Coulomb excitation of Na-29,Na-30: Mapping the borders of the island of inversion

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Coulomb excitation of Na-29,Na-30: Mapping the borders of the island of inversion Seidlitz, M.; Reiter, P.; Altenkirch, R.; Bastin, B.; Bauer, C.; Blazhev, A.; Bree, N.; Bruyneel, B.; Butler, P. A.; Cederkäll, J.; Davinson, T.; De Witte, H.; DiJulio, D. D.; Diriken, J.; Gaffney, L. P.; Geibel, K.; Georgiev, G.; Gernhäuser, R.; Huyse, M.; Kesteloot, N.; Kröll, T.; Krücken, R.; Lutter, R.; Pakarinen, Janne; Radeck, F.; Scheck, M.; Schneiders, D.; Siebeck, B.; Sotty, C.; Steinbach, T.; Taprogge, J.; Van Duppen, P.; Walle, J. Van de; Voulot, D.; Warr, N.; Wenander, F.; Wimmer, K.; Woods, P. J.; Wrzosek-Lipska, K. Seidlitz, M., Reiter, P., Altenkirch, R., Bastin, B., Bauer, C., Blazhev, A., Bree, N., Bruyneel, B., Butler, P. A., Cederkäll, J., Davinson, T., De Witte, H., DiJulio, D.D., Diriken, J., Gaffney, L. P., Geibel, K., Georgiev, G., Gernhäuser, R., Huyse, M., . . . Wrzosek-Lipska, K. (2014). Coulomb excitation of Na-29,Na-30: Mapping the borders of the island of inversion. Physical Review C, 89(2), Article 024309. https://doi.org/10.1103/PhysRevC.89.024309 2014 PHYSICAL REVIEW C 89, 024309 (2014) Coulomb excitation of 29,30Na: Mapping the borders of the island of inversion M. Seidlitz,1P. Reiter,1R. Altenkirch,1B. Bastin,2C. Bauer,3A. Blazhev,1N. Bree,2B. Bruyneel,1P. A. Butler,4J. Cederk¨ all,5 T. Davinson,6H. De Witte,2D. D. DiJulio,7J. Diriken,2L. P. Gaffney,4K. Geibel,1G. Georgiev,8R. Gernh¨ auser,9M. Huyse,2 N. Kesteloot,2T. Kr ¨ oll,3,9R. Kr¨ ucken,9,10 R. Lutter,11 J. Pakarinen,12 F. Radeck,1M. Scheck,13,14 D. Schneiders,1B. Siebeck,1 C. Sotty,15 T. Steinbach,1J. Taprogge,1,16 P. Van Duppen,2J.VandeWalle, 15,17 D. Voulot,15 N. Warr,1F. Wenander,15 K. Wimmer,9,18 P. J. Woods,6and K. Wrzosek-Lipska2,19 1Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, 50937 K¨ oln, Germany 2Instituut for Kernen Strahlingsfysica, K.U. Leuven, 3001 Leuven, Belgium 3Institut f¨ ur Kernphysik, Technische Universit¨ at Darmstadt, 64289 Darmstadt, Germany 4Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom 5Department of Nuclear Physics, Lund University, SE-221 00 Lund, Sweden 6School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom 7European Spallation Source AB, SE-221 00 Lund, Sweden 8Centre de Spectrom´ etrie Nucl´ eaire et de Spectrom´ etrie de Masse, 91405 Orsay, France 9Physik Department E12, Technische Universit¨ at M¨ unchen, 85748 Garching, Germany 10Science Division, TRIUMF, Vancouver, British Columbia, V6T 2A3 Canada 11Department of Physics, Ludwig Maximilian Universit¨ at M¨ unchen, 85748 Garching, Germany 12Department of Physics, University of Jyv¨ askyl¨ a, FI-40014 Jyv¨ askyl¨ a, Finland 13School of Engineering, University of the West of Scotland, Paisley PA1 2BE, United Kingdom 14Scottish Universities Physics Alliance, Glasgow G12 8QQ, United Kingdom 15Physics Department, ISOLDE, CERN, 1211 Geneva 23, Switzerland 16Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain 17Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, 9747 AA Groningen, Netherlands 18Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA 19Heavy Ion Laboratory, Warsaw University, 02-093 Warsaw, Poland (Received 8 October 2013; published 19 February 2014) Nuclear shell evolution in neutron-rich Na nuclei around N=20 was studied by determining reduced transition probabilities, i.e., B(E2) and B(M1) values, in order to map the border of the island of inversion. To this end Coulomb-excitation experiments, employing radioactive 29,30Na beams with a final beam energy of 2.85 MeV/nucleon, were performed at REX-ISOLDE, CERN. De-excitation γrays were detected by the MINIBALL γ-ray spectrometer in coincidence with scattered particles in a segmented Si detector. Transition probabilities to excited states were deduced. The measured B(E2) values agree well with shell-model predictions, supporting the idea that in the Na isotopic chain the ground-state wave function contains significant intruder admixture already at N=18, with N=19 having an almost pure two-particle–two-hole deformed ground-state