Br nuclei were produced in the fragmentation of relativistic 78Kr projectiles impinging on a 5-mm thick Be target. The 78Kr primary beam was delivered by the RILAC2-RRC-fRC-IRC-SRC acceleration system with an energy of 345 MeV/nucleon and an average intensity of 38 pnA Nishida et al. (2016). The exotic fragmentation residues were separated and selected in the BigRIPS separator using the $\Delta E-B\rho-ToF$ method, which is based on an event-by-event measurement of the energy loss ($\Delta E$), magnetic rigidity ($B\rho$), and time-of-flight ($ToF$) of the ions. Multi-sampling ionization chambers, parallel-plate avalanche counters, and plastic scintillators were located in the focal planes of the beam line for this purpose. Fragmentation products were then identified by their mass-to-charge ratio (A/Q) and atomic number (Z) using standard particle-identification procedures Fukuda et al. (2013); Blank et al. (2016).

The nuclei were transported in-flight to a $\beta$-decay station located at the exit of the ZeroDegree spectrometer Mizoi et al. (2008). The setup consisted of the Wide-range Active Silicon Strip Stopper Array for Beta and ion detection (WAS3ABi), used to measure the energy, time, and position of implantations and $\beta$ particles, and the EUroball-RIKEN Cluster Array (EURICA), used for the measurement of the energy and time of $\gamma$-ray transitions following implantation or $\beta$ decay Nishimura (2012); Söderström et al. (2012).

The nuclei were implanted in WAS3ABi with the help of a homogeneous aluminum degrader 1.2 mm thick. A plastic scintillator (henceforth called the veto detector) was located behind WAS3ABi to identify ions passing through the active stopper. In the present experiment, WAS3ABi consisted of a compact array of 3 double-sided silicon-strip detectors (DSSSD), each with $6\times 4$ cm2 area and 1 mm thickness. The DSSSD detectors were segmented in 60 vertical (X) and 40 horizontal (Y) strips, providing 2400 pixels with an active area of $1\times 1$ mm2 each. Energy and time signals from each strip were read by standard analogue electronics in a high-gain branch suited for the energy range of decay particles. The energy range of the X strips was set to 4 MeV to optimize the energy resolution for $\beta$ particles, while that of the Y strips was extended to 10 MeV to detect high-energy protons. In-flight fragments reaching WAS3ABi with energies well above 1 GeV were registered as overflow signals. Since high-energy ions passing through WAS3ABi typically overflowed more than one strip, their implantation position was determined from the identification of the X and Y strips with the fastest time signals Nishimura et al. (2013).

The EURICA $\gamma$-ray array was composed of 84 HPGe detectors grouped in 12 clusters of 7 crystals each. The clusters were placed surrounding WAS3ABi at an average distance of 22 cm, achieving a total absolute detection efficiency of 10% at 662 keV. The $\gamma$ rays were registered up to 100 $\mu s$ after the detection of a triggering signal in WAS3ABi. This allowed for the detection of isomeric states ranging from several ns up to some ms in both parent and daughter nuclei.

III Correlation procedure

Implanted nuclei and $\beta$ particles were identified and separated offline. Implantations were defined by (1) a high-energy signal in the last fast-plastic scintillators of the BigRIPS and the ZeroDegree spectrometers, (2) an overflow energy signal in WAS3ABi, and (3) no energy signal in the veto detector. On these criteria, about 1.3$\times 10^{6}$ 70Br implantation events were registered in the central DSSSD of WAS3ABi. The implantation position was determined from the identification of the X and Y strips with the fastest time signal as described before. For each valid implantation, $\beta$ particles were accepted in correlation if (a) no high-energy signal was registered in the last fast-plastic scintillators of the BigRIPS and the ZeroDegree spectrometers, (b) no overflow energy signal was registered in the Y strips of WAS3ABi, (c) an energy signal above a variable threshold (see discussion in Sec. VA) was detected in WAS3ABi in the same pixel as the implantation event, and (d) the time elapsed between the implantation and all subsequent $\beta$ particles was shorter than 20 s. The energy released by $\beta$-like events was obtained by adding the energies of neighboring strips in each DSSSD detector and their position was defined as the energy-weighted mean of the X and Y strips added together. The resulting activities were sorted as a function of time to extract $\beta$-decay half-lives.

