application/xmlBeta decay studies of nuclei near 32Mg: Investigating the ν(f7/2)–(d3/2) inversion at the N=20 shell closureA.C MortonP.F ManticaB.A BrownA.D DaviesD.E GrohP.T HosmerS.N LiddickJ.I PrisciandaroH SchatzM SteinerA StolzPhysics Letters B 544 (2002) 274-279. doi:10.1016/S0370-2693(02)02544-3journalPhysics Letters BCopyright © 2002 Elsevier Science B.V. All rights reserved.Elsevier B.V.0370-26935443-426 September 20022002-09-26274-27927427910.1016/S0370-2693(02)02544-3http://dx.doi.org/10.1016/S0370-2693(02)02544-3doi:10.1016/S0370-2693(02)02544-3http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/

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PLB19111S0370-2693(02)02544-310.1016/S0370-2693(02)02544-3Elsevier Science B.V.Experiments

Fig. 1

33Al decay curve, showing fit components.

Fig. 2

Gamma-ray spectra from the decay of 33Al: (a) decay time, td, less than 0.5 s; (b) td<0.5 s; (c) 0.5 s⩽td<1.0 s.

Fig. 3

33Mg decay curve, showing fit components.

Table 1

Transitions in the 33Al β-delayed γ ray spectrum

Eγ (keV)Iabs(%)Identification1010.2±0.51.0±0.3β-delayed; decay of first 1/2+ state in 33Si1431.5±0.6N/A33Si decay [13]1847.0±0.4N/A33Si decay [13]1940.5±0.22.5±0.3βn-delayed; decay of first 2+ state in 32Si4341±111.3+0.7−0.6β-delayed; decay of first 5/2+ state in 33SiTable 2

Results of an sd shell model calculation for 33Al β decay

Input Jπ,T (33Al g.s.)5/2+,7/2Experimental Qβ11.990 MeVCalculatedObservedTβ1/2 (ms)34.841.7±0.2β-decay BR to states in 33Si (%):Neutron-bound daughter states:0.000 MeV (3/2+)87.789+1−33.985 (7/2+)0.24.378 (5/2+)1.81.3+0.7−0.64.421 (3/2+)3.14.693 (3/2+)1.1Neutron-unbound daughter states:All 3/2+1.3All 5/2+3.3All 7/2+1.6⩽2.5Total6.28.5±0.7 [16]Table 3

Gamma-ray intensities for the decay of states in 33Si populated in the β decay of 33Al

CalculatedObservedJiEi (MeV)JfEf (MeV)Eγ (keV)Iabs (%)Eγ (keV)Iabs (%)3/24.6933/20.00046930.21/20.84838450.97/23.9857080.05/24.3783150.03/24.4212720.03/24.4213/20.00044211.91/20.84835731.27/23.9854360.05/24.378430.05/24.3783/20.00043781.74341±111.3+0.7−0.61/20.84835300.07/23.9853930.07/23.9853/20.00039850.21/20.8483/20.0008482.11010.2±0.51.0±0.3Beta decay studies of nuclei near 32Mg: Investigating the ν(f7/2)–(d3/2) inversion at the N=20 shell closure

A.C

Morton

morton@nscl.msu.edu

P.F

Mantica

B.A

Brown

A.D

Davies

D.E

Groh

P.T

Hosmer

S.N

Liddick

J.I

Prisciandaro

Schatz

Steiner

Stolz

aNational Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USAbDepartment of Chemistry, Michigan State University, East Lansing, MI 48824, USAcDepartment of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA

Editor: J.P. Schiffer

Abstract

32Mg lies within a region of deformed nuclei commonly referred to as the “island of inversion”. The β decay of 33Al and 33Mg has been studied to learn about nuclear structure near 32Mg. Decay curves and precise half-life measurements are presented for both species. Gamma-ray spectra from correlated 33Al decay events are also presented. The β-decay properties of 33Al are shown to be well-described by an sd shell model calculation, suggesting that the ground state of 33Al lies primarily outside the island of inversion.

