Pygmy Gamow-Teller resonance in the N = 50 region: New evidence from staggering of β-delayed neutron-emission probabilities

D. Verney,1 D. Testov,1,2,* F. Ibrahim,1 Yu. Penionzhkevich,2,3 B. Roussière,1 V. Smirnov,2 F. Didierjean,4 K. Flanagan,5 S. Franchoo,1 E. Kuznetsova,2 R. Li,1,† B. Marsh,6 I. Matea,1 H. Pai,7 E. Sokol,2 I. Stefan,1 and D. Suzuki1,‡ 1Institut de Physique Nucléaire, CNRS-IN2P3, Univ. Paris-Sud, Université Paris-Saclay, 91406 Orsay Cedex, France 2Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Moscow region, Russia 3National Research Nuclear University, Kashirskoye Shosse 31, Moscow 115409, Russia 4Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France 5University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom 6CERN, CH-1211 Geneva 23, Switzerland 7Nuclear Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064, India (Received 20 March 2017; published 23 May 2017)


I. INTRODUCTION
The possible existence of low-lying structures in the βstrength function above the neutron-separation energy (S n ) had given rise to-sometimes bitter-debates in the past (see, e.g., Refs. [1][2][3][4] and, in particular, the conclusion in Ref. [5]). However, the occurrence of structures in the tail of the Gamow-Teller giant resonance (GTGR), energetically accessible in the β decay of very neutron-rich nuclei, is now a long-well-established, widespread phenomenon (see Ref. [4] and references therein) and has been shown to have important consequences for r-process calculations [6]. The existence of low-lying satellites of the GTGR, thereafter interpreted as components of a pygmy Gamow-Teller resonance (GTPR), was in fact predicted quite early by Ikeda and Fujita as a natural consequence of the violation of the Wigner supermultiplet symmetry due to spin-dependent components of the nuclear interaction. A nice illustration of the underlying mechanism leading to the creation of the GTPR can be found, e.g., in Fig. 7 of Ref. [7].
One of the consequences of the existence of these structures, which has seldom been noticed, is the clear oscillation of the β-delayed one-neutron emission probabilities (P 1n ) just after a neutron shell closure for a given (odd-Z) chain of precursors. The P 1n value for a [Z,N m + 1] (N m : the magic neutron number) precursor is obviously small because the emitter is a closed neutron shell nucleus and the P 1n value for a [Z,N m + 2] precursor much higher due to the closed-shell + one-neutron nature of the emitter. But the P 1n value can decrease significantly for the [Z,N m + 3] precursor while the (Q β − S n ) window still increases from (N m + 2) to (N m + 3).
This phenomenon clearly occurs in the Z = 19 chain after the N = 28 shell closure [8] as illustrated by Fig. 1. According the authors of Ref. [8], the oscillation in opposition of phase of the emitters S n curve and precursors P 1n curve is interpreted as due to allowed GT transitions to states belonging to a low-lying (≈5.5 MeV) shell-model configuration, that is to say a lowlying structure in the β-strength function (i.e., a component pertaining to the GTPR). In this physical picture, it is because of the natural oscillation of the S n values (see Fig. 1), between the [Z,(N m ,N m + 1,N m + 2)] emitters, probing this low-lying region of the β strength and its structures, that a sizable P 1n staggering is observed.
But this effect is most probably not restricted to this light-mass region. It could, for example, explain the systematic occurrence of irregularities (clear spikes), after each neutron-shell closure, in the effective density parameters of a structureless β-strength function, obtained after a global fit to the experimental P 1n values; see Fig. 1 in Ref. [13].
In a recent neutron-spectroscopy study of the [Z = 31,(N m = 50) + 2] precursor, 83 Ga, Madurga et al. [14] have clearly observed accumulations of β strength in specific excitation-energy regions of the 83 Ge emitter. According to the previous remarks, the Ga chain, beyond N m = 50, should then be an excellent test case to investigate further the (N m + 1,2,3) P 1n -oscillation phenomenon. It would appear at first sight that this phenomenon is absent from the Ga chain when considering, Fig. 2, the previous (somewhat discrepant) P 1n values accumulated for the 83,84 Ga precursors, which were obtained using various counting techniques. While overall these previous results point towards a trivial, regular increase of the P 1n values from the (N m + 1) to the (N m + 3) precursor, on the contrary, the most recent results from Ref. [14] interestingly suggest for the first time a P 1n -slope inversion at (N m + 2). We felt then that further investigation of the question could be in order.
We report in this paper on the P 1n measurements of the 82,83,84 Ga (N = 51,52,53) precursors performed in one single experiment using the 3 He neutron-counter TETRA [21,22] at the ALTO facility in Orsay [23]. Our results for 82 Ga were already reported in Ref. [22]. Since it is for this precursor that the best agreement between P 1n values obtained from different counting techniques was previously found (see Fig. 2), it was used as a test case to validate our experimental procedure. Consequently, the experimental details and analysis procedure will be only briefly reviewed in Sec. II; they have been already presented and extensively discussed in Ref. [22]. However, we provide details about further improvements of our analysis procedure introduced to demonstrate the reliability of the P 1n measurement for the 83 Ga precursor. The results from this experiment for both the A = 83 and 84 Ga precursors will be presented in Sec. III. In particular, we make detailed β-neutron doubly gated γ -spectroscopy data on 83,84 Ge available for the first time in literature. Altogether, our results for the three A = 82,83, and 84 Ga isotopes point toward a strong P 1n staggering in the N = 50 region, similar to the one already known in the N = 28 region, hinting at a similar mechanism. For that reason, this result is discussed in Sec. IV, highlighting the possible microscopic origin of this behavior, i.e., the existence in the N = 50 region of a low-lying component of the GTPR, well established at Z = 36 and persisting toward 78 Ni.