Examples of $\beta$-decay time spectra for the $9^{+}$ and $0^{+}$ isomers are shown in Fig. 1. These were fitted to the Bateman equations Bateman (1910) to obtain the half-lives. In the fitting procedure we used a $\chi^{2}$ minimization algorithm for the evaluation of parameters and goodness-of-fit. Because the standard $\chi^{2}$ test works properly for histogram data only if both Gaussian and Poisson statistics are applicable, the number of counts in the histogram bins was kept larger than $\sim 10$. Thus, we did not subtract the random ion-$\beta$ correlations from the decay curves, but added a constant background function to the fit. The background was evaluated in separate time-correlated spectra including the so-called backward-time correlations Kurtukián-Nieto et al. (2008); Morales et al. (2014), which were built between implantations and preceding $\beta$ particles using the conditions (1) to (3) and (a) to (d) as for the normal time correlations.

In Fig. 1, the minimized fitting functions are indicated as continuous lines. It should be noted that at least the first 2 ms were excluded from the fits in order to avoid decay-dependent dead-time contributions due to the electronic processing of implantation events Goigoux et al. (2016). For the sake of clarity, the contributions from the $0^{+}$ and $9^{+}$ activities are indicated as dashed and dotted lines, respectively, while the constant background is shown as a dot-dashed line. The goodness of the fits in describing the data is confirmed by the reduced $\chi^{2}$ values and the bin-by-bin residual plots, which are also shown in the figure.

In order to obtain $\beta$-delayed $\gamma$-ray energy spectra, the maximum time elapsed between implantations and $\beta$ particles was fixed to five half-life periods. In addition, the time difference between $\beta$ particles and $\gamma$ rays (henceforth called $\beta(\gamma)$ correlation) was set to 800 ns to include low-energy $\gamma$ rays affected by the electronic time walk, though it could be extended up to 100 $\mu s$ in the presence of isomeric transitions. Background contributions from other nuclear species present in WAS3ABi were evaluated in separate $\beta$-delayed $\gamma$ spectra including the backward-time correlations.

IV $\beta$ decay of the T=0 (Jπ=9+) isomer

IV.1 Half-life

The half-life of the $T=0~{}(J^{\pi}=9^{+})$ isomer was extracted from the time behavior of the transitions at 945, 964, 1033, and 1093 keV, which were unambiguously assigned to 70Se in Refs. Piechaczek et al. (2000); Roeckl (2002); Rainovski et al. (2002). For each peak, spurious correlations with Compton $\gamma$ rays were evaluated by sorting ion-$\beta(\gamma)$ time distributions with well-defined close-lying Compton background. These spectra were normalized to the area under the peak defined by a linear-polynomial background function, and were subtracted from the ion-$\beta(\gamma)$ time-correlated spectrum for each transition. The resulting summed $\gamma$-ray time-decay histogram, divided in time bins of 20 ms, is shown in Fig. 1(a) for an interval of 20 s. The fitting function includes the exponential $\beta$ decay of the $T=0~{}(J^{\pi}=9^{+})$ state and a fixed background extracted from a constant linear fit to the backward-time distribution of ion-$\beta$ correlations. The final half-life is obtained from the average of the half-lives resulting from varying the bin width, the fitting range, and the starting fitting time of the time-correlated spectra. The overall half-life deduced is $t_{1/2}=2157^{+53}_{-49}$ ms. The error results from the quadratic sum of the statistical and systematic uncertainties, which amount to $\pm 30$ ms and ${}^{+44}_{-38}$ ms, respectively. Note that the systematic error is obtained from the quadratic sum of the uncertainties associated to the fixed background (${}^{+24}_{-11}$ ms), the bin width ($\pm 18$ ms), the fitting range ($\pm 8$ ms), and the starting fitting time ($\pm 31$ ms).