configuration. DOI: 10.1103/PhysRevC.89.024309 PACS number(s): 21.60.Cs,23.20.Js,25.70.De,29.38.Gj I. INTRODUCTION Shell structure is one of the most important frameworks in nuclear physics for describing properties of many atomic nuclei. The key feature of the nuclear shell model is the presence of magic numbers, indicating shell closures. However, recent experimental and theoretical findings indicate that magic numbers are subject to the proton-to-neutron ratio. Thus, well-known shell closures vanish and new magic numbers are revealed when going to more exotic nuclei far from the valley of stability. A first indication for such a vanishing of a shell closure was found in early mass measurements for 31,32Na [1]. Campi et al. suggested a deformed ground state for these nuclei [2]. Later shell-model calculations by Warburton et al. proposed an anomalous inverted level structure, which is based on two-particle–two-hole (2p2h) neutron cross shell configurations in the ground state [3]. Recent shell-model calculations trace this phenomenon back to the residual nucleon-nucleon interaction [4–8]. The monopole term of the proton-neutron tensor interaction is strongly attractive for the spin-flip proton-neutron partner (j>and j<) and repulsive for the isospin partner in the same jorbital [8]. It has been shown that the monopole interaction VT=0 d5/2d3/2is the most attractive in the sd shell [4]. Around 30Si, protons in the πd5/2orbital strongly interact with neutrons in the νd3/2orbital. The νd3/2 orbital becomes lower in energy with respect to the νf7/2 orbital, resulting in the classical magic number N=20 [4]. By removing protons from the πd5/2orbital the VT=0 d5/2d3/2residual interaction decreases due to the missing S=0 partner protons and the νd3/2orbital is shifted to higher energies. The energy gap to the pf shell becomes smaller, causing a new (sub-)shell closure at N=16. The neutron-rich isotopes of Ne, Na, and Mg are located in the transition region between the shell closures at N=20 and N=16. Compared to 34Si, the shell gap between the neutron d3/2and the pf orbitals is reduced by about 1 MeV for the Mg isotone and about 2 MeV for the Ne isotone 0556-2813/2014/89(2)/024309(10) 024309-1 ©2014 American Physical Society M. SEIDLITZ et al. PHYSICAL REVIEW C 89, 024309 (2014) [9]. Thus, excitations of 2p2h intruder configurations of sd and pf orbitals are increased for the neutron-rich Ne, Na, and Mg isotopes. The intruder configurations gain correlation energy, i.e., deformation energy, comprising proton-neutron and neutron-neutron monopole and quadrupole terms [10]. If this gain of correlation energy largely compensates the loss of energy promoting two neutrons from the d5/2orbital across the N=20 shell gap to a pf orbital (2Egap), the ground-state wave function contains a dominant 2p2h admixture. Thus, normal (0p0h) and intruder (2p2h) configurations are inverted in those nuclei at the island of inversion. Moreover, due to deformation of the ground state, nuclei which reside in the region of the island of inversion, show largely collective behavior, e.g., reduced E(2+) and increased B(E2,0+→2+) values for even-even isotopes. In addition to the shell-model calculations, the low-lying 2+ 1states and increased B(E2) values were reproduced also by the quasiparticle random-phase approximation [11] and configuration mixing with angularmomentum projection [12,13]. Mean-field calculations result in a spherical shape for the ground state of 32Mg [14,15]. However, it is calculated to be very soft against quadrupole deformation. A number of experimental and theoretical studies have been carried out in order to understand the coexistence of normal 0p0h and intruder 1p1h and 2p2h configurations at low energies for different isotopes in the region of the island of inversion. However, the driving mechanisms are not fully understood yet and the predictive power of most theories is not good enough to provide reliable information on the low-energy structure and experimental observables for many nuclei in this region. Detailed theoretical information is rare, especially for nuclei with odd Nand/or odd Z, although these