A. Experimental details
All details concerning this experiment from the experimental arrangement to the chosen methodology for the extraction of P 1n values can be found in Ref. [22] and we only recall here briefly some of the most relevant aspects for the present article.
Selectively laser-ionized Ga beams were collected onto an Al-coated Mylar movable tape at the geometrical center of the 3 He neutron-counter TETRA. The collection point was surrounded by a plastic scintillator for β detection. A coaxial HPGe detector (EUROGAM-1) was used for γ detection. The counting cycles were divided in three phases. A short beam-off counting time T bg was allowed before each beam collection to measure the background level and to monitor possible activity build-in off the tape. After a beam collection of T coll duration, the beam was deflected and the decay of the source counted for T dec . Then the tape was moved for 2 m to transport the source outside the detection array. The time parameters T bg, coll, dec and the number of cycle repetitions N cycles for the A = 82,83,84 measurements are summarized in Table I.

B. P 1n extraction procedure
As explained in Ref. [22], the β-delayed one-neutron emission probability P 1n and beam rate φ (pps) were determined from the observed grow-in/decay β and neutron activity curves, cumulated over N cycles , by solving the corresponding Bateman equation system. Once P 1n and φ are determined, the individual contributions to the total observed β-activity curves, stemming from the β activities of the mother and all 054320-2 possible β and β-n daughter nuclei, were determined. This information was used as a consistency test. A constant average beam rate φ over N cycles was assumed for a given mass setting based on the fact that, due to the primary electron beam microstructure, the radioactive ion beam at ALTO is continuous in nature. Strictly speaking, φ is not really independent of time during the measurement because of the inevitable slow modification of target-ionsource conditions under continuous heating and irradiation. But this cannot modify the collection curve shapes unless the radioactive ion beam has a time structure (i) varying strongly within T coll and (ii) varying periodically with a period of the order of the tape cycle and in phase with it. These two conditions are simply not met: The observed variations of the beam intensity at ALTO are slow, with characteristic times of the order of tens of minutes, and random in nature. The fact that the correct precursor half-life can be obtained from the neutron activity curves restricted to the grow-in part, as shown in Ref. [22], further supports this assumption. However, for this present article we have decided to further investigate this question.