IV.2 $\beta$-delayed $\gamma$ spectroscopy

The background-subtracted $\beta$-delayed $\gamma$-ray energy spectrum including $\beta(\gamma)$ coincidences within 20 s after implantation of 70Br ions is shown in Fig. 2. A total of 28 $\gamma$ rays are attributed to the $\beta$ decay of the $T=0~{}(J^{\pi}=9^{+})$ isomer, of which the 661-, 1103-, 1561-, and 1749-keV transitions are reported here for the first time and the rest were reported in previous works Wadsworth et al. (1980); Ahmed et al. (1981); Mylaeus et al. (1989); Piechaczek et al. (2000); Roeckl (2002); Schmidt et al. (2002); Rainovski et al. (2002). The $\beta$($\gamma\gamma$) coincidence spectra gated on the new transitions and on the 958- and 1609-keV $\gamma$ rays are shown in Fig. 3. They are sorted for a maximum $\gamma$-$\gamma$ time difference of 300 ns. From these coincidence relations and $\gamma$-ray intensity-balance analysis, the $\beta$-decay scheme for 70Se is built as shown in Fig. 4. In the figure, arrow widths are proportional to transition intensities, spins and parities are in parentheses if not firmly assigned, and new (or modified) information is indicated in gray. Apparent $\beta$ feedings are extracted from $\gamma$-ray intensity balances. It is assumed that the direct ground-state $\beta$ feeding is null given the large spin difference ($9^{+}\rightarrow 0^{+}$) between the initial and final states. Hence, the intensities of the $\beta$-delayed $\gamma$ rays are normalized to the summed intensity of the $2^{+}_{1,2}\rightarrow 0^{+}$ $\gamma$ transitions. The log$ft$ values are calculated for a $Q_{EC}$ energy of $12.19(11)$ MeV, which was measured using a total absorption spectrometer Karny et al. (2004). Note that any missing $\gamma$ intensity from states located above the observed ones has not been considered, thus $\beta$ feedings and log$ft$ values should be taken as upper and lower limits, respectively Hardy et al. (1977).

In general, we find a good agreement with previous $\gamma$-spectroscopy works Wadsworth et al. (1980); Ahmed et al. (1981); Mylaeus et al. (1989); Piechaczek et al. (2000); Roeckl (2002); Schmidt et al. (2002); Rainovski et al. (2002), with the exception of the location of the 1609-keV transition which was previously suggested to feed the $2^{+}_{1}$ state from a $(4^{+})$ candidate at 2553 keV Mylaeus et al. (1989). Looking at our $\beta$-delayed $\gamma$-gated coincidence data in Fig. 3, we attribute this transition unambiguously to the $(6^{+}_{2})\rightarrow 4^{+}_{1}$ decay. We also confirm the placement of the 958-keV transition as connecting the $(8^{+}_{2})$ and $(6^{+}_{2})$ states as proposed in earlier conference proceedings Roeckl (2002); Schmidt et al. (2002).

Apart from the structure already reported in the literature, two new states are tentatively placed at 3945 and 4752 keV. The location of the 4752-keV level is supported by the observation of two de-exciting transitions, one at 1749 keV feeding the $6^{+}_{1}$ state and the other at 1103 keV feeding the $(6^{+}_{2})$ level. Based on this $\gamma$-decay pattern and on the observation of direct $\beta$ feeding from the $9^{+}$ isomer in 70Br, we propose a spin and parity $J^{\pi}=(8^{+})$ for the new level. On the other hand, the 3945-keV state is indicated by a dashed red line in Fig. 4 because the ordering of the 661- and 1561-keV coincident $\gamma$ rays cannot be established unambiguously from the $\gamma$ intensity balance. We propose a $661\rightarrow 1561$-keV $\gamma$ cascade connecting the $(8^{+}_{2})$ and $4^{+}_{2}$ states based on comparison with shell-model calculations (see Sec. VI.2 and Fig. 7). Given its $\gamma$ de-excitation pattern, its most likely spin and parity is $(6^{+})$. This assignment is supported by the non-observation of direct $\beta$ feeding from the $9^{+}$ state in 70Br.

V $\beta$ decay of the T=1 (Jπ=0+) isomer

V.1 Half-life

As will be discussed later, no $\gamma$ rays were observed in the decay of the $T=1~{}(J^{\pi}=0^{+})$ isomer (see Fig. 6). Therefore, the half-life of the superallowed Fermi transition was extracted directly from time correlations between $\beta$ particles and implantations of 70Br. These are sorted in Fig. 1(b) for a time bin of 1 ms and a correlation time interval of 5 s. The activities of the $9^{+}$ isomer, daughter (70Se) and grand-daughter (70As) nuclei were included in the fitting function, together with a fixed background extracted from a constant linear fit to the backward-time correlated spectra. The half-life of the $T=0~{}(J^{\pi}=9^{+})$ state was fixed to the value measured in the present work, $t_{1/2}=2157^{+53}_{-49}$ ms, while those of 70Se and 70As were fixed to the literature values of $2466\pm 18$ s and $3156\pm 18$ s respectively ENSDF . The fixed half-life parameters were varied by one standard deviation to evaluate their contribution to the overall uncertainty. Furthermore, we searched for other factors that could influence the evaluation of the half-life, such as the bin width of the time-correlated spectra, the correlation time interval, the starting time of the fitting range, the $\beta$ threshold, and the ion-$\beta$ correlation strip. The only free parameters in the fit were the half-life of the $T=1~{}(J^{\pi}=0^{+})$ ground state, the number of decays in the first time bin, and the production ratio of the $9^{+}$ isomer.

