Competition of $\beta$-delayed protons and $\beta$-delayed $\gamma$ rays in $^{56}$Zn and the exotic $\beta$-delayed $\gamma$-proton decay

Remarkable results have been published recently on the $\beta$ decay of $^{56}$Zn. In particular, the rare and exotic $\beta$-delayed $\gamma$-proton emission has been detected for the first time in the $fp$ shell. Here we focus the discussion on this exotic decay mode and on the observed competition between $\beta$-delayed protons and $\beta$-delayed $\gamma$ rays from the Isobaric Analogue State.

discussion on this exotic decay mode and on the observed competition between β-delayed protons and β-delayed γ rays from the Isobaric Analogue State.

Introduction
Decay spectroscopy is a powerful tool for exploring the structure of nuclei at the drip-lines. β-decay studies, in particular, provide direct access to the absolute values of the Fermi and Gamow-Teller transition strengths, B(F) and B(GT), respectively.
The proton-rich 56 Zn nucleus was observed for the first time at GANIL in 1999 [1]. 56 Zn is a weakly-bound nucleus lying very close to the proton drip-line. It has a quite small proton separation energy, S p = 560(140) keV [2], and third component of the isospin quantum number T z = -2.
The first study of the β decay of 56 Zn was reported in ref . [3]. More recently, some interesting results on 56 Zn decay have been reported in ref . [4]. Among them the discovery of a rare and exotic decay mode, β-delayed γproton decay, which has been seen for the first time in the fp shell. The consequences of this rare decay sequence for the determination of the Gamow-Teller (GT) strength have also been analyzed.

The experiment
The experimental study of 56 Zn decay was performed at GANIL in 2010. The experiment used a primary beam of 58 Ni 26+ to produce 56 Zn. The 58 Ni beam, of 3.7 eμA and accelerated to 74.5 MeV/nucleon, was fragmented on a natural Ni target, 200 μm thick. The fragments were selected by the LISE3 separator and implanted into a Double-Sided Silicon Strip Detector (DSSSD). The detection set-up comprised the aforementioned DSSSD detector, 300 μm thick, a silicon ΔE detector located 28 cm upstream, and four EXOGAM Ge clovers surrounding the DSSSD.
The EXOGAM clovers were used to detect β-delayed γ rays. The purpose of the DSSSD was the detection of both the implanted fragments and the subsequent charged-particle decays, i.e., β particles and β-delayed protons. An implantation event was defined by simultaneous signals in both the ΔE and DSSSD detectors. A decay event was defined by a signal above threshold (50-90 keV) in the DSSSD and no coincident signal in the ΔE.
The implanted ions were identified and selected by putting a gate in a two-dimensional identification matrix, obtained by combining the energy loss signal from the ΔE detector and the Time-of-Flight. The latter was defined as the time difference between the cyclotron radio-frequency and ΔE signal.

Results on the β decay of 56 Zn
The results on the β decay of 56 Zn [4] are summarized in the decay scheme in fig. 1 and in table 1, and discussed below.
A half-life of T 1/2 = 32.9(8) ms was obtained for 56 Zn, in agreement with ref . [3]. To determine T 1/2 , a decay-time spectrum has been constructed from the time correlations between a decay event in a given pixel of the DSSSD (with a total of 256 pixels) and any implantation signal that occurred before and after it in the same pixel, satisfying the identification condition required to select 56 Zn. The analysis of the charged-particle spectrum measured in the DSSSD has provided new spectroscopic information on the energy levels populated in the 56 Cu nucleus, the β-daughter of 56 Zn. These levels are shown in fig. 1. The comparison of this level spectrum with that of the mirror 56 Co, obtained by the 56 Fe( 3 He,t) charge exchange reaction [5], has been very fruitful.
The analysis of the γ spectrum measured in the EXOGAM clovers and γ-proton coincidences have identified three γ rays at 309, 861 and 1835 keV.
Absolute B(F) and B(GT) strengths have been determined (table 1).

