High-sensitivity study of levels in Al-30 following beta decay of Mg-30 Olaizola , B . 2016-11-21

Olaizola , B , Mach , H , Fraile , L M , Benito , J , Borge , M J G , Boutami , R , Butler , P A , Dlouhy , Z , Fynbo , H O U , Hoff , P , Hyldegaard , S , Jeppesen , H B , Jokinen , A , Jollet , C , Korgul , A , Koster , U , Kroell , T , Kurcewicz , W , Marechal , F , Mrazek , J , Nilsson , T , Plociennik , W A , Ruchowska , E , Schuber , R , Schwerdtfeger , W , Sewtz , M , Simpson , G S , Stanoiu , M , Tengblad , O , Thirolf , P G & Yordanov , D T 2016 , ' High-sensitivity study of levels in Al-30 following beta decay of Mg-30 ' Physical Review C , vol. 94 , no. 5 , 054318 . DOI: 10.1103/PhysRevC.94.054318


I. INTRODUCTION
In the region known as the island of inversion around 32 Na [1], shell-model configurations are strongly rearranged.Calculations using only the sd model space fail to predict properties of these nuclei and one has to include the intruder pf orbits in their description [2].Many studies choose to simultaneously probe nuclei outside of the island of inversion, nuclei at the transition point, and nuclei inside the region.The neutron-rich aluminum nuclei are located at an interesting junction just at the north-western border of this special region, thus their nuclear structure is particularly challenging.This study is focused on 30 Al, which is located just outside of the island of inversion, where in principle the shell-model calculations performed in the sd valence space should work quite well.On the other hand it is not clear to what extent the intruder pf orbits influence the structure of the excited states in this nucleus and also in the 32 Al isotope.
There have been a number of recent studies on 30 Al and 32 Al probing the application of the shell-model sd valence space for the description of these nuclei.The magnetic moments of the neutron-rich aluminum isotopes, including 30,31,32 Al, were measured by Ueno et al. [3,4].The magnetic moment is an observable that is very sensitive to the orbits where the valence nucleons reside [3], and the authors found that for 27−32 Al, the shell-model calculations using the "universal" (ls, 0d) interaction (USD) effective interaction reproduce quite well the experimental values of magnetic moments, implying that the dominant configurations can be described within the sd model space [4].However, unlike for 32 Al, for 31 Al they have measured an electric quadrupole moment whose value is 30% lower than predicted by the model.This difference remains an enigma, since it cannot be explained by the addition of deformation driving pf configurations nor by the extended calculations within the sd model space.Nevertheless, the authors conclude that, as far as the ground-state magnetic dipole and electric quadrupole moments are concerned, 30−32 Al are located outside of the island of inversion.
As for the low-energy structures the situation is more complicated.In particular the low-lying levels in 32 Al represent a puzzle.The identification of a J π = (4 + ) 200-ns isomer at 957 keV [5] created an experimental sequence of 1 + , 2 + , and 4 + levels that cannot be reproduced either by the shell model with sd orbits only, or by those that include also the pf configurations [5,6].There is also evidence that the pf orbits influence the low-energy structure of heavy aluminum isotopes.Fornal et al. [7] have identified a new state at 1178 keV in 32 Al that only feeds the 200-ns isomer and represents a good candidate for a 4 − level arising from the intruder configurations.A 4 − level at such low excitation entails a reduction in the gap between sd and pf orbits.On the other hand, an indication of a significant admixture of the intruder pf configuration in the ground state of 33 Al was reported by Himpe et al. [6] based on g-factor measurements.
Hinners et al. [8] used the 18 O( 14 C ,pnγ ) reaction to search for negative-parity states in 30 Al, which are associated with a lowering of the pf orbits.The charged particles from the reaction were detected in a E-E silicon particle detector, while the γ rays were detected in a Compton-suppressed high-purity germanium (HPGe) array.They have identified candidates for the negative-parity states starting with a level at 2298 keV, whose possible spin-parity assignment is 4 − , analogous to 32 Al.If correct, it would represent a drop of 1.2 MeV for the 4 − state when going from 28 Al to 30 Al.It would be also consistent with a further drop of 1.1 MeV between this state in 30 Al and the proposed 4 − state at 1178 keV in 32 Al [7].The study by Hinners et al. also encountered problems in the identification of the low-lying 2 + 2 and 2 + 3 states, since these states are strongly nonyrast.They have proposed two candidates for the 2 + states, at 1562 and 1802 keV, although the experimental γ -ray branching ratios strongly deviate from those predicted by the shell model.
