Search for Weak Side Branches in the Electromagnetic Decay Paths of the 6526-keV 10 + Isomer in 54 Fe

: High-spin nuclear isomers in N ≈ Z nuclei between doubly magic 40 Ca and 56 Ni provide an excellent testing ground for the nuclear shell model and questions related to isospin symmetry breaking in the vicinity of the proton drip line. The purpose of the present study is to investigate the possibility of weak electromagnetic decay branches along the decay paths of the 6526-keV 10 + isomer in 54 Fe. The isomer was strongly populated by means of the fusion-evaporation reaction 24 Mg( 36 Ar, α 2 p ) 54 m Fe. The Gammasphere array was used to detect γ -ray cascades emitted from the isomeric state. By means of γγγ coincidences, weak non-yrast decay branches can be discriminated, with the isomer’s half-life conﬁrmed at T 1/2 = 363 ( 4 ) ns. The yrast 6 + 1 → 2 + 1 E 4 cross-over transition was interrogated. The observations are compared with shell-model calculations.


Introduction
In the vicinity of self-conjugated N ≈ Z nuclei between 40 20 Ca 20 and 56 28 Ni 28 , strongly attractive two-body matrix-elements between neutron and proton f 7/2 particles (or holes) give rise to spin-gap isomers with high angular momenta. Examples near 56 Ni are I π = 7 + in 54 27 Co 27 , I π = 12 + in 52 26 Fe 26 , or I π = 19/2 − in case of the A = 53 ( 53 26 Fe 27 and 53 27 Co 26 ) 'mirror isomers', respectively. The I π = 10 + 'mirror isomers' in the A = 54 nuclei 54 26 Fe 28 and 54 28 Ni 26 are core-excited states. To first order, they arise from closely lying multiplets of states, which are based on the coupling of a respective A = 53 'mirror isomer' with a single nucleon in the upper f p shell. In fact, energy differences between excited states in N = 3, f p-shell mirror nuclei have been and continue to be a rich source of information on isospin symmetry breaking at or beyond the proton dripline. For background material as well as more recent developments, see, for instance, Refs. [1][2][3][4][5][6][7] and references therein.
For some neutron-deficient mirror partners, e.g., 53m Co and 54m Ni, Q values allow for intriguing competition between electromagnetic decays (E2 and/or E4), β-decay, and proton radioactivity. In fact, the observation of a weak = 9 proton-emission branch from the 3174-keV 53m Co isomeric state into the ground state of 52 Fe marked the discovery of proton radioactivity in atomic nuclei in 1970 [8,9]. Interestingly, it took more than 50 years to disentangle the complete decay pattern of this isomeric state by means of a combination of Penning-trap-assisted decay spectroscopy and 4D imaging of charged-particle decays with a time-projection chamber [10]. In the same experimental campaign, both protonemission branches of 54m Ni were determined [11,12]. The new experimental results were compared to cutting-edge shell-model and barrier penetration calculations for these (very) high-protons with = 5, 7, and 9, all (very) far beyond the N = 3, f 7/2 shell [10,11]. Further, the complete decay pattern of 54m Ni allowed the derivation of reduced transition strengths, B(E2; 10 + 1 → 8 + 1 ) and B(E4; 10 + 1 → 6 + 1 ), for the two competing γ-ray transitions from 54m Ni [13]. By means of a comparison with their well-known 'mirror transitions' in T z = +1 54 Fe, effective charges for E4 transitions near N = Z 56 Ni could be suggested. The 53m Fe has recently been used to study effective charges for E6 transitions [14].
A basic requirement for any elaborate study on isospin symmetry breaking is comprehensive knowledge of the relevant observables of the more neutron-rich partner. Here, we report on a dedicated study to complement the electromagnetic decay pattern of the well-known 6526-keV, 10 + isomer 54m Fe [15][16][17].