Table 1 lists the sources of errors evaluated in this work together with their contribution to the total uncertainty in the half-life of the $T=1~{}(J^{\pi}=0^{+})$ ground state. The total error amounts to 0.51 ms after adding in quadrature the listed uncertainties, as indicated in the last row of the table. The overall half-life measured in this work is $t_{1/2}=78.42\pm 0.51$ ms, reaching a precision better than $7$ parts in a thousand. The new result is slightly more precise and in excellent agreement with the best value reported thus far in the literature, $t_{1/2}=78.54\pm 0.59$ ms Burch et al. (1988). Looking at the second column of table 1, we can see that the main error contribution in this measurement comes from the statistical uncertainty associated to the fit. This is due to the fact that the production ratio of the $9^{+}$ isomeric state is also a free parameter of the fit. The resulting value is $R^{m}=41.6(8)\%$.

The half-life of the $T=1~{}(J^{\pi}=0^{+})$ ground state can also be evaluated with an independent procedure which is based on fitting separately the decay-time spectra for each X and Y strip. Accordingly, we can consider $N_{x}$ or $N_{y}$ uncoupled measurements of the half-life and calculate the weighted Gaussian mean of the distribution Hardy and Towner (2005). The only limitation comes from the statistical significance of the measurement for each individual strip, which requires, as mentioned above, a number of counts in the histogram bins greater than 10. As a consequence, the strips that do not fulfill this condition are excluded from the analysis (see panels (c) and (d) of Fig. 5). The resulting half-life is $t_{1/2}=77.2\pm 3.0$ ms ($\chi^{2}_{\nu}=1.107$) in the case of the X-strip analysis and $t_{1/2}=76.8\pm 2.9$ ms ($\chi^{2}_{\nu}=1.199$) for the Y-strip study. In spite of the rather large uncertainties, the extracted half-lives are in agreement with the result from the analysis of the summed spectra.

In Fig. 5, the half-life of the $T=1~{}(J^{\pi}=0^{+})$ ground state is shown as a function of (a) the fitting range, (b) the $\beta$ threshold, (c) the X strips, and (d) the Y strips. The half-lives shown in panels (a), (c), and (d) are obtained without imposing any specific condition on the $\beta$-threshold. Error bars indicate fit uncertainties for each data point. The average half-life deduced is shown as a thick continuous line and the total error as a dotted-dashed line. Panels (a) and (b) also show, in dots, the isomeric ratio of the $T=0~{}(J^{\pi}=9^{+})$ state for each lifetime fit and, in thick dashed line, the overall deduced value. For the sake of clarity, the corresponding scale is indicated on the right axis. In all cases the half-lives and isomeric ratios fluctuate statistically around the mean values, except for $\beta$ thresholds above 200 keV for which the results are out of the error bars. This is because the statistics drop significantly for these data points (note that the associated errors are bigger and, in the case of the half-life, consistent with the overall mean value). The flat behavior of the half-life in panel 5(a) indicates that no contaminant activities apart from those already included in the fit are present in the time-correlated spectra.

V.2 Branching ratio through the $2^{+}_{1}$ level

The Gamow-Teller (GT) branching ratios in the $\beta$ decay of selected $62\leq A\leq 74$ nuclei were calculated by J. C. Hardy and I. S. Towner using the shell model Hardy and Towner (2002). Because the $Q_{EC}$ values of these heavy nuclei are large, the total GT branching fraction is the sum of many individual weak GT transitions. In the case of 70Br, a total of 325 $1^{+}$ states are expected to be fed through GT $\beta$ transitions, resulting in a GT branching ratio of $1.59\%$ Hardy and Towner (2002). In the calculation, $63\%$ of the GT intensity is expected to de-excite through the $2^{+}_{1}$ level, resulting in $R^{GT}(2^{+}_{1})=1.59\times 0.63\approx 1\%$.