The region near 32Mg is interesting from a nuclear structure standpoint. Mass measurements of 31Na and 32Na by Thibault et al. [1] produced the first evidence of nuclear deformation in neutron-rich nuclei near the N=20 shell closure. This deformation has been attributed to an inversion of the order in which the ν(f7/2) and ν(d3/2) orbitals are filled [2–4]. In its ground state, 3212Mg20 has been shown [5–7] to lie within this region of deformation, the so-called “island of inversion” [3]. The ground state of 3414Si20, with two additional protons, is believed to be spherical [8–10]. The structure of 3313Al20 is unknown.Beta decay properties of nuclei far from the valley of stability can serve as probes of nuclear structure. In the current work, we have studied the β decay of 33Al and 33Mg to learn about structure near 32Mg. Precise half-lives have been deduced for both species. A β-delayed γ-ray spectrum for the decay of 33Al has also been obtained and absolute γ-ray intensities determined. These results are compared with those of shell model calculations.33Mg, 33Al and other neutron-rich species were produced by projectile fragmentation of 140 MeV/nucleon 40Ar18+ in a 1455 mg/cm2 beryllium target using the new Coupled Cyclotron Facility at the National Superconducting Cyclotron Laboratory at Michigan State University. Nuclides of interest were separated from other reaction products using the A1900 fragment analyzer and delivered to the experimental end station. A 4 cm×4 cm double-sided silicon strip detector (DSSD) was used as both a fragment implantation target and a monitor of β-decay activity [11]. This detector is highly segmented with 40 one-millimeter-wide strips in each direction and is 985 μm thick, providing sufficient depth of silicon for the observation of high-energy β decays. The energy resolution of the DSSD was measured using α particles from a 228Th source; that of individual strips was found to be better than 80 keV FWHM at 8.78 MeV. Aluminum degraders were used to reduce the energy of the incoming fragments so that they would be stopped in the front 200 μm of the DSSD. Three 5 cm×5 cm silicon PIN diodes were placed near the DSSD to differentiate implantation and decay events. The first of these was 488 μm thick and was placed 22 mm upstream of the DSSD. The other two, 309 and 303 μm thick, were placed 23 and 27 mm downstream of the DSSD, respectively. An additional 5 cm×5 cm×500 μm PIN diode was located ∼1 m upstream of the DSSD array to provide energy loss and time-of-flight information for particle identification purposes. A parallel-plate avalanche counter (PPAC) located just upstream of this PIN provided redundant position information. Finally, two high-purity germanium (HPGe) γ-ray counters were installed in close geometry in order to study βγ coincidences. One, with 80% efficiency relative to a 3″×3″ NaI detector, was placed on the beam axis 8.9 cm downstream of the DSSD. The second had an efficiency of 120% and was placed 14.0 cm from the center of the DSSD. This HPGe detector was located 45° off the beam axis on the upstream side of the DSSD. The total peak γ-ray detection efficiency was 0.76% at Eγ=1.0 MeV. The energy resolution of the 80% HPGe detector was measured to be 3.5 keV FWHM at 1.33 MeV; that of the 120% detector was measured to be 4.8 keV.Dual-output preamplifiers with separate low- and high-gain outputs were used with the DSSD in order to obtain energy information for high-energy (∼1 GeV) implantation events and low-energy (∼1 MeV) β decays, respectively. Data acquisition was triggered solely on high-gain signals. Events were identified as fragment implantations if low-gain signals were observed in both front and back strips in coincidence with signals in both upstream PIN diodes. Decay events were identified by the observation of high-gain signals in both front and back strips in anticoincidence with signals in the furthest upstream PIN. Implant and decay events were directly correlated on a pixel-by-pixel basis within the DSSD. Each event was time-stamped with 30.5 μs resolution; decay times were determined by subtracting the time at which a fragment was implanted from that of its subsequent β decay.The direct correlation of implants and decays requires that a given implanted fragment decay before the next fragment is implanted within that pixel. In order to maximize the time between implants within a specific pixel, the incoming fragment beam was deliberately defocused in both the x- and y-directions to illuminate as many pixels as possible. The fragment distribution was roughly Gaussian in both x and y with a full width at half maximum of 20 strips in each direction. Typical total implantation rates were 20–50 s−1 so that the average time between implants within a given pixel was 30–80 s (i.e., much longer than the decay times of the nuclei of interest). When two implantations were recorded in one pixel before the observation of a decay event, both were rejected if the time between the implants was less than the greater of five times the half-life of the initial implanted nucleus (or, in the case of 33Al, that of the 33Si daughter) or 1 s. Correlated 33Al and 33Mg events with decay times longer than 1 or 5 s, respectively, were also rejected. Correlation efficiencies of 14 and 38% were observed for 33Al and 33Mg, respectively.Data were taken in two consecutive running periods. A 330 mg/cm2 Al wedge was placed at the dispersive plane of the A1900 fragment analyzer to reduce background components in the secondary beams. During the first period, the magnetic rigidity of the A1900's first two dipole elements, Bρ1, was set to 3.5300 T·m while that of the second two dipoles, Bρ2, was set to 3.2958 T·m. This optimized the yield of 33Al. Over two days, 1.95×106 fragments were implanted. 33Al ions accounted for 62.1% of these fragment implants. The main beam impurities were 34Si and 35Si, accounting for 33.9% and 2.6% of the implants, respectively. In the second period, Bρ1 was set to 3.9444 T·m and Bρ2 to 3.7462 T·m to optimize the yield of 33Mg. Beam contaminants included 31Na, 34,35Al, and 36Si. In 14 hours 3.39×105 fragments were implanted. Of these, 12.9% were 33Mg ions, 31.1% were 34Al ions, and 50.9% were 35Al ions. By defining appropriate gates in the energy loss versus time-of-flight spectra from correlated implant events, β-decay lifetime curves were obtained for both 33Al and 33Mg. Beta-delayed γ-ray spectra were also obtained for the decay of 33Al.The 33Al decay curve is shown in Fig. 1