nuclei are a sensitive probe for the competing structure of 0p0h, 1p1h, and 2p2h configurations at low energies. In the neutron-rich Mg isotopes with N=20–22, the inverted level structure of normal and intruder configurations at low energies has been firmly established in a series of experiments [16–20]. More recently it could be confirmed that already at N=19 the wave functions of the ground and low-lying states contain a dominant admixture of intruder configurations [21–23]. For the neighboring N=18,19 Na isotopes, 29,30Na, measurements of the magnetic dipole moments and electric quadrupole moments revealed significant deviations from the universal sd-shell (USD) model [24,25], indicating a dramatic change in the underlying shell structure also for these nuclei. While the experimentally deduced magnetic dipole moment of 29Na could be reproduced in USD calculations, its electric quadrupole moment exceeded the USD value by about 30% [25,26]. Monte Carlo shell model (MCSM) calculations with the SDPF-M interaction reproduced this anomalous electric quadrupole moment, as well as the close-lying ground and first excited states with spin values 3/2+and 5/2+, observed in β-decay studies [27,28], supposing a large mixing of intruder configurations by about 42% for the wave function of the ground state [26]. Moreover, the MCSM calculation yields an E2 excitation strength of the low-lying states with B(E2,3/2+→5/2+)=135 e2fm4, compared to 111 e2fm4 obtained by the USD model. Results of a recently published 5/2 3/2 3/2 1/2 9/2 7/2 5/2 3/2 5/2 3/2 (5/2 ) USD 5/2+ 3/2+ 1/2+ 9/2+ + + + + + + + SDPF−M 72 0 + + 1249 + +1588 Exp. 29Na FIG. 1. Comparison of the energy levels of 29Na, deduced by experiment (middle) and by shell-model calculations using the USD (left) and SDPF-M interactions (right). The E2 excitation strengths from the ground state are indicated by the width of the arrows. The figure was adapted from Refs. [26–28]. Coulomb-excitation experiment favored the former value with B(E2)↑=140(25) e2fm4[29]. Other low-lying states are supposed to be dominated by normal 0p0h configurations and are hardly connected to the ground state. Thus, very small B(E2) values are expected. Utsuno et al. predicted higher-lying 3/2+ 2,5/2+ 2, and 7/2+ 1states dominated by intruder configurations at around 2 MeV [26](cf.Fig.1). New β-decay studies assigned states at 1249 and 1588 keV to have Jπ=3/2+ 2and (5/2+ 2), respectively [28]. Additional MCSM calculations obtained 65% and 77% 2p2h admixture for the 3/2+ 2state and 5/2+ 2state, respectively [28]. Due to the large intruder mixing in the ground state these states are supposed to have a noticeable overlap with the ground state in their wave functions. Thus, the related B(E2) values are sensitive probes related to the intruder content and the N=20 shell gap. A value of B(E2,3/2+ gs →7/2+ 2)=57 e2fm4has been reported [26] and is awaiting experimental verification. The magnetic dipole moment of 30Na was experimentally deduced by Keim et al. to be 2.069(2) μ2 N, which is significantly lower than the predicted value from USD model calculations, which yielded μ=2.687 μ2 N[25]. Moreover, an anomalous electric quadrupole moment was measured [24,30]. Its value and also its sign differ markedly from the USD prediction. MCSM calculations with the SDPF-M interaction 024309-2 COULOMB EXCITATION OF 29,30Na: MAPPING THE . . . PHYSICAL REVIEW C 89, 024309 (2014) (3 ) 1 2 1 1 2 5 6 1+ 2+ 3+ 0+ 4+ (2 ) + + +151 424 516 +0 +926 2 3+ + + 4 1+ 2+ 0+ 1+ 2+ 3+ 3+ +2114 4+ 0+ 4+ 2+ 1+ 3 4− − − − − 3+ 2+ USD Exp. SDPF−M 30Na 2p2h 0p0h 1p1h K=1K=2 2p2h FIG. 2. Comparison of the energy levels of 30Na, deduced by experiment (middle) and by shell-model calculations using the USD (left) and SDPF-M interactions (right). The E2 excitation strengths from the ground state are indicated by the width of the arrows. The figure was adapted from Refs. [26–28]. reproduced the measured μand Q0values very well [26]. Thus, the properties of the electromagnetic moments indicate that already at N=19 the ground state in 30Na is dominated by intruder configurations. A rotational K=2 band was obtained by the MCSM calculations, built