Experimentally, non-analog branching ratios (including both GT and non-analog Fermi $\beta$ strength) are usually obtained from the intensities of the observed $\gamma$ rays feeding the ground state. Because in some cases the strong fragmentation of the $\beta$ feeding prevents a direct observation of the de-exciting transitions Hardy et al. (1977), an estimate can be obtained from the measured $\gamma$ imbalance of the $2^{+}_{1}$ level, which acts as a collector of an important part of the non-analog intensity Piechaczek et al. (2003).

Figure 6 shows the $\beta$-delayed $\gamma$-ray spectrum sorted in a time interval $2-400$ ms after the detection of 70Br implantations to enhance $\gamma$ rays emitted following the decay of the $T=1~{}(J^{\pi}=0^{+})$ state. All the observed $\gamma$ transitions were identified before as resulting from the decay of the high-spin isomer. Yet we can estimate the fraction of the branching ratio from the $T=1~{}(J^{\pi}=0^{+})$ ground state that decays to the “collector” $2^{+}_{1}$ level from the measured intensity of the $2^{+}_{1}\rightarrow 0^{+}_{1}$ 945-keV $\gamma$ transition in two variable time windows. The first, $\Delta t_{1}$, contains the decay of both the high-spin isomer and the ground state, while the second, $\Delta t_{2}$, includes only the decay of the high-spin isomer. In order to let the $T=1~{}(J^{\pi}=0^{+})$ activity exhaust, we constrain the starting time of the second time interval to, at least, 15 half-life periods.

The number of counts in the 945-keV peak in each of the two time intervals can be expressed as

[TABLE]

[TABLE]

where $N^{\beta}_{0}$ is the total number of decays, $F(\Delta t,J^{\pi})$ is a correction factor that takes into account the finite time of the measurement (it is defined as the ratio between the activity integrated in the time-correlation window and an infinite time window), $R^{m}$ is the production ratio of the $T=0~{}(J^{\pi}=9^{+})$ isomer in the fragmentation reaction, $I_{\gamma}^{T}$ is the absolute intensity of the $2^{+}_{1}\rightarrow 0^{+}_{1}$ transition following $\beta$ decay of the $T=0$ or 1 isomers, and $\varepsilon_{\gamma}$ is its absolute photopeak efficiency. Note that the internal conversion coefficient, $\alpha_{tot}$, of the 945-keV transitions is not taken into account in expressions 2 and 3. This is a good approximation given the calculated value for a pure $E2$ transition, $\alpha_{tot}=4.81(7)\times 10^{-4}$ Kibédi et al. (2008). Furthermore, no dead-time corrections are included since $\gamma$-ray information was only recorded in coincidence with accepted $\beta$-like signals from WAS3ABi.

From expressions 2 and 3 we can estimate the total branching fraction from the $T=1~{}(J^{\pi}=0^{+})$ ground state in 70Br that decays through the $2^{+}_{1}$ level in 70Se. The resulting value, $R(2^{+}_{1})=I_{\gamma}^{T=1}(2^{+}_{1})=1.3\pm 1.1\%$, can be combined with the GT feeding accumulated by the $2^{+}_{1}$ state as calculated in Ref. Hardy and Towner (2002), $R^{GT}(2^{+}_{1})\approx 1\%$, to estimate the ratio between the non-analog Fermi and Gamow-Teller feedings decaying through the $2^{+}_{1}$ state in 70Se, $R^{F/GT}=30\%$. This value is in between the ones measured for the neighboring $N=Z$ nuclei 62Ga and 74Rb, $R^{F/GT}\sim 10\%$ Finlay et al. (2008) and $R^{F/GT}\sim 57\%$ Dunlop et al. (2013), respectively.

VI Discussion

VI.1 Testing CVC with the present results

The fraction of the branching ratio going through the $2^{+}_{1}$ level obtained in the previous section can be combined with the shell-model predictions of Ref. Hardy and Towner (2002) to estimate the superallowed $0^{+}_{gs}\rightarrow 0^{+}_{gs}$ branching fraction of 70Br. According to the theoretical result, 63% of the summed GT strength goes through the $2^{+}_{1}$ level. If we assume that the ratio between the $\gamma$ intensities decaying from non-analog Fermi and Gamow-Teller states is the same for the ground state, we can estimate a total non-analog branch $R^{na}=2.06\pm 1.75\%$ for this decay. This results in a superallowed $0^{+}_{gs}\rightarrow 0^{+}_{gs}$ branching ratio $R=97.94\pm 1.75\%$.