The same reaction, although in inverse kinematics, was used by Steppenbeck et al. [9] at the Argonne National Laboratory.Recoiling fragments were analyzed using the fragment mass analyzer [10], while the γ rays were detected at the target position by the Gammasphere array [11].This study also failed to identify the negative-parity states in 30 Al and had similar problems in identifying the 2 + states.The authors found no evidence for the 1562-keV state reported in [8], but identified a new state at 2015 keV, which was then proposed as a candidate for the 2 + level.The identical nuclear reaction was used by Kozub and collaborators [12] to perform γ -ray yield curves, angular distributions, and level lifetimes using the Dopplershift attenuation method (DSAM) in 30 Al.They have measured the lifetime of the 688-keV state, T 1/2 = 0.7(2) ps, and four lifetime limits including three in the subpicosecond range.The half-life for the 244-keV state they quote in a wide range from 2.8 ps to 8.3 ns.
The aforementioned work by Hinners et al. [8] also included a study on the β decay of 30 Mg into the levels in 30 Al.The aim of their work was to identify the low-lying 1 + states predicted by the shell model.They observed five γ rays and three excited states, including a new 1 + state at 2413 keV.
In the present study we use γ -ray and fast-timing spectroscopy to investigate levels in 30 Al populated by the βdecay chain of 30 Na [T 1/2 = 49.4(20)ms [13]], that decays to 30 Mg [T 1/2 = 317(5) ms [13]] and subsequently to 30 Al [T 1/2 = 3.62(6) s [14]].Our investigation takes advantage of a much higher beam intensity, which yielded ∼4 × 10 6 detected 30 Al photopeak events, at least 2-3 orders of magnitude higher than in previous studies.The aim is three fold: First, we intend to search for the additional 1 + states in 30 Al.Second, with the higher beam intensity and thus higher statistics, we have an opportunity to populate and study the little-known low-lying 2 + states.Finally, using the advanced time-delayed (ATD) βγ γ method [15,16], we intend to measure the lifetime of the 243.8-keV state, which was predicted by the USD model to be T 1/2 = 17 ps [12].Based on the close agreement between the measured values for the ground-state magnetic moments in the Al nuclei and the model predictions [3,4], one expects a good agreement also for the B(M1) transition rates.Our investigation is part of a wider fast-timing study of the N ≈ 20 island of inversion that was carried out at the ISOLDE facility at CERN [17].

II. TECHNICAL ASPECTS
The activity of 30 Na was produced at the protonsynchrotron booster (PSB) of the ISOLDE facility at CERN by bombardment of a 45 g/cm 2 UC x /graphite target with 1.4-GeV proton pulses from the PSB.The pulses are interspaced in multiples of 1.2 s.The A = 30 ions were mass separated and deposited onto a thin aluminum stopper directly in front of a β detector.There was no moving-tape system to take away the decay products, thus creating a saturated source that included short-and long-lived activities coming from several radioactive decays.
The measuring station included five detectors positioned in a close geometry around the beam implantation point.The fast-timing β detector was a 3-mm-thick NE111A plastic scintillator placed directly behind the radioactive source.The γ -ray detectors included two fast-response scintillating BaF 2 crystals of the Studsvik design [18] and two HPGe detectors with relative efficiency of 100%.
The experimental setup and data collection were optimized for the application of the ATD βγ γ (t) method described in [15,16,19], thus only a few details are given below.A time-delayed βγ (t) coincidence system was set between the β detector and each of the γ detectors and thus three parameters were required per coincident βγ (t) event: the energies of the β particle and the γ ray, and the time-delay between the β and γ events.
Triple-coincident βγ γ events were identified when two βγ (t) events were recorded within a time gate of 8.1 μs.The data analysis used coincident events collected in the β-HPGe-HPGe or β-HPGe-BaF 2 combination of detectors.These sets allowed identification of γ rays observed in the spectra and the construction or verification of the level scheme.Moreover, it allowed the identification of γ rays present in the coincident BaF 2 energy spectra characterized by much worse energy resolution than HPGe spectra.The HPGe detectors were calibrated using 24 Na, 88 Rb, and 140 Ba / 140 La, off-line sources.This calibration was further verified using the most intense γ lines in 30 Si from the experiment.
In the ATD method [15,16,19] the time responses of the fast-timing γ detectors (BaF 2 crystals with a FWHM time resolution around 100 ps at 1 MeV) are carefully calibrated (to a picosecond precision) for various types of interactions of γ rays in the crystal (Compton and full energy peak (FEP) events).It is also checked that the shape of time spectra for prompt radiation is close to symmetric quasi-Gaussians over the range of the γ -ray energies of interest.In particular, timewalk (the energy dependence of the time response) calibrations of the BaF 2 detectors were obtained off-line using sources of 24 Na, 88 Rb and 140 Ba / 140 La.