C. Cycle-per-cycle analysis
In Ref. [22], the total cumulated neutron and β activities were analyzed using the corresponding Bateman equation system. In the present work, in order to achieve a quantitative evaluation of the beam fluctuations and to understand their influence on the obtained P 1n values, the Bateman equation system was solved for the β and neutron activity curves obtained for each individual cycle of the A = 83 setting. An example of single-cycle analysis is illustrated by Fig. 3. Two distributions of N cycles = 4405 values, for P 1n and φ, were then obtained, which are reported in Fig. 4.
The distribution of the P 1n values can be fitted by a Gaussian function, the corresponding mean value of the distribution isP 1n ( 83 Ga) = 0.850 (2). Inclusion of the statistical errors determined for each individual cycle allows obtaining two shifted distributions representing the maximum and minimum values within ≈1σ statistical uncertainties, which are represented by the hatched histograms in Fig. 4. This leads to a range ofP 1n ( 83 Ga) possible values given by 0.824 (2) P 1n ( 83 Ga) 0.878 (2). TheP 1n ( 83 Ga) range reflects both statistical uncertainties and part of the systematic uncertainties associated to beam fluctuations. The other sources of systematic uncertainties originate from the β and neutron-detection efficiency ( β and n ) determination. As in Ref. [22], these detection efficiencies were determined from the observed ratios of peak areas in singles, β and β-n gated γ spectra (see Ref. [22] for more details). The adopted β , n values and associated uncertainties are summarized in Table II. Some of the ratios used to obtain these adopted values are reported in Tables IV and VI of Sec. III, when possible. In the case of 84 Ga, due to the very low production yield, peaks were difficult to exploit in the singles spectra. For that reason, The result from the total cumulated curve analysis, as shown in Fig. 5 of Sec. III, leads to P 1n ( 83 Ga) = 85(4)%. This value is quite consistent with the observedP 1n range, being located exactly at the range midvalue, and the associated uncertainty is also consistent with the range width. This definitely proves that-within the specific experimental conditions found at ALTO-the assumption of an average constant beam rate over the full number of tape cycles for a given mass setting is correct. The beam intensity distribution in Fig. 4 can readily be interpreted as representing the beam fluctuations. It is seen in particular that despite the presence of a low-intensity tail, the beam was quite stable with an average beam rate around 400 pps. It is worth, for the rest of the discussion, to recall here that usually a reliable ion counting is difficult to obtain with movable-tape collector-based techniques due to the very low energy of the beam and its interception by the tape. The simultaneous registration of the β and neutron curves actually provides a robust working method for obtaining ion counting independently from any prior knowledge of the γ branching ratios in the decay chain. However, it should be noted that this method entirely relies on (i) a reliable set of half-life values for all the decay daughters and (ii) the correct determination of the βand neutron-detection efficiencies.

Results from the cumulated activity curves
The cumulated β and neutron curves obtained for A = 83 are shown in Fig. 5. All neutrons detected for the A = 83 setting were attributed either to the background or to the 83 Ga β-n decay: β-delayed neutron emission is indeed less energetically possible for the higher-Z A = 83 isobars and has not been reported so far. The fit to the grow-in and decay TABLE II. β and neutron detection efficiency values, β and n , used for the analysis. The efficiencies are obtained from the observed ratios of peak areas in singles, β, and β-n gated γ spectra.   (20) patterns of the cumulated neutron activity curve, as shown in Fig. 5, leads to a 83 Ga half-life value of 0.312(1) s, where the uncertainty is the uncertainty from the fit. This value is compatible within error bars with all previous measurements (see Refs. [24,25]) with the exception of the one at 308(1) ms from Ref. [17] (but very close to it). As explained earlier φ and P 1n are determined by solving the Bateman equation system associated to the βand neutronactivity curves, we obtain φ = 370(20) pps and P n = 85(4)% (all the results are summarized in Table III). As can be seen in Fig. 2, this value is larger than any of the previously reported ones. This confirms the fact, first discovered by Winger et al. [20], that 83 Ge is a much stronger β-delayed neutron emitter than thought before and that the β-n channel dominates by far the 83 Ga decay. As far as we can understand, the reported P 1n = 62.8(25)% value obtained in Ref. [20] relied on the 82 Ge population estimation from γ counting, based on an unspecified branching ratio to the 1092-keV transition in 82 As. In the very recent work by Madurga et al. [14], an even lower value (P 1n = 56(7)%) was obtained from an integral of the neutron spectrum. This spectrum shows that the neutron energy spectrum is peaked around 2 MeV and extends below this energy. This is the energy regime where the detection efficiency can be directly measured with TETRA using a 252 Cf source [22]; i.e., it is well under control. Our measurement is based on the robust simultaneous, individual β, and neutron counting with 4π detectors, and, thanks to the cycle-per-cycle analysis procedure, is statistically highly significant. A possible explanation for the possibly missing (≈30%) β-delayed neutron strength in Ref. [14] could be that a significant fraction of the neutrons are emitted at very low energy (possibly below the claimed 70-keV energy threshold in this reference). This hypothesis would be consistent with the microscopic origin of the P 1n staggering as will be tentatively explained in Sec. IV.
Once φ, T 1/2 , and P 1n for the precursor are determined, one can restore the expected total β-activity curve as well as the individual β contributions to it due to the precursor itself and its daughters' activities, using the tabulated daughter half-life values, as consistency test. Including the uncertainties, one obtains the red region as shown in the top panel of Fig. 5. This curve is in good agreement with the measured one. However, one sees that the measured activity is somewhat lower than the calculated one near the end of the decay part of the cycles. A perfect reproduction can be obtained if, for instance, one uses a longer half-life value for 82 Ge of 8 s, instead of the recommended value of 4.55(5) s [26]. This might indicate the presence of a weak, unidentified long-lived β-activity component, maybe an unidentified β-decaying isomer in one of the nuclides in the decay chain.