Both the half-life and the $0^{+}_{gs}\rightarrow 0^{+}_{gs}$ branching fraction discussed in this work have been used to estimate the $\mathcal{F}t$ value associated with the decay of the $T=1~{}(J^{\pi}=0^{+})$ state of 70Br. This allows one to check how well it agrees with the average $\overline{\mathcal{F}t}$ value obtained from the best 14 cases in the last compilation of superallowed $0^{+}\rightarrow 0^{+}$ transitions Hardy and Towner (2015). In the determination of ${\mathcal{F}t}$ we have followed the procedure outlined in Ref. Hardy and Towner (2015), which implies obtaining the partial half-life $t$ using the following formula:

[TABLE]

where $t_{1/2}$ is the half-life of the parent state, $R$ is the branching ratio of the superallowed transition, and $P_{EC}$ is the electron-capture fraction.

The values of $Q_{EC}$, $t_{1/2}$, $f$, $R$ and $P_{EC}$ employed in the calculation are presented in Table 2 together with the uncorrected $ft$ and corrected $\mathcal{F}t$ values. In the first line of the table we show the $\mathcal{F}t$ value calculated using the total transition energy obtained in a measurement of the positron end-point energy, $Q_{EC}$=9970(170) keV Davids (1980), which was proposed in the last compilation of superallowed Fermi transitions Hardy and Towner (2015). In this case we have used the $f$ value calculated by Ref. Hardy and Towner (2015). In the second line of the table we have determined the $\mathcal{F}t$ value for a total transition energy $Q_{EC}$=10504(15) keV, which was adopted in the last atomic mass evaluation Wang et al. (2017) from a Penning-trap mass measurement Savory et al. (2009). In this case the $f$ value has been determined using the LOGFT code available in the National Nuclear Data Center (NNDC) website NNDC .

Looking at the table, the $\mathcal{F}t$ value determined in the first row, $\mathcal{F}t=3086\pm 293$ s, is in good agreement with the last average value, $\overline{\mathcal{F}t}=3072.27\pm 0.72$ s Hardy and Towner (2015). On the other hand, the $\mathcal{F}t$ value obtained in the second row, $\mathcal{F}t=4074\pm 83$ s, differs dramatically from the mean $\overline{\mathcal{F}t}$, pointing to a possible incorrect determination of the $Q_{EC}$ value from the masses measured in the Penning-trap experiment Savory et al. (2009). The $Q_{EC}$ value of this decay is specifically discussed in Ref. Hardy and Towner (2015) because it does not follow the trend of the rest of the $Q_{EC}$ values for $T_{Z}$=0 superallowed transitions. In addition, it is in clear conflict with the CVC hypothesis, as shown by the resulting ${\mathcal{F}t}$ value listed in Table 2. In order to achieve a better sensitivity for the CVC test, both the $Q_{EC}$ value and the branching fraction of the superallowed transition in 70Br should be measured with improved uncertainties.

VI.2 Comparison with Shell-Model Calculations

The structure of 70Se has been interpreted using large-scale shell-model calculations performed in the $p$+$f_{5/2}$+$g_{9/2}$ model space. Both the effective interactions PMMU Kaneko et al. (2015) and JUN45 Honma et al. (2009) have been employed. The former is based on the unified realistic shell-model Hamiltonian PMMU Kaneko et al. (2014), which includes the pairing-plus-multipole Hamiltonian and a monopole interaction extracted from empirical fits starting from the monopole-based universal force. The latter is derived from the realistic Bonn-C nucleon-nucleon potential and a Linear Combination fit Chung (1976) to 400 experimental energies of 69 nuclei with $A=63-96$. Both interactions have successfully been used to describe the nuclear properties of $N\approx Z$ nuclei in the $A=64-80$ mass region Kaneko et al. (2014, 2015); Honma et al. (2009). In the present calculations, the effective charges for proton and neutron have been taken as $e_{p}=1.5$e and $e_{n}=0.5$e, respectively, which provide a good agreement with the observed B(E2) values in $A\sim 70$ nuclei Lüttke et al. (2012); Nichols et al. (2014). Furthermore, the PMMU Hamiltonian has been modified so as to fit the higher spin states of 70Se.