Experiment
The experiment was conducted at Argonne National Laboratory (ANL). A beam of 36 Ar 11+ ions accelerated to 88 MeV was provided by the ATLAS facility. With typical intensities of ≈ 40 enA, the beam impinged on a 0.43 mg/cm 2 thick foil of 99.92 % enriched 24 Mg. This self-supporting foil was positioned inside a vacuum chamber in the center of the Gammasphere array used for high-fold γ-ray detection purposes [18]. At the time of the experiment, Gammasphere operated with 70 Compton-suppressed Ge detectors, because the experimental set-up comprised a number of ancillary devices to detect, for instance, evaporated neutrons with the help of 32 liquid scintillator detectors [19]. These occupied the respective slots for Gammasphere modules at forward angles with respect to the beam direction. Further, a combination of the 4π CsI(Tl) array Microball [20] and two CD-type double-sided Si strip detectors (DSSD) facilitated the detection, tracking, and spectroscopy of light-charged particles such as protons, deuterons, and α particles. Information on recoiling residual nuclei entering the Fragment Mass Analyzer (FMA) [21] in a narrow cone in the beam direction and reaching its focal plane was stored as well. More information on the complete experimental set-up can be found in, for instance, Chap. 2 of Ref. [22].
For the present study on the electromagnetic decay paths of 54m Fe, only Comptonsuppressed γγ and γγγ coincidence events from the Gammasphere array are relevant. High-spin states of 54 Fe are populated in the reaction 24 Mg( 36 Ar,α2p) 54 Fe with the majority of the yield populating the 6526-keV, 10 + isomer 54m Fe [17]. The isomer has a reported T 1/2 = 364(7) ns [15,16]. Further, for the vast majority of the events of interest, the evaporation of an α particle in the production process causes 54 Fe recoils to be deflected from the beam direction, such that they are implanted and stopped in Ta foils protecting the DSSDs from radiation damage. In essence, this yields a stationary radioactive source of 54m Fe close to the center of the Gammasphere array. Moreover, this source is continuously produced during the experiment. It primarily emits a cascade of five E2 transitions with energies E γ = 146, 411, 1130, 1408, and 3432 keV (see Figure 1 and Ref. [17]), thereby covering the typical energy range relevant for γ-ray spectroscopy experiments.  [15,17] relevant for the present study. Energy labels are in keV. The thickness of the arrows scales with the relative intensities of the γ rays. Those with the thinnest arrows are not observed in the present study and are only shown for completeness. The 10 + isomeric state as well as the 10 + → 8 + 146-keV transition, which was used to select its decay paths, are shown in blue. Known transitions populating the isomer are indicated in gray. Previously unknown transitions connecting the 6380-keV 8 + state with side branches are marked green.
Prior to the experiment, a provisional energy calibration of the Gammasphere Ge detectors was accomplished with the help of radioactive 207 Bi sources. Between the present experiment, using the fusion-evaporation of 36 Ar+ 24 Mg, and the second experiment of the campaign at ANL, using 40 Ca+ 24 Mg [22], extensive γ-ray energy and efficiency calibration data were taken using 133 Ba, 152 Eu, and 182 Ta sources placed in the center of the array.