. To properly account for both the 33Al parent activity and the 33Si daughter, the decay curve was fitted with a two-component function with a long-lived exponential background where the components of the fit were calculated from Bateman equations [12]. Based on the observation of 1.7×105β decays correlated with 33Al implant events, the β-decay half-life, Tβ1/2, was deduced to be 41.7±0.2 ms. No prior measurement of the half-life has been published.

Correlated γ-ray spectra are shown in Fig. 2

. Figs. 2(a) and 2(b) include events with decay time, td, less than 0.5 s and contain all of the observed 33Al decay γ rays. Fig. 2(c) includes events with 0.5 s⩽td<1.0 s and is dominated by γ rays from the decay of the daughter nucleus, 33Si [13]. Peaks in the 33Al β-delayed γ-ray spectrum are listed in Table 1

. This is the first reported observation of delayed γ rays from 33Al β decay. With the exception of that at 4341±11 keV, these peaks were fitted with Gaussian distributions over linear backgrounds using the spectrum analysis package DAMM [14].

The 33Al decay spectrum contains a peak at 1940.5±0.2 keV with an absolute intensity of 2.5±0.3%. This is identified as the decay of the first excited 2+ state in 32Si [15] populated by β-delayed neutron emission from 33Al, and represents the first observation of a βn-delayed γ ray from the decay of 33Al. Reeder et al. claim a total β-delayed neutron probability, Pn, for 33Al of 8.5±0.7% [16]. The present result does not contradict this earlier, unpublished, measurement as the current experiment is not sensitive to all βn decay channels.The peak at 1010.2±0.5 keV with an absolute intensity of 1.0±0.3% is identified as the decay of the first excited state in 33Si. This state has been shown to have Jπ=1/2+[17,18] so that β feeding from the 5/2+33Al ground state would be second-forbidden. The population of this state is instead attributed to the deexcitation of higher-energy states populated in the β decay of 33Al.A sharp cutoff in the γ-ray spectrum is observed near 4350 keV, similar to that reported by Pritychenko et al. [18]. This is identified as the deexcitation of the first excited 5/2+ state in 33Si. The FWHM of a peak at this energy was estimated to be 12 keV, based on measurements made at lower energies with calibration sources. The intensity of the transition was determined by integrating over a 30 keV range of γ-ray energies centered on an apparent excess of counts above background near 4340 keV. The observed γ-ray energy of 4341±11 keV is consistent with that reported by Enders et al. (4290±140 keV [17]) and with the previously-measured level energy of 4320±30 keV [8]. An absolute intensity of 1.3+0.7−0.6% is observed.The strongest observed transition associated with the decay of 33Al has an absolute intensity of less than 3%, while the total intensity of the observed decays from 33Al (4.8±0.7%) is less than that of the 1847.0±0.4 keV γ ray from the decay of the 33Si daughter (5.1±0.5%). This indicates that 33Al decays primarily to the ground state of 33Si. The branching ratio for this decay can be estimated by taking the transitions at 1010.2±0.5 and 4341±11 keV to be independent of one another and including the Pn of Reeder et al. After considering the error due to the possibility of further, unobserved, weak transitions, we adopt a value of 89+1−3% for the previously-unmeasured branching ratio for the ground-state β decay of 33Al.The 33Mg decay curve is shown in Fig. 3

. As the 33Mg parent activity; the β-decay daughter, 33Al; the β-decay granddaughter, 33Si; and the βn daughter, 32Al; were all expected to contribute to the curve, it was fitted with a four-component function with an additional exponential background. The contribution of each nucleus was again determined using Bateman equations, with the β-delayed neutron branch taken to be 17% [19]. On the basis of 1.6×104 observed 33Mg-correlated decay events Tβ1/2 was determined to be 90.5±1.6 ms, in excellent agreement with, and an order of magnitude more precise than, the previously-reported value of 90±20 ms [19].