In Fig. 7 the experimental low-lying structure of 70Se is compared to the level schemes calculated using the PMMU (left) and JUN45 (right) interactions. Arrows connecting experimental levels stand for electromagnetic transitions observed in the present work, while arrows connecting calculated levels indicate large theoretical B(E2$\downarrow$) values. Spectroscopic quadrupole moments are also shown on the left of the theoretical states. They are expressed in units of e$\cdot$fm2.

In general, the excitation energies of the observed levels are well reproduced by both calculations, with the PMMU having a better accuracy for spins up to $6^{+}$ and the JUN45 for the $8^{+}$ and $10^{+}$ states. Similarly, the calculated spectroscopic quadrupole moments are in good agreement, except for the second $4^{+}$ and $6^{+}$ levels and the third $8^{+}$ state for which JUN45 predicts negative values and PMMU positive ones. Note that the experimental $(8^{+}_{3})$ level has been placed in the band built on the $2^{+}_{2}$ state. This is due to the non-observation of a $(8^{+}_{3})\rightarrow(6^{+}_{3})$ $\gamma$ transition connecting the two newly observed states. Instead, the $(6^{+}_{3})$ level is only fed by the $(8^{+}_{2})$ state at 4606 keV. This results in an inversion of the $(8^{+})$ states of bands 2 and 3.

Both calculations predict a prolate-deformed shape for the yrast $8^{+}$ level, as indicated by the large negative spectroscopic quadrupole moments $Q_{s}$ shown in Fig. 7. On the contrary, the yrast states up to $J^{\pi}=6^{+}$ have positive $Q_{s}$ values and can be interpreted as being dominated by oblate-deformed configurations. These calculations are consistent with the experimental evidence found thus far in the region: previous Coulomb excitation Hurst et al. (2007) and recoil-distance Doppler shift Ljungvall et al. (2008) measurements revealed a positive sign for the quadrupole moment of the first $2^{+}$ state in 70Se, thus confirming its oblate shape. As well, spectroscopic works on the neighboring 69,71Se provided good experimental evidence for oblate deformation in the low-lying levels of the $g_{9/2}$ band Wiosna et al. (1988). On the other hand, the $9^{+}$ state of 70Br is predicted to have a large negative $Q_{s}$ value ($Q_{s}=-120$ e$\cdot$fm2 for PMMU and $Q_{s}=-117$ e$\cdot$fm2 for JUN45), which indicates strong prolate deformation as for the yrast $8^{+}$ states in 70Se. The calculated Gamow-Teller transition strength to these levels results in B$(GT)=0.156$ and log$ft=4.62$ for PMMU and B$(GT)=0.131$ and log$ft=4.69$ for JUN45. These results compare well with log$ft=4.40(4)$ measured in the present work for the $(8^{+}_{2})$ level, indicating that they can be interpreted as their theoretical counterparts.

Experimentally, the $(8^{+}_{2})$ state is connected to the $8^{+}_{1}$ and $(6^{+}_{2})$ levels by intense transitions of 569- and 958-keV energy, respectively. This indicates a strong overlap of the wave functions of the three states and, hence, of configuration mixing. Instead, the 1603-keV $\gamma$ ray decaying to the yrast $6^{+}_{1}$ state is suppressed by a factor $\sim$3 with respect to the $(8^{+}_{2})\rightarrow(6^{+}_{2})$ transition at 958-keV even if it is energetically favored by a factor $\sim$13. This suggests a change in the wave functions of the $(8^{+}_{2})$ and $(6^{+}_{2})$ states with respect to the $6^{+}_{1}$ level that is theoretically supported by the JUN45 calculation, which predicts differing prolate and oblate characters for them. This is not the case for the PMMU calculation, for which the $6^{+}_{2}$ state is predicted to have a positive $Q_{s}$ value and then a mainly oblate character. Our results can also be compared with state-of-the-art nuclear models such as the complex Excited VAMPIR variational approach Petrovici et al. (2003); Petrovici (2015) and the adiabatic self-consistent collective coordinate (ASCC) method Hinohara et al. (2009), which predict a strong mixing between oblate and prolate configurations in the yrast band up to spin $J\sim 4$ and a clear dominance of prolate configurations at higher spins.

As a final remark, one should note that the experimental and theoretical results reported thus far show a rather complex shape-coexistence picture at low excitation energies in 70Se. The main missing piece in this puzzle is the first excited $0^{+}$ state predicted at a low excitation energy by the shell model Kaneko et al. (2015). Its observation would provide strong evidence for shape coexistence and clarify largely the present picture.