Data Analysis and Results
Regarding the γ-ray analysis of the experimental campaign, a base calibration of all Ge detectors was established from the aforementioned source data [22]. Small variations of, e.g., environmental conditions during the week-long experiments can give rise to small drifts of the amplified and digitized signals of the Ge detectors. Therefore, the complete data set was divided into 10-to 12-hour long sub-sets, and the gain of each individual Ge detector was re-aligned for each sub-set. For the present experiment, a semi-automated procedure was developed using the distinct 146 and 3432-keV peak positions of the ample 54m Fe decays, as well as the 511-keV peak stemming primarily from β + -decay related positron annihilation [23].
Apart from marginal, i.e., practically non-existing contributions of the 10 + mirror isomer in 54 Ni [13,15], a prompt coincidence with the 146-keV 10 + 1 → 8 + 1 transition highlights decays of 54m Fe. To establish an appropriate choice of time differences, ∆t, a correlation matrix ∆t(γ 1 , γ 2 )-E γ2 was created, pre-selected with E γ1 = 146 keV. As a result, the γ-ray spectrum in blue in Figure 2a shows the background-subtracted spectrum of events with ∆t = [−20, 60] ns. The spectrum is selective for γ rays depopulating the 6380-keV yrast 8 + 1 state in 54 Fe. In turn, the background-subtracted spectrum in grey in Figure 2a corresponds to ∆t = [0.15, 2.00] µs. It shows broad peaks of Doppler-shifted γ-ray transitions feeding the 10 + isomer in 54 Fe (cf. Figure 1). In fact, selecting several of these feeding γ-ray transitions, projecting on ∆t, and analyzing the resulting time spectrum, a half-life value of T 1/2 = 363(4) ns of the 10 + isomer in 54 Fe can be derived. This is consistent with the literature value T 1/2 = 364(7) ns [15]. Note that the 511-keV line in Figure 2a arises from escape events following pair-production detection of the high-energy 3432-keV transition (cf. Figure 1), in combination with its single and double escape peaks. In the next step of the γ-ray analysis, an E γ2 -E γ3 γγ correlation matrix was sorted, preselected by E γ1 = 146 keV and using a prompt time window ∆t(γ 1 , γ i ) = [−20, 60] ns, i = 2, 3. Corresponding matrices for delayed coincidences with the 146-keV line, ∆t = [0.15, 2.00] µs, and random coincidences, ∆t = [−2.00, −0.50] µs, were created, inspected, and used for reference. A search was undertaken for (i) γ-ray transitions connecting the 6380-keV 8 + 1 state with known 6 + and 7 + states in 54 Fe, other than the 2948-keV yrast 6 + 1 level [17], and (ii) the possible 1541-keV, 6 + 1 → 2 + 1 E4 decay. The results concerning hitherto unobserved transitions are exemplified in Figure 2b-d. They are summarized in Table 1. The experimental branching ratios are deduced from efficiency-corrected γ-ray yields of observed peaks in appropriate coincidence spectra as described in the following. First, a weak E γ3 = 453-keV line is seen in prompt coincidence with the E γ2 = 2980 keV, 7 + 1 → 6 + 1 transition. This coincidence is seen more clearly in the spectrum shown in Figure 2b, where E γ3 in the above mentioned prompt coincidence matrix is shown, selected by the E γ2 = 411, 1130, and 1408-keV transitions forming the 6 + 1 → 4 + 1 → 2 + 1 → 0 + 1 yrast cascade. Figure 2b also reveals a weak peak at 2980 keV, altogether confirming the presence of the 453-keV connection between the 6380-keV 8 + 1 and 5928-keV 7 + 1 levels, rather than that peak originating from Compton-scattered events of the main 3432-keV transition between two Ge detectors (cf. Figure 19 in Ref. [23]). Table 1. Comparison of experimental results with predictions from shell-model calculations. See text for details. Level energies, E x , and spin-parity assignments, I π , are taken from Ref. [17]. Transition energies, E γ and relative branching ratios, b γ , are from the present study. The γ-ray spectrum in Figure 2c represents E γ3 selected by the previously known E γ2 = 737, 757, and 1249-keV transitions, which form the most intense cascade between the 5280-keV 6 + 3 and 2537-keV 4 + 1 states [17]. The spectrum shows an obvious peak at 1100 keV, next to the 1130 and 1408-keV yrast transitions. This combination assures the placement of the former between the 6380-keV 8 + 1 and 5280-keV 6 + 3 states, establishing another weak decay path parallel to the intense 3432-keV yrast transition. Next, the γ-ray spectrum in Figure 2d shows E γ3 selected by the unknown E γ2 = 1336-keV transition, placed between the 6380-keV 8 + 1 and the 5046-keV 6 + 2 states in Figure 1. The spectrum reveals weak coincidences with the cascade depopulating the 6 + yrast level (only the 1408-keV line is shown for clarity), and also with the 2097-keV 6 + 2 → 6 + 1 transition. Further connections between the yrast 8 + 1 state and other yrare 6 + or 7 + states (cf. Figure 1) cannot be identified. Hence, only upper limits of their branching ratios can be provided in Table 1.
Similarly, also the search for a (411 + 1130) keV = 1541 keV, 6 + → 2 + E4 cross-over transition proved negative. Though spectra in coincidence with the yrast E γ2 = 1408 and 3432 keV transitions show a peak at E γ3 ≈ 1540 keV, a peak at E γ3 = (411 + 1408) keV = 1819 keV is observed with similar yield in spectra in coincidence with E γ2 = 1130 and 3432 keV transitions, respectively. The presence of the ≈ 1540 keV peak (and the 1819 keV peak) is thus primarily caused by coincident summing, i.e., simultaneous hits of a single Ge-detector crystal by two γ rays stemming from the same isomeric decay event.
Note that the present results were cross-checked and found consistent with data sets from earlier experiments with Gammasphere and fusion-evaporation reactions leading to the same compound nucleus 60 Zn [17].

Discussion and Conclusions
The experimental results on branching ratios are compared with shell-model calculations in Table 1. The calculations correspond to those labeled KB3G56 in Ref. [13]. They include the isospin-breaking terms V CM , V C s , V Cr , and V B:2 , as outlined in Ref. [13], and are conducted in the full f p space, with up to t = 6 particles allowed to cross the shell gap at N = Z = 28. Electromagnetic transition rates are calculated using bare g factors for M1 transitions, effective charges p = 1.15e and n = 0.80e for E2 transitions [24], and p = 1.40e and n = 0.30e for E4 transitions [13].

Data Availability Statement:
The data presented in this study are available on reasonable request from the corresponding author.