upon the 2+ground state (cf. Fig. 2), characterized by highly collective E2 intraband transitions. The reduced transition probabilities amounted to a B(E2,2+ 1→3+ 1)=168 e2fm4and B(E2,2+ 1→4+ 1)= 90 e2fm4[26]. To probe these values intermediate-energy Coulomb-excitation experiments of 30Na were performed. Values of Eγ=433(16) keV with B(E2)↑=130+90 −65 e2fm4 were published by Pritychenko et al. [30] and confirmed very recently by Ettenauer et al., who measured Eγ=424(3) keV and B(E2)↑=147(21) e2fm4[31]. Both results agree well with the predicted decay of the first excited 3+ 1state. Collective transitions of higher-lying states were not observed. In the particle-rotor model the strong prolate deformation of 30Na can be described with an intrinsic state, which couples the deformed 28Ne rotor with a proton in the π[211]3/2+Nilsson orbital and a neutron in the ν[200]1/2+orbital, allowing for a K=1orK=2 yrast band. The MCSM calculations predicted the K=2 band to be energetically favored with respect to the K=1 band [26], which is consistent with the measured ground-state spin. The K=1 bandhead was calculated at 0.31 MeV and its J=2 and 3 members at around 1 MeV excitation energy (cf. Fig. 2). A promising candidate for the K=1 bandhead was found by a new β-decay experiment, which observed a 1+state at 150 keV [28]. States, dominated by normal, spherical 0p0h configurations, were expected at around 1–1.5 MeV. Moreover, the MCSM calculations predicted rather low-lying negative-parity states, which were dominated by 1p1h excitations across the N=20 shell gap [26]. Thus, in 30Na normal and intruder configurations were supposed to compete with each other at low excitation energies. Detailed experimental studies of these states would reveal excellent information on the underlying shell-model modifications around N=20. To probe the predicted collective properties of the first and higher-lying excited states in 29,30Na, Coulombexcitation experiments in inverse kinematics were proposed at REX-ISOLDE, CERN, employing postaccelerated radioactive 29,30Na beams at “safe” energies, i.e., the distance of closest approach is >15 fm and the contribution of nuclear interaction to the total excitation cross section is <0.1% [32]. The intruder configurations also at higher excitation energy were a subject of these experiments to obtain new information about the underlying shell structure and the evolution of the shell gaps far from stability. Compared to the results published by Hurst et al. [29] and Ettenauer et al. [31], the presented experiments should benefit from the more intense radioactive ion beams at REX-ISOLDE, a reduced background at energies below 250 keV and the high energy resolution and detection efficiency of the MINIBALL setup. II. EXPERIMENTAL SETUP AND DATA ANALYSIS The Coulomb-excitation experiments of 29,30Na were performed at the REX-ISOLDE facility at CERN [33,34]. The short-lived radioactive 29,30Na beams (half-lives T1/2= 44.9(12) ms (29Na) [35] and T1/2=48(2) ms (30Na) [36]) were produced by bombarding an approximately 50-g/cm2-thick UCxtarget with 1.4-GeV protons, provided by the CERN PS Booster, with a maximum intensity of 3.2×1013 p/pulse. The pulses were spaced in time by integer multiples of 1.2s, allowing for an average proton current of 2 μA. The produced Na ions were surface ionized on a tungsten surface and were mass separated by the ISOLDE High Resolution Separator (HRS). The ion beam was then guided to REX-ISOLDE, where the ions were first accumulated, cooled, and bunched in a Penning trap before injecting into an Electron Beam Ion Source (EBIS) [37]. In the REXEBIS the ions were charge bred to high charge states. Due to the very short half-lives of the isotopes, special attention had to be paid on the optimization of the working cycle of the REX-ISOLDE charge breeding system in order to minimize losses caused by in-trap decay. Therefore the trap accumulation and charge breeding times were set to 20 and 13 ms, respectively. After an A/q separation with A/q =4.143 for 29Na and A/q =4.286 for 30Na (both q=7+) the radioactive beam was postaccelerated by the REX linear accelerator and