βn-gated γ spectroscopy
We present in Fig. 6 the β and β-n gated γ spectra obtained for the A = 83 setting of the mass separator. Practically all the observed lines could be attributed to the β and β-n decays of the collected 83 Ga beam and its daughter chains (with the exception of two obviously visible lines in the 2800to 2900-keV region). This proves that the beam was indeed quite pure. The energies and relative intensities of the γ transitions which could be attributed to the β and β-n channels of the 83 Ga decay from these spectra are reported in Table  IV. The branching ratios to the 82,83 Ge levels and absolute γ intensities were obtained using the ion-counting method described previously, i.e., without the need of any γ -branching ratios to As daughters. Transitions placements from previous works (see first column in Table IV) were used to deduce the β and β-n branching ratios. All the lines previously attributed to the β-n decay of 83 Ga by Winger et al. [20] could be confirmed. We could also confirm some of the transitions in 82 Ge observed in additional spontaneous-fission and 82 Ga β-decay studies [25,27]. A set of previously unreported lines and their proposed assignment is listed in Table V. Strict criteria were used to propose these new γ rays. Assignment to the 83 Ga β-n decay is made only if the three following conditions are fulfilled: (i) the net count S (above background) in the peak region in both β and β-n gated spectra (S γβ and S γβn respectively) is above the critical limit (see Ref. [28,29] for a proper definition) for 95% confidence; (ii) the ratio S γβn /S γβ is compatible with the measured neutron-detection efficiency ( n in Table II), and (iii) the relative uncertainty S/S 0.75. We decided to assign new γ rays to the 83 Ga β-channel only if they were also unambiguously observed in the 84 Ga β-n channel (see following subsection). In the end, only the line at 1795.1 keV passed this test; the other unidentified peaks were left unassigned and marked by ? in Fig. 6.
We also note energy-unresolved excesses of counts in the β-n gated spectra in the region above 600 keV and in the one centered around 844 keV. The former, with a typical triangular shape, is easily explained by inelastic neutron scattering on Ge nuclei of the detector's crystal subsequently detected by TETRA, leading to spurious γ -n coincidences. The latter is most probably due to neutron inelastic scattering on 56 Fe, though the presence of iron in our setup should be extremely marginal. This may also explain the slight excess of counts observed at 1238 keV in the β-n gated spectrum while the 1238 keV unambiguously belongs to the 83 Ge level scheme. At last, the peak observed in the β-n gated γ spectrum at 1092 keV, which is the main γ line in the 82 Ge decay to 82 As, is due to random γ -n coincidences. Its intensity is ≈2% of the corresponding one in the β-gated spectrum, a value consistent with a 128-μs opening of the γ -n coincidence window [30].
The observed γ -intensities relative to 1348-keV transition are, on the overall, in fair agreement with those reported in Ref. [20]. However, one should note the large difference of the dominant β-n branching ratio, to the 2 + the present case, the uncertainties on the absolute quantities are large (and probably somewhat conservative). They reflect the uncertainty of the calibration source positioning in a very closed geometry where even an error of the order of ≈1mm can result in significant change in the measured absolute efficiency. Nevertheless, we note that we found a similar (≈45%) value in the more recent measurements at ALTO, reported in Refs. [35,36], where γ -γ coincidence relationships could be established and transitions placements were possible.