Competition of β-delayed protons and β-delayed γ rays
In the first study of the 56 Zn β decay [3], the emission of β-delayed protons was observed but no β-delayed γ rays were seen. This was not a surprise because, in general, in proton-rich nuclei the proton decay is expected to dominate for states well above (>1 MeV) the proton separation energy S p . The consequence is that normally the β feeding is directly inferred from the measured intensities of the proton peaks. However, cases where there is a competition between β-delayed proton emission and β-delayed γ deexcitation have also been observed, e.g., in ref s. [3,6].
In the T z = −2 → −1, β + decay of 56 Zn to 56 Cu, the 56 Zn ground state decays with a Fermi transition to its Isobaric Analogue State (IAS) in 56 Cu. It should be noted that the de-excitation of this T = 2, J π = 0 + IAS via proton decay to the ground state of 55 Ni (T = 1/2, J π = 7/2 − ) is isospin forbidden. Therefore the proton emission that we observe can only happen through a T = 1 isospin impurity present in the IAS. Moreover in general, when the proton emission is isospin forbidden, the competitive emission of de-exciting γ rays from the IAS also becomes possible and can be observed even from IAS lying at an excitation energy well above S p [3,6].
The competition between β-delayed protons and γ rays has indeed been observed in 56 Zn. The γ decays represent 56(6)% of the total decays from the 3508 keV IAS. Thus one has to take into account the intensities of both the proton and γ peaks to determine the Fermi strength correctly.
We have also found evidence for the fragmentation of B(F) due to a strong isospin mixing with a 0 + state at 3423 keV [4], which is important in terms of the mass evaluation [7]. The isospin impurity in the 56 Cu IAS, α 2 = 33(10)% (defined as in ref . [5]), and the off-diagonal matrix element of the charge-dependent part of the Hamiltonian, H c = 40(23) keV, which is responsible for the isospin mixing of the 3508 keV IAS (T = 2, J π = 0 + ) and the 0 + part of the 3423 keV level (T = 1), are similar to the values obtained in the mirror 56 Co nucleus [5].
Thus, the proton decay of the IAS proceeds thanks to the T = 1 component. However, considering the quite large isospin mixing in 56 Cu, the much faster proton decay (t 1/2 ∼ 10 −18 s) should dominate on the γ deexcitation (t 1/2 ∼ 10 −14 s in the mirror). This is not the case since we are still observing the γ decay of the IAS in competition with it.
The knowledge on the nuclear structure of the three nuclei involved in the decay, i.e., 56 Zn, 56 Cu and 55 Ni, can provide us with a possible explanation for the hindrance of the proton decay. Shell model calculations are in progress to clarify this point.

The β-delayed γ-proton decay
Besides the competition between β-delayed proton emission and γ decay, the exotic sequence of β-delayed γ-proton decay has been detected. Indeed 56 Zn does β decay to its IAS in 56 Cu and from there we observe the emission of two γ rays of 861 and 1835 keV, populating the 56 Cu levels at 2661 and 1691 keV, respectively. Due to the low S p , these levels are still proton-unbound and thereafter they decay by proton emission. Consequently the rare and exotic β-delayed γ-proton decay has been observed. In addition to these two branches, there is a third case. The 1691 keV level emits a γ ray of 309 keV, going to the level at 1391 keV that is again proton-unbound and then it de-excites by proton emission.
The β-delayed γ-proton decay has been observed here for the first time in the fp shell. This rare decay mode was seen only once before, in the sd shell in 32 Ar [6], but the consequences for the determination of B(GT) were not addressed in ref [6].
The observation of this special decay mode is very important because it does affect the conventional way to determine B(GT) near the proton drip-line. For a proper determination of B(GT), indeed, it is crucial to correct the intensity of the proton transitions for the amount of indirect feeding coming from the γ de-excitation. This finding indicates that it is important to employ γ detectors in such studies. This decay mode is expected to be significant in heavier proton-rich nuclei with T z ≤ −3/2 under study at RIKEN.