delivered with a final beam energy of 2.85 MeV/nucleon onto the secondary target inside the highlyefficient MINIBALL setup [38]. The average intensities of the 024309-3 M. SEIDLITZ et al. PHYSICAL REVIEW C 89, 024309 (2014) postaccelerated ion beams amounted to 2700(100) ions/s and 650(250) ions/sfor29Na and 30Na, respectively. During the Coulomb-excitation experiments two enriched 104Pd and 120Sn targets were used with effective thicknesses of 4.1 mg/cm2and 4.0 mg/cm2, respectively. The 104Pd target was a stack of two targets (2.2 mg/cm2and 1.9 mg/cm2). The beam-on-target times added up to 64 h for the 29Na beam and 84 h for the 30Na beam. The scattered beam nuclei were detected by a CD-shaped, 500-μm-thick, double-sided silicon strip detector (DSSSD), consisting of four identical quadrants [38,39]. Each quadrant comprised 16 annular strips at the front side and 12 pairs of sector strips at the back side for identification and reconstruction of the trajectories of the scattered nuclei. Calibration of all DSSSD segments was done with an αsource, containing 239Pu, 241Am, and 244Cm. The detector covered forward angles between 16.8◦and 53.7◦in the laboratory system. De-excitation γrays following Coulomb excitation of projectile and target nuclei were detected by the MINIBALL γ-ray spectrometer, consisting of eight triple cluster detectors in close geometry, each containing three sixfold segmented HPGe crystals [38,40]. To calibrate the MINIBALL clusters and to determine their individual, energy-dependent efficiency down to 50 keV, 60Co, 133Ba, and 152Eu sources were mounted onto the target frame at target position. The total photopeak efficiency of the array at 1.3 MeV was 8.4(2)% after the addback procedure was applied, i.e., coincident signals of the three detectors of a MINIBALL cluster were combined. At low γ-ray energies around 81 keV the photopeak efficiency amounted still 23.8(4)%. For Doppler correction, all angles of the cluster detectors had to be known exactly. Therefore an angle-calibration measurement was performed, using Dopplershifted γrays after the neutron pick-up reaction d(22Ne, 23Ne)p. The high segmentation of the setup ensured a proper Doppler correction for in-flight γ-ray emission at v/c ∼8% by combining the angular information of the γray with the direction and velocity of the scattered beam particle that was detected in coincidence. Data of the Coulomb-excitation measurements were recorded using prompt particle-γcoincidences, i.e., events with a maximum time difference of typically 800 ns between particle and γray were registered. In Coulomb-excitation experiments with radioactive beams, possible beam contaminations have to be carefully investigated, because all beam components contribute to Coulomb excitation of the target material, which is used for normalization. For the extraction of the transition probabilities it was mandatory to monitor and to determine the exact beam composition during the experiment, using two different techniques. First, the time dependence of the RIB intensity with respect to the proton-beam impact on the primary ISOLDE target was analyzed as shown in Fig. 3.Dueto their fast release out of the primary target [41] and their short lifetimes the 29Na and 30Na ions showed a high intensity only for the first ∼280 ms after the proton pulse. For longer times longer-lived contaminants, in particular isobaric Al and Mg isotopes, dominated the beam composition. By setting an appropriate time gate, the amount of beam contaminants could be reduced by a factor of 6.5 and 4.3 for the 29Na and 30Na data, respectively. In a second step the exact beam composition was 10000 Counts / 20 ms 0500 1000 tpart - tproton [ms] 1000 10000 Counts / 20 ms 29Na 30Na T1/2 = 44.9(12) ms T1/2 = 48(2) ms Δt29 = 260 ms Δt30 = 270 ms (a) (b) FIG. 3. (Color online) Time-dependent intensity of A=29,30 ions, scattered into the DSSSD, with respect to the last proton beam impact onto the ISOLDE target for the 29,30Na runs. The time gates tAset to select the short-lived Na isotopes and to reduce the amount of beam contaminants in the analysis are indicated in red. determined with help of an ionization