Results from the cumulated activity curves
The β and neutron activity curves cumulated over 17 971 tape cycles are presented in Fig. 7. In the case of the A = 84 measurement, neutrons observed have two possible origins, one from the decay of 84 Ga and the other from the decay of its daughter 84 Ge. The neutron contribution from the last was determined using the recommended value of P 1n ( 84 Ge) = 10.2(9) [37]. As can be seen in Fig. 7, thanks to the large difference between the two neutron precursors' half-lives and the chosen tape cycling (see Table I), the neutron contribution from the 84 Ge decay remained marginal.
From Table III, one can immediately point out that the measured production rate for 84 Ga was lower by two orders of magnitude with respect to the one for 83 Ga. This 84 Ga production yield of 5(2) pps only is to be compared to the one of ≈120 pps obtained in our previous experiment using laser ionization for Ga with similar electron primary beam intensity and target mass [38]. This reflects the progressive degradation of the laser ion-source conditions that was observed during the present experiment (the A = 84 measurement was the last of the experiment).
Despite a longer counting time devoted to the A = 84 setting (see the different N cycles values in Table I), the collected statistics remained limited and cycle-per-cycle analysis technique could not be used. With the standard method of Ref. [22] we obtain P 1n = 53(20)% for the 84 Ga β-delayed neutron emission probability, assuming emission of one single neutron (two neutron emission is likely, see later, but the effect is meaningless within our large error bars). With this value, 054320-6 TABLE IV. Photopeaks attributed to the β and β-n decays of 83 Ga identified in the spectra recorded for the A = 83 setting of the mass separator. γ intensities are given relative to the one of the transition observed at 1348 keV. In the fourth column (Spec) are specified the γ spectra of Fig. 6 which were used to determine the different quantities, labeled γβ and γβn for the singly β-gated and doubly β-neutron gated γ spectra respectively. Following the methodology introduced in Ref. [22], S γβ /S γ and S γβn /S γβ are the quantities used to determine the β and neutron effective detection efficiencies reported in Table II. Placements in the daughter level schemes are from references quoted in the first column. Bracketed γ energies correspond to transitions observed elsewhere but not in the present work. Direct β-branching ratios (I β ) to the levels quoted in the first column are apparent branching ratios based only on the γ transitions observed in the present work.  12.9 f γβ (γ unobserved) a Weak line, but the net count is above the critical limit for 95% confidence. A transition at 487.0 keV depopulating the level at 2702.1 keV was observed in the β decay of 82 Ga in Ref. [31] (placement is uncertain). b This line is probably present in our spectra too. But its close proximity to the 74 Ge(n,n ) prevents any quantitative determination of the peak surface both in β-gated and β-n-gated spectra. c Weak line, the net count is at the critical limit for 95% confidence, it might correspond to the 1908.9-keV line reported in Ref. [27]. d To be considered only as an upper limit for the direct β-n branching to the 82 Ge ground state. e The time behavior in the collection-decay cycles for this line is characteristic of a mixture with the 249.1-keV line observed in the decay of 82 Ge [33,34]. I rel γ was obtained from the analysis of these curves assuming two time components. f We report I β = 16(4)% to (neutron-unbound) levels in the 4-9 MeV energy region in a separate article [35] (this result was obtained from a measurement dedicated to β-delayed high-energy γ emissions from 83 Ge at ALTO). Consequently the direct β-branching ratio to the 83 Ge ground state must be close to zero.
we confirm a significant decrease of the P 1n value from 83 Ga to 84 Ga recently hinted at in Ref. [14].
The fit to the neutron curve ( Fig. 7) looks less satisfactory than in the 83 Ga case, but the integral of the neutron counts is quite stable against parameter changes, so is the resulting P 1n . The origin of the uncertainty on this P 1n value is in fact mainly of statistical nature. The fit shown in Fig. 7 was done assuming T 1/2 ( 84 Ga) = 84 (7) ms. This value is obtained as the TABLE V. Previously unreported photopeaks observed in the spectra recorded for the A = 83 setting of the mass separator. Second column (Spec): γ spectra of Fig. 6 where the peaks were observed (γβ and γβn for the singly β-gated and doubly β-neutron gated γ spectra respectively). I rel γ : intensities relative to the transition observed at 1348.5 keV (n.o., not observed). Forth column: ratios of peak areas measured in the β-neutron gated and β-gated γ spectra to verify the consistency with the measured neutron efficiency. No placement is proposed for these transitions. weighted average of all the half-lives from the γ -ray decay curves reported in Table I of Ref. [38] (the currently adopted value is 85(10) ms [37] originating from Ref. [17]).