VII Summary and Conclusions

The $\beta$ decays of the $T=1~{}(J^{\pi}=0^{+})$ and $T=0~{}(J^{\pi}=9^{+})$ isomers in 70Br have been simultaneously investigated at the RIBF facility of the RIKEN Nishina Center using the BigRIPS and EURICA setups. Improved values are obtained for the half-lives of both states, $t_{1/2}(9^{+})=2157^{+53}_{-49}$ ms and $t_{1/2}(0^{+})=78.42\pm 51$ ms. In the case of the $T=1~{}(J^{\pi}=0^{+})$ ground state, an estimate of the total branching fraction decaying through the $2^{+}_{1}$ state, $R(2^{+}_{1})=1.3\pm 1.1\%$, is provided for the first time. These results have been combined with the shell-model predictions of2 Ref. Hardy and Towner (2002) to test the CVC hypothesis in the heavy self-conjugate nucleus 70Br. We have confirmed that the corrected $\mathcal{F}t$ value for the Penning-trap mass measurement accepted in the last atomic mass evaluation Savory et al. (2009); Wang et al. (2017) does not satisfy CVC, while that for an old $\beta$ end-point measurement Davids (1980); Hardy and Towner (2015) does. At present, this $Q_{EC}$ value is the major contributor to the large uncertainty in the $\mathcal{F}t$ estimate for 70Br. In order to improve the sensitivity of the CVC test for this nucleus, a new mass measurement is needed. In addition, improved error budgets for the half-life and the superallowed branching fraction are desirable.

In the decay of the $T=0~{}(J^{\pi}=9^{+})$ isomer, two new excited states at 3945 and 4752 keV with $J^{\pi}=(6^{+})$ and $(8^{+})$ have been proposed for the first time. Their nature has been discussed in terms of large-scale shell-model calculations including the PMMU Kaneko et al. (2015) and JUN45 Honma et al. (2009) interactions for the $p_{3/2}$, $p_{1/2}$, $f_{5/2}$, and $g_{9/2}$ configuration space. For most of the levels the excitation energies are well reproduced by the calculations. Theoretical B$(GT)$ values have also been calculated from the prolate-deformed $9^{+}$ state in 70Br to the yrast $8^{+}_{1}$ level in 70Se, resulting in log$ft=4.62$ for PMMU and log$ft=4.69$ for JUN45. These results are in agreement with the experimental log$ft=4.40(4)$ to the $(8^{+}_{2})$ state at 4606 keV, suggesting that the latter is the corresponding prolate experimental state. Based on this and on the internal de-excitation pattern of the $(8^{+}_{2})$ level, we propose a slightly modified shape-evolution picture in 70Se in which the oblate-to-prolate transition in the yrast band might take place more slowly than previously expected.

Acknowledgements

We want to express our gratitude to the RIKEN accelerator staff for providing a stable and high intensity 78Kr beam during the experiment, the EUROBALL Owners Committee for the loan of germanium detectors, and the PRESPEC Collaboration for the readout electronics of the cluster detectors. Part of the WAS3ABi was supported by the Rare Isotope Science Project, which is funded by the Ministry of Science, ICT and Future Planning (MSIP) and National Research Foundation (NRF) of Korea. Support from the Spanish Ministerio de Economía, Industria y Competitividad under Grants No. IJCI-2014-19172, No. FPA2011-24553 and No. FPA2014-52823-C2-1-P, Centro de Excelencia Severo Ochoa del IFIC SEV-2014-0398, and Junta para la Ampliación de Estudios Programme (CSIC JAE-Doc contract) cofinanced by FSE is acknowledged. This work was also financed by Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale (PRIN) number 2001024324_01302, by JSPS KAKENHI Grant No. 25247045, by the Chilean FONDECYT projects INICIACION No.11130049 and REGULAR No. 1171467, by the Istanbul University Scientific Project Unit under Projects No. BYP-53195, by the Max-Planck Partner group, by the NSF Grant No. PHY-1404442, by the UK Science and Technology Facilities Council (STFC) Grant No. ST/F012012/1, by the Japanese Society for the Promotion of Science under Grant No. 26 04808, by MEXT Japan under Grant No. 15K05104, and by the French-Japanese “Laboratoire international associé” FJ-NSP. D.Zs. acknowledges the financial support through the GINOP-2.3.3-15-2016-00034 project.