chamber, consisting of a gas cell and a Si detector in succession for the Egas and Eres measurements, respectively, which was mounted downstream after the scattering chamber at the beam-dump position (see Fig. 4). For the A=29 beam the accumulated radioactive beam composition of the experiment amounted to 29.5(7)% for 29Na within a time window of 260 ms after the proton pulse impact, which was applied in the further analysis of the measured γ-ray intensities. Other beam fractions were found to be 12.1(3)% for 29Mg, 57.7(9)% for 29Al, and 0.7(1)% for 29Si. For the A=30 beam the accumulated radioactive beam composition of the experiment amounted to 47.3(21)% for 30Na within a time window of 270 ms after the proton pulse impact. Other beam fractions were found to be 13.6(9)% for 30Mg, 38.5(19)% for 30Al, and 0.6(2)% for 30Si. Coulomb-excitation data analysis commenced by selecting scattered projectile nuclei, i.e., 29,30Na, which were detected by the DSSSD. The kinematics of the scattered beam or target nuclei is clearly separated by the measured correlation of particle energy and scattering angle. A time window with a width of typically tp∼145 ns was applied on the time difference between the particle and the γray to select the prompt Coulomb-excitation events and to suppress random coincidences from room background, i.e., βdecay and bremsstrahlung. The prompt Coulomb-excitation spectrum for 024309-4 COULOMB EXCITATION OF 29,30Na: MAPPING THE . . . PHYSICAL REVIEW C 89, 024309 (2014) [arb. units] res E 400 800 1200 1600 [arb. units] gas EΔ 300 500 700 900 1100 w/o timegate Al 29 Mg 29 Na 29 [arb. units] res E 400 800 1200 1600 0 40 80 120 160 200 with timegate Δt = 260 ms Al 29 Mg 29 Na 29 FIG. 4. (Color online) Egas-Eres spectra of the beam composition, taken with the ionization chamber during the 29Na beam time. The A=29 isobars are well separated and can be clearly identified. While for the left spectrum no time gate is applied, the right spectrum contains only those ions, which arrive at the ionization chamber within the first 260 ms after the proton pulse impact. A significant reduction of beam contaminants is achieved, in particular for 29Al, while the number of 29Na ions remains constant. More information is given in the text. the further analysis is particularly clean of any background transitions after background subtraction with a long time window tr∼1450 ns. All observed γ-ray transitions are due to Coulomb excitation of either beam or target nuclei. III. RESULTS A. Coulomb excitation of 29Na Scattered 29Na ions were selected by a particle gate on the measured correlation of particle energy and scattering angle in the DSSSD. Using the energy and position information of the scattered particle and the coincident γray, which were provided by the segmentation of the DSSSD and the MINIBALL detectors, respectively, a proper Doppler correction of the emitted γrays was performed. For the projectile, Doppler correction is essential due to the relatively high recoil velocities β>5%. The resulting prompt, background-subtracted γ-ray spectra are shown in Fig. 5. Deexcitation γrays of excited states of both projectile and target nuclei were observed. The well-known 2+→0+transition in 104Pd at 555.8 keV [42] was the strongest γ-ray transition in the spectrum. Another γ-ray transition was observed in the spectra at 72 keV, which was assigned to the depopulation of the proposed 5/2+state in 29Na, already known from β-decay studies [43]. At this low γ-ray energy, special attention had to be paid to the background radiation, especially strong x-ray radiation following βdecay of long-lived decay products of 200Po, studied at the MINIBALL setup prior to the Coulomb-excitation experiment on the neutron-rich Na isotopes, interfering with the 72-keV transition of 29Na. MCSM calculations by Utsuno et al. predicted γ-ray transitions depopulating deformed 3/2+ 2,5/2+ 2, and 7/2+ 1 states in 29Na at around 2 MeV, which could be excited with a moderately large excitation strength [26]. For instance, a possible 7/2+ 1state is predicted to be excited with a transition strength of B(E2,3/2+ 1→7/2+ 1)=57 e2fm4[26]. No clear