βn-gated γ -spectroscopy
The β and doubly β-n gated γ spectra recorded at the A = 84 mass-separator setting are shown in Fig. 8. Due to insufficient statistics, only the strongest lines observed from the 84 Ga decay in Ref. [38] were visible (see Table VI). No transition with an intensity lower than 10% of the strongest 248 keV one could be observed. The relative intensities of the strongest lines reported in Table VI are in good agreement with those from Ref. [38]. It seems, however, that we somewhat overestimate those of the weaker lines, which appear as small peaks, resulting in large I γ uncertainties.
Despite ungrateful data, two interesting findings may worth being pointed out. First, we clearly observe a peak at 307 keV in the doubly βn-gated γ spectrum (marked with the symbol ♣ in Fig. 7). It is the strongest γ line known in the β decay of 83 Ge [24] and is indeed clearly visible in the β-gated γ spectrum. However, the obtained ratio S γβn /S γβ = 10(3) is at the same time far above the expected level of 2% for random γ -n coincidence (see previous subsection) and far below the 57(5)% neutron efficiency. This is easily explained by the fact that the 307-keV line in the β-gated spectrum contains two contributions, one from the β channel of the 83 Ge decay, and the other from the β-n channel of the 84 Ge decay. While in the doubly βn-gated spectrum only one of the two components is present. This confirms the assignment of the 307-keV γ ray to the βn decay of 84 Ge recently reported in Ref. [39].
Second, one can notice an accumulation of statistics in the 1348-keV energy region (corresponding to the 2 + 1 → 0 + gs transition in 82 Ge) of the βn-gated spectrum, marked with a symbol in Fig. 8, and actually forming a peak. The net count in this peak above the (low) background of the βn-gated spectrum is above the critical limit for 95% confidence. However the estimation of the corresponding peak surface in the singly β-gated γ spectrum is very difficult. This peak was also visible in the spectra of Ref. [38] but not assigned in this reference. It may constitute the first experimental evidence for the emission of two neutrons following the β decay of 84 Ga. We note that this nucleus has long been predicted to be a β-delayed 2n precursor [40,41]. Further investigations on the possible β-2n decay of 84 Ga, with higher statistics, will be necessary in order to be able to obtain a reliable P 2n value. FIG. 8. β gated and β-n gated (shaded in gray) γ spectra recorded for the A = 84 setting of the mass separator. 054320-9 TABLE VI. Photopeaks attributed to the β and β-n decays of 84 Ga identified in the spectra recorded for the A = 84 setting of the mass-separator. γ intensities are given relative to the one of the transition observed at 248 keV. All assignments are from Ref. [38] unless marked by an asterisk, in which cases the assignment is from the present work and additional explanation is provided in footnotes. Other quantities have the same meaning as in Table V (7) 42 (21) a This line was also present in the spectra of Ref. [38] but (wrongly) attributed to a contamination from neutron-rich Rb decays. b Weakest among the identifiable lines. The peak is visible but in a chaotic, large background region, for that reason the net count is below the critical limit for 95% confidence. However, it is well above this critical limit in the much cleaner βn-gated spectrum. c Poor energy agreement with the line observed at 1245.7 keV and recently attributed to the β decay of 83 Ga in Ref. [25] (probably due to note b ).

IV. DISCUSSION
As can be seen in Fig. 9 our results point toward a sizable (N m + 1,2,3) P 1n oscillation for the Ga chain, with an amplitude exceeding by far what previous measurements, Fig. 2, could suggest. P 1n odd-even staggering is a very wellknown phenomenon, attributed to pairing effects. However, the effect which is observed here considerably exceeds what can be expected from this trivial origin: This is illustrated by the results from the so-called gross theory, reported in Fig. 9, which exhibit only a change of the slope of the P 1n evolution.

Use of the McCutchan et al. empirical formula
It is informative now to compare also our results with the predictions of a new empirical P 1n formula introduced by McCutchan et al. [44] considering the P 1n /T 1/2 ratio as a (power) function of Q βn and an improved alternative to the Kratz-Hermann [45] formula. The use of this ratio comes  9. Experimental P 1n for the 82−84 Ga precursors from the present work ("TETRA") compared to theoretical results using QRPA approaches ("Moller97" from Ref. [40] and "Borzov12b,Borzov12" from Ref. [42], with and without blocking effects, respectively) or the gross theory for β decay [43]. Results from the use of the empirical formula by McCutchan et al. [44] ("McCutchan12") are also represented with the associated uncertainties materialized by the gray zone. from the basic, though previously unexploited recognition that it directly represents the integrated β strength available in the (Q β − S n ) energy window [44]: where S β (E) is the β-strength function and f (Z,Q β − E) is the Fermi integral. An interesting aspect of this new approach is that this quantity is free from the strong and strongly varying effects due to GT transitions to the low-lying (below S n ) part of the emitter energy spectrum. In Fig. 9, we report the results given by the formula using (i) the fit parameters obtained in Ref. [44] for light fission fragments, (ii) the 82−84 Ga half-lives from our work, except for 84 Ga where the value of 84(7) ms from Ref. [38] was used, and (iii) evaluated [46] Q βn values. For A = 82,83 the agreement between predictions from the formula and our results is impressive. In Ref. [47], Fig. 2 is their formula's result) for the Ga isotopes. The only case where R was lower than 1 was 83 Ga. R < 1 means a too small P 1n or a too large T 1/2 . Since consistent and precise values for 83 Ga half-life are now available (Refs. [17,25] and the present work) the problem necessarily came from an underestimated experimental P 1n . With our P 1n value, R( 83 Ga) is brought back very close to unity.
Our uncertainties on the P 1n ( 84 Ga) determination are large, but it is seen that the central value is at the upper limit of the range of possible values computable using the empirical formula. This range of possible values, represented by the shaded region in Fig. 9, was obtained taking into account the uncertainties on all the quantities entering into the formula (e.g., the Q βn window is only an estimated extrapolation in the database [46]). The expected central value is P 1n = 29%; our experimental value is compatible with it within ≈1σ .