III. RESULTS ON 30 Al
For the analysis, data were prepared by selecting a time gate of 300-1200 ms after the proton impact.This allowed the 30 Na to decay away and enhanced the 30 Mg activity (see Fig. 1).The identification of γ transitions in 30 Al from the β decay of 30 Mg was done based on the time behavior of the activity (see below) and on coincidences with already known transitions.As an example the HPGe energy spectrum in coincidence with the strongest 243.8-keV transition is shown in Fig. 2. Together with the most intense coincident γ lines, smaller peaks are visible with sufficient statistics.   Al peaks identified.A time gate of 300-1200 ms after the proton impact on target was selected to enhance the 30 Mg activity.In this time range the 30 Na has decayed away.In a second step, the 30 Al decay to 30 Si was subtracted.This did not suppress the 29 Al peaks (the A = 29 chain was present in the experiment due to the β-n branch in 30 Na [13]) but oversubtracted the peaks in 29 Si.The data acquisition system employed in the experiment suffered from severe dead time, as can be seen in Fig. 3.This problem was tracked down to the writing of data buffers and it was corrected during the off-line analysis (black dots in Fig. 3).The correction was done by multiplying the time spectra by the dead-time-to-live-time ratio as a function of the time since proton impact.The goodness of this correction was cross-checked by satisfactorily fitting the various halflives of the isotopes down the decay chain.The 30 Al was fitted to obtain the half-life of 30 Mg using the time reference of the proton beam impacting on the target.The fit yielded T 1/2 = 335(10) ms.The statistical error was below 1 ms, but a systematic error of 10 ms was introduced to account for uncertainties in the correction of the dead time.Nevertheless different fits were performed varying the fit range and binning and the results were found to be very consistent, well below the conservative 10-ms systematic error.Our result seems to FIG. 3. 30 Al activity gated on the 243.8-keV transition.The red (gray) dots show the activity before the dead-time correction and the black dots after the off-line correction.The green (light gray) line is a fit to the dead-time-corrected activity and the purple vertical line shows the fitting-range limit.The Bateman equation for a decay chain [20] was used for the fit, with the half-life of 30 Na [T 1/2 = 49.4(20)ms [13]] as a fixed parameter and a constant background, a normalization factor, and the 30 Mg half-life as free ones.  3Al populated following the β − decay of 30 Mg from this work.For absolute intensity per 100 decays, multiply by 0.94 (5).Q β value was obtained from [24].fit better with older results (see compilation in Ref. [13]) than with the T 1/2 = 316(5) ms obtained by Hinners et al. [8], but they still agree within 2σ .
Steppenbeck et al. [9] reported levels at 242.9(1), 685.7(1), and 1798.0(5)keV populated in the 14 C( 18 O ,pnγ ) reaction.We observe these levels in our level scheme, but at systematically higher energy, and well beyond the 1σ error bar.Conversion electrons were deemed negligible for all transitions [23].No direct feeding of the 30 Al ground state was assumed, due to the J = 3 difference between the parent and daughter ground states.
Using the centroid shift technique described in Ref. [15] the mean lifetime of the 243.8-keV level was measured.Because the experiment employed two fast crystals, the value was measured independently twice, both in perfect agreement: τ 1 = 22(8) and τ 2 = 21(8) ps.For an example of a time spectrum of one of the crystals, see Fig. 5.The final result is given as a weighted average of the two values, T 1/2 = 15(4) ps.Since the statistics for both the 30 Al data and the calibration is very high, the main source of error comes from the uncertainty in the lifetimes in the 140 La calibration source employed.It has to be noted that the half-life of the 467.6-keV level in FIG. 5. Time difference of the β − BaF 2 (t) coincidence with a gate on the 243.8-keV transition, shown for the second BaF 2 .To precisely select a particular γ -cascade decay, an additional coincidence with the 443.8-keV transition was made with the HPGe detectors.To obtain the final τ = 21(8) ps, the centroid shift C shown must be corrected by the energy-dependent time walk of the BaF 2 crystal, −7 (7) ps in this case, and the Compton contribution, +2(1) ps. 140La is T 1/2 < 7.7 ps [25] and not T 1/2 < 7.7 ns, as it is wrongly quoted in the database [26].A pure M1 character for the 243.8(1)-keV transition was already determined by the fit of the angular distribution [8], which with the new experimental half-life yields B(M1) = 0.10(3) W.u. (Table I).This transition rate is of the same order of magnitude as that of other reported M1 transitions in 30 Al measured in nuclear reactions (see Table II in Ref. [12]).