experimental sign was found for such transitions in the range of 1500–2400 keV, due to the low count rate and insufficient statistical significance, i.e., fewer than three counts (cf. Fig. 5). The most promising candidate at 1518(4) keV was already known from β-decay studies as depopulating transition of a (5/2+ 2) state at 1588 keV [43]. The unknown reduced transition probabilities of excited states of 29Na were determined using the relative deexcitation γ-ray yields between 29Na and the Coulomb excited, wellknown 2+state of 104Pd. The deexcitation yield of the 555.8-keV transition of 104Pd was corrected with the deduced effective beam composition, including the different Coulombexcitation cross sections of the isobars for excitation of the target material, yielding a 29Na fraction of 32.2(10)% for the excitation of the 2+state. To fit the electromagnetic transition matrix elements to the experimental data, the coupled-channels Coulomb-excitation code GOSIA [44,45]was used. The calculations were performed by integrating over the scattering angle range of c.m.=20.9–66.2◦, which is covered by the DSSSD, and the energy loss of the projectile in the target material. Corrections of the measured γ-ray yields for angular distribution effects and internal conversion were taken into account as well as position and relative efficiency of the MINIBALL cluster detectors. The spin and parity of the 72-keV level were determined to be Jπ=5/2+[28], in agreement with MCSM calculations which favor a 5/2+above the 3/2+ground state [26]. The spectroscopic quadrupole moment of the ground state was measured by β-nuclear magnetic resonance (NMR) spectroscopy, yielding a value of Q3/2+=+0.086(3) eb[25]. This quadrupole moment was included in the calculations as diagonal matrix element 3/2+||E2||3/2+. For the 72-keV level the diagonal matrix element was assumed to be |5/2+||E2||5/2+| = 0.039(3) eb within a rotational model with K=3/2. Including this information, the GOSIA calculations yielded a reduced transition probability of B(E2,3/2+→5/2+)= 150(20) e2fm4for the Coulomb excitation of the 5/2+state at 024309-5 M. SEIDLITZ et al. PHYSICAL REVIEW C 89, 024309 (2014) 0 200 400 600 0 10 20 30 40 60 80 100 0 40 80 0 400 800 1200 Energy [keV] 0 50 100 150 Counts / 2 keV 1600 2000 2400 0 5 10 15 Counts / 4 keV 2+ 0+ 200Tl(EC) 5/2+ 1 3/2+ 1 (5/2+ 2) 5/2+ 1 (5/2+ 2) 3/2+ 1 DC for 104Pd background subtr. DC for 29Na background subtr. β=0 β~6% θγc.m. >90° FIG. 5. (Color online) Doppler-corrected and background-subtracted γ-ray spectra of the Coulomb excitation of 29Na in coincidence with scattered beam particles. Doppler correction (DC) was performed for the 104Pd target (top) and 29Na beam (bottom). γ-ray transitions from the Coulomb excitation of 29Na and 104Pd nuclei were detected. The sharp line at 1275 keV is artificial from 200Tl EC decay. Please note the different scaling on the yaxis. The inset for the low-energy spectrum of 29Na shows the line shape of the 72-keV transition detected in backward direction, with the properly Doppler-corrected γ-ray events emitted in flight (β∼6%). For 29Na ions implanted in the DSSSD the γrays would be wrongly Doppler corrected (β=0). 72 keV. The quoted error is dominated by the statistical error of almost 10% for the measured γ-ray yield but also includes a 6% error for the correction for the x-ray radiation background and a 5% error for unobserved feeding from higher-lying excited states. Uncertainties of the beam composition and target excitation were included with 3% and 2%, respectively. The obtained value agrees very well with the transition strength of B(E2)↑=140(26) e2fm4, which was published by Hurst et al. [29]. The average time-of-flight of the scattered A=29 ions between target and DSSSD was 2.0 ns. Most of the γrays were detected with a certain Doppler shift, indicating a dominant in-flight decay. Thus, the lifetime of the 72-keV level has to be significantly shorter than the average time-of-flight. An upper limit of 1.5 ns was assumed from the measured spectrum. To reproduce the observed lifetime limit, deexcitation of the 72-keV level has to proceed via a strong M1 transition. The