054320-10
The conclusion which can be drawn from this extensive exploitation of the new empirical formula by McCutchan et al. must be clear at this point: The jump of the P 1n value observed for 83 Ga is simply due to a sudden increase of the β strength available in the Q βn window with respect to 82 Ga. While this effect is certainly in part a mechanical consequence of the natural increase of the window's size, it is also necessary that GT-fed states are present in the lowest part of the window. Moving from 83 Ga to 84 Ga, the fraction of the β strength present inside the Q βn window increases by only ≈1/3 while the decay rate is increased by a factor ≈3.7. This means that for 84 Ga a significant fraction of the β strength-and necessarily the lowest-energy part of it-now escapes the Q βn window, lying below S n in the emitter 84 Ge, resulting in a reduced P 1n . This is exactly the same phenomenon that was invoked in Ref. [8] to explain the P 1n trend in the K isotopic chain (see Sec. I).

Comparison with QRPA results
The real question is now to know what could be the microscopic origin of these low-lying GT-fed states. Meanfield approaches, particularly including a treatment of correlations within the quasiparticle random-phase approximation (QRPA), are generally the best suited (and preferred) tools to investigate such a question. Calculations of β-decay properties using shell-model approaches are made difficult because of the large valence spaces, including several major shells, which are in principle needed. This is especially true for the region considered here, located near a major shell closure. Selected results from QRPA calculations are also reported in Fig. 9. The only calculation showing a P 1n oscillation for 82−84 Ga, of amplitude similar to the one observed, that we could find in the literature is part of the global QRPA calculations performed by Möller et al. [40] 20 years ago. However, the same calculations completely fail to reproduce the P 1n sequence of the K isotopic chain represented in Fig. 1. More recent calculations by Borzov [42] including both a treatment of the first-forbidden β transitions and of blocking effects are also shown in Fig. 9. Calculations without blocking show a trend similar to the one from the gross theory, while the inclusion of blocking leads to a clear P 1n oscillation but with an amplitude much lower than the one observed experimentally.

A phenomenological attempt toward a detailed microscopic interpretation
In a further attempt to gain deeper insight into the microscopic nature of the low-lying GT-fed states possibly responsible for the observed phenomenon, we have considered the configurations and valence space shown in Fig. 10 in a phenomenological way. In this simplistic approach, the ground state of the precursor is assumed to be represented as a one proton quasiparticle (QP) j p0 state. GT transitions from this state to the neutron-hole proton-particle configurations coupled to J π = 1 + ("doorway configurations") schematically represented in Fig. 10(a), with all possible combinations allowed by the valence space represented in Fig. 10(b), were considered. The unperturbed (effective single particle) energies of the doorway configurations were extracted from spectroscopic information on the N = 49 isotones within a core-coupling approach using the procedure of Ref. [34]. Configuration energy was calculated taking into account an effective residual proton-neutron interaction in the J π = 1 + channel derived from the observed splittings of the J π multiplets in the odd-odd N = 49 nuclei, similar to what was done also in Ref. [34]. The low-lying 1 + states in these nuclei involve indeed exactly the same neutron-hole proton-particle configurations as represented in Fig. 10. QP occupation coefficients were determined using a BCS approximation and pairing gaps from existing experimental mass data. However, in this voluntarily simplistic first approach, configuration mixing and phonon coupling were not included. Their inclusion would lead to two seemingly opposite effects, the former depriving the lowest lying states of their GT strength while shifting them to higher energy, while the latter introduces low-lying small GT-strength components. Only proper, detailed QRPA (or very large-scale shell-model) calculations can provide the correct balance.
We have tested our approach on the analogous case of the N = 52 87 Br precursor to the N = 51 87 Kr emitter β decay for which detailed experimental GT-strength distributions are available [48,49]. The resulting GT-strength function is shown in Fig. 11, and it is in good agreement with the one experimentally obtained; see Fig. 4 in Ref. [48] or Fig. 8 in Ref. [49]. In particular, the energy location and width of the resonance-like structure centered around 5.5 MeV are nicely reproduced. According to the calculations, it is centered around a dominant ν1g 9/2 → π 1g 9/2 CP component. This agreement means that the existence of this broad structure and its energy location are consistent with the rest of the observed lower-lying spectroscopy. The experimentally observed accumulation of strength just below Q β is missed by the calculations, but this is probably simply due to the lack of configuration mixing, which could lead to an accumulation of strength on the (maybe also underestimated) ν1f 7/2 → π 1f 5/2 SF component.
Following these encouraging results, calculations were pursued for the 83 Ga 52 → 83 Ge 51 β decay and the associated GT-strength distribution is reported in Fig. 12 the strength function from the previous heavier N = 51 case is not trivial. The 5.5-MeV-centered resonance-like structure is apparently still present, but is broadened and split into rather well-separated components collecting similar strength. Interestingly enough, the lowest one is formed by the rather strong BSF ν2p 1/2 → π 2p 3/2 transition, somewhat isolated from the rest of the structure. Its excitation energy is located FIG. 12. Same as Fig. 11 but for the decay of the 83 Ga ground state, assumed as a proton j p0 ≡ 1f 5/2 QP state, to the J = 3/2,5/2,7/2 GT doorway states in 83 Ge. The vertical doted and dashed-dotted lines indicate the position of the neutron threshold in the 83 Ge emitter and the Q β of the 83 Ga precursor, respectively. very near the neutron separation threshold (inclusion of configuration mixing would push it just above). It seems then that it is indeed due to this particular structure in the lowest part of the GT-strength distribution that P 1n reduction is observed when going from 83 Ga to 84 Ga. The neutron separation threshold increases from 3633(3) keV in 83 Ge to 5243(4) keV 84 Ge [46], thus suddenly excluding this specific BSF component (and maybe also part of the CP components) from the Q βn window. This effect is magnified by the Fermi function: This sole BSF configuration attracts already 27% (at maximum) of the β population.
Neutrons emitted from these states must have a very small energy, leaving the n-emitted residue 82 Ge in its ground state. But one of the characteristics of the TETRA 3 He neutron counter is precisely to have a negligible neutron-energy threshold [22]. Incidentally, we report 20(8)% γ -unobserved βn feeding (see Table IV), which compares favorably with the 27% feeding to the BSF states. It is worth pointing out that it is also consistent with the ≈30% missing βn strength in the measurement of Ref. [14].
In conclusion, this phenomenological study, while having the clear advantage to allow for a simple picture in terms of the single-particle states involved, provides strong additional support to the conclusion drawn from the use of the empirical P 1n formula.