By employing the parallel transitions technique (for a detailed explanation see [15]), it was possible to set an upper limit to the lifetime of the 687.6-keV level.Two time spectra were generated.In one of them the 2169.1-keVtransition was selected in the HPGe detector.In the other one this detector had a condition on the 1724.6-keVline.Both spectra had an energy gate on the 243.8-keV transition in the BaF 2 crystals.From the difference of the centroids of both time distributions an upper limit of <5 ps for the 687.6-keV level was obtained.This limit is consistent with the T 1/2 = 0.7(2) ps result from [12], a value that is below the precision of the current experiment.Table I shows the limits for the reduced transition probabilities for transitions depopulating this level.
The level found at 1801.5 keV in this work has been observed in β decay for the first time, but most likely it can be identified as the 1802-keV state observed in the 18 O( 14 C, pnγ ) reaction [8], and in the same reaction but in inverse kinematics at 1798.0(5) in [9].It presents a negligible β feeding, which suggests a spin of 2 or higher.It is populated by the 611.1-keV transition from the 1 + state above it, so spins higher than 3 can be discarded.We tentatively propose a spin-parity of (2,3) + for this level.Negative-parity assignments have not been considered for this level because shell-model calculations do not predict any 1 − states below 3.5 MeV nor a 2 − state below 2.5 MeV (see Refs. [8,9]).just based on the similarity of energies, despite the total disagreement in the branching ratios.
The two newly identified levels in this work, at 3163.9 and 3362.5 keV, have log(f t) values of 5.19 (11) and 4.84 (7) respectively.According to Ref. [29], the feeding to the 1 + 1 state at 687.6 keV exhausts almost all the β-decay strength.This and their high energy make it very unlikely that any unobserved γ transitions populate them from above with significant intensity.Because of this direct β feeding, these two levels are tentatively assigned as new (1 + ) states.
By using the intensity of all the γ rays directly populating the ground state we calculated a normalization factor of 0.94(5) (again, no direct β feeding was assumed for the ground state).This result does not agree with the value of 0.74(10) calculated in the compilation [28], most likely obtained from an older β-decay work on the region [22].Our normalization factor can be favorably compared to that obtained by Hinners et al. of 0.98(3) [8].even if they acknowledged essentially no agreement with the calculated branching ratios.Steppenbeck and collaborators [9] also suggest a (2 + ) spin assignment based on shell-model calculations for their state at 1798 keV (which they match to the one at 1802 keV in Ref. [8]) and claim a better agreement with the theoretically predicted branching ratios.They observed a transition between this state and the 1 + 1 at 687.6 keV of ∼1113 keV, ∼10 times weaker than the transition from this level to the 2 + 1 state.We have made a dedicated search for a 1113.9-keVtransition (according to the energy difference of the states seen in this work) connecting the 1801.5-keVlevel to the 687.6-keV state, but if it exists its intensity is below our sensitivity limit of 0.05 units at this energy.Shell-model calculations predict a more intense transition from the 2 + 2 to the ground state, but it has not been observed either in this or in previous works.

V. CONCLUSIONS
γ -ray and fast-timing spectroscopy were used to study levels in 30 Al populated following the β − decay of 30 Mg.Our present work verifies the known level scheme of 30 Al with increased precision.Furthermore, we have expanded it with five new transitions and three new levels not seen previously in β decay, for which tentative spins and parities have been assigned.Two new levels were observed for the first time, at 3163.9 and 3362.5 keV, that are firm candidates to be 1 + states, expected at this excitation energy.Using the ATD βγ γ (t) method, the lifetime of the first excited state at 243.8 keV has been measured for the first time to be T 1/2 = 15(4) ps.
An upper limit has been set for the half-life of the second excited state, consistent with the previously reported value.The 1801.5-keV level is the only one observed in this study that could be a candidate for the second excited 2 + state, but discrepancies with the predicted γ branching ratios still remain.
The measured B(M1) transition rates, in perfect agreement with the shell-model calculations using only a full sd model space, confirm that 30 Al is indeed outside the island of inversion and no significant occupation of the pf intruder orbits is required to describe the low-lying positive-parity states.This is further supported by the finding in this work of the predicted 1 + 3 state, in relatively good agreement with the calculated energy.
Hinners et al.were not able to perform angular correlations on the 1802-keV level, but they identified it as the 2 + 3 state predicted by the calculations

TABLE I .
Levels, transitions, lifetimes, and reduced transition probabilities measured in30Al, see text for details.The transition relative intensity has been normalized to 100 for the 243.8-keV γ ray.The † indicates levels and transitions seen for the first time in this work.The * indicates levels and transitions not seen previously in β decay but observed in nuclear reactions at similar energies.