Shell-model results for the β decay of 33Al and the subsequent γ decay in 33Si were obtained in the full sd shell basis with the USD Hamiltonian and the effective Gamow–Teller and electromagnetic operators summarized in [20]. The β-decay properties for these neutron-rich sd shell nuclei were predicted in 1983 using the same USD Hamiltonian [21]. The present β-decay calculations differ from those reported earlier in the use of a more precise effective Gamow–Teller operator and the inclusion of updated experimental β-decay Q values; in 1983, that of 32Mg β decay was not known. For the N=20 nuclei on the edge of the island of inversion, the β-decay half-lives from the present calculation are 3100, 34.8 and 26 ms for 34Si, 33Al and 32Mg, respectively, compared to experimental values of 2800±200 [21] for 34Si, 41.7±0.2 from the present experiment for 33Al, and 120±20 [19] for 32Mg. From the half-life information alone, 32Mg is clearly inconsistent with an sd shell structure and is expected to lie within the island of inversion. Previous work has shown this to be the case [5–7].A more exacting test of the structure of the 33Al ground state is provided by a detailed comparison of the experimental and theoretical β-decay branching ratios given in Table 2

and γ-ray intensities given in Table 3

. 33Al is observed to decay to the ground state of 33Si with a branching ratio of 89+1−3%; this agrees with the calculated ground state branch of 87.7%. The γ decay of the first excited 2+ state in 32Si populated by βn decay from 33Al is observed with an intensity of 2.5±0.3%. As the current experiment is not sensitive to all modes of neutron decay, this intensity provides a lower limit on Pn. Furthermore, the branching ratio for β decay to 7/2+ states above the neutron decay threshold must be less than 2.5%, as these states cannot decay directly to the 0+ ground state of 32Si. In comparison, the total β-decay branching ratio to neutron-unbound states in 33Si is calculated to be 6.2%, with a 1.6% branch to 7/2+ states. The absolute intensity of the decay of the first excited state in 33Si, with J=1/2, is observed to be 1.0±0.3%. This is identified with the calculated J=1/2 state at 0.848 MeV predicted to decay with an absolute intensity of 2.1%. Finally, the first 5/2+ state in 33Si is observed to decay to the ground state with an absolute intensity of 1.3+0.7−0.6%, consistent with the predicted intensity for this transition of 1.8%. Considering the half-life and the branching ratios for both β and βn decay, the observed decay of 33Al is well-described by the sd shell model calculation, suggesting that 33Al, in its ground state, lies primarily outside the island of inversion.

An additional shell model calculation has been carried out for the β decay of 33Mg. Because of the presence of a neutron in the pf shell, it is more complex than the sd shell model calculation used to describe the decay of 33Al. The present calculation assumed the 0ℏω configuration for the ground state of 33Mg, with Jπ=7/2−, and used the sd-pf Hamiltonian from [3]. A β-decay half-life of 77 ms is predicted. Nummela et al. report an inversion of the ν(f7/2) and ν(d3/2) orbitals in the 33Mg ground state based on a tentative spin/parity assignment of 3/2+[22]. This result, from study of the β decay of 33Na, is inconsistent with the configuration used for the current calculation. More details of the experimental decay scheme and more complete shell model calculations are required for an understanding of the 33Mg structure.The continuing improvement of experimental facilities promises to extend the range of β-emitting nuclei available for study. We have used the National Superconducting Cyclotron Laboratory's new Coupled Cyclotron Facility to investigate the β decay of 33Al and 33Mg. A precise determination of the β-decay half-life of 33Al, 41.7±0.2 ms, has been made. A half-life of 90.5±1.6 ms has been deduced for the β decay of 33Mg, in agreement with, and considerably more precise than, previous measurements. A γ-ray spectrum from the decay of 33Al has been obtained and absolute intensities reported for several transitions. Unlike 32Mg, 33Al, in its ground state, has been shown to be well-described by a shell model calculation made in the sd shell, suggesting that it lies mainly outside the island of inversion near the N=20 shell closure.

Acknowledgements

This work was supported in part by the National Science Foundation, Grants PHY-95-28844, PHY-01-10253 and PHY-00-70911. The authors wish to thank the operations staff at the NSCL for their assistance during this experiment. We also thank J.A. Winger of Mississippi State University and P.L. Reeder of Pacific Northwest National Laboratory for providing unpublished 33Al results for comparison.

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