V. CONCLUSION
β-delayed neutron emission probabilities of the 82−84 Ga precursors were measured in simultaneous β and neutron counting mode using the 4π long-counter TETRA at the ALTO ISOL facility. Detailed β and neutron-gated γ -spectroscopy data were collected. First experimental evidence for βdelayed two-neutrons emission from the 84 Ga precursor was also found. P 1n = 22(2),85(4), and 53(20)% were obtained for 82 Ga, 83 Ga, and 84 Ga respectively. The P 1n extraction procedure was validated on the 82 Ga case [22] and further improvements were introduced in the present work for the case of 83 Ga, where statistics was sufficient to extract one P 1n value per individual tape cycle, thus dramatically improving the statistical significance of the final result.
The trend which emerges from this set of three values is that of a large amplitude P 1n staggering. The decrease of the P 1n value from 83 Ga to 84 Ga recently pointed out in Ref. [14] is confirmed but is even more dramatic, starting from a much higher P 1n value for 83 Ga than reported before. Such a large P 1n oscillation for neutron precursors having a magic number N m of neutrons +1,2, and 3 additional ones was already observed in the case of the K isotopes beyond the N m = 28 shell closure by Carraz et al. [8]. This phenomenon was interpreted by these authors as originating from low-lying structures in the β-strength function. An analysis using the new empirical P 1n formula recently introduced by McCutchan et al. [44] supports a same interpretation for the present case. Further investigation on possible GT doorway configurations available at low energy according to the N = 49 spectroscopy points toward the presence of a strongly fed proton-particle neutronhole [π 2p 1 3/2 ν2p −1 1/2 ] 1 + ⊗ π 2f 5/2 back-spin-flip configuration located exactly in the region of the neutron threshold.
By its magnitude, this (N m + 1,2,3) P 1n -staggering phenomenon seems to bear some characteristics of a resonant process and may belong to a wider class of nuclear threshold phenomena. In any case, it is most probably not a simple curiosity restricted to the K or Ga cases. It may indeed explain the anomalies of the effective density parameters of structureless β-strength functions in an attempt to fit to the whole set of experimentally available P 1n value, as in Ref. [13]. Further investigation in the N m = 82 region, in particular "south" of 132 Sn, would provide valuable clues about the possible generality of this (N m + 1,2,3) P 1n -staggering phenomenon.
While it is in general difficult to exploit integrated quantities like P 1n (or half-lives, masses, etc.) for nuclear structure purposes, their measurements for a series of (N m + 1,2,3) nuclei can really be hoped to bring new insights on the structure of the closed (or supposedly closed) shell regions in question. These integrated quantities are in general the first available for very exotic nuclei, because their measurements are achieved using high-sensitivity or high-efficiency detectors. In those conditions, they can be truly viewed as a first step towards spectroscopy-viz., in the case of systematic P 1n measurements, towards spectroscopic studies of the neutron-threshold region of the excitation spectrum.