GOSIA calculations yielded a lower limit of B(M1,5/2+→ 3/2+)>0.06 μ2 Nfor the M1 strength. This corresponds to a multipole mixing ratio |δ|<0.025. An upper limit can be calculated for the excitation of the 1588-keV state, known from β-decay studies [28,43]. Spin and parity of this state are assigned to 1/2+,3/2+,or 5/2+due to the measured log ft =4.64 value in combination with the 3/2+ground state of 29Ne [28,35]. However, the calculated excitation strength varies only marginally (∼5%) with the assumed spin value of the 1588-keV state, yielding B(E2,3/2+→(5/2+ 2)) <70 e2fm4. For the proposed 7/2+ state [26], as well as for any other higher-lying excited state in 29Na, only an upper limit could be given for the reduced transition probability. Therefore a detection limit of 2.5 counts was assumed for a transition on an average background of almost 0.1 counts/keV, measured in this experiment with the MINIBALL setup in the energy range between 1600 and 2500 keV. It was assumed that the 7/2+state had to decay to the 5/2+state at 72 keV with a branching ratio of almost 100%. Any other branching, e.g., the direct decay into the ground state, was neglected. To reproduce the measured γ-ray yields the E2 excitation strength of the 3/2+→7/2+ transition has to be smaller than the upper limit indicated by the solid line in Fig. 6. Thus, an excitation to a 7/2+state 1600 1800 2000 2200 2400 excitation energy Ex [keV] 0 50 100 150 200 250 B(E2, 3/2+ 7/2+) [e2fm4] Detection limit for possible 7/2+ state above 1600 keV with decay to 72 keV FIG. 6. Calculated upper limit for the excitation strength of a possible 3/2+→7/2+transition in 29Na between 1600 and 2450 keV (solid line) in the present experiment in order to reproduce the measured γ-ray yields. Detailed information is given in the text. 024309-6 COULOMB EXCITATION OF 29,30Na: MAPPING THE . . . PHYSICAL REVIEW C 89, 024309 (2014) 0 200 400 600 800 1000 1200 Energy [keV] 0 20 40 60 Counts / 4 keV 925 keV (30Na) DC for 30Na background subtr. sum of Sn and Pd data 424 keV (30Na) 556 keV (104Pd) 501 keV (30Na) FIG. 7. (Color online) Sum spectrum of the Coulomb-excitation experiments on 30Na, using the data sets taken with the 104Pd target and the 120Sn target, background subtracted and Doppler corrected (DC) for 30Na. In addition to the known 424-keV transition there is evidence for two weak transitions at 925(4) keV and 501(4) keV (arrows), depopulating an excited state at 925(5) keV. Events with 511 keV coming from background radiation were suppressed. below 1900 keV would have to have a B(E2) value similar to or even smaller than the predicted 57 e2fm4[26], whereas a higher-lying 7/2+state with such a B(E2) value could not be detected at all in the present experiment. A 7/2+state at around 2300 keV would need to be connected to the ground state with B(E2)↑≈230 e2fm4, to be detected with 2.5 counts. B. Coulomb excitation of 30Na In addition to the 29Na experiment, another Coulombexcitation experiment in inverse kinematics on the neighboring N=19 isotope 30Na was carried out to further study the expected transition from spherical sd shell to deformed sd-pf shell configurations at the island of inversion. As in the 29Na experiment, scattered 30Na nuclei were selected by means of the measured correlation between scattering angle θCD and energy deposited in the DSSSD. Figure 7shows the resulting Doppler-corrected and background-subtracted γ-ray spectra of the two parts of the experiment, employing the 120Sn and 104Pd target. In order to facilitate observation and identification of weak γ-ray transitions in 30Na, data sets taken with both targets, i.e., 120Sn and 104Pd, were summed. γ-ray transitions, depopulating excited states, were observed for both target and projectile nuclei. Doppler correction for scattered A=30 projectiles revealed a strong γ-ray transition at 424 keV, which was already observed in a previous Coulomb-excitation experiment of 30Na by Ettenauer et al. [31]. These γ-ray events were assigned to the deexcitation of a(3 +) state at 424 keV to the 2+ground state. Deexciting transitions of low-lying excited 1+states, which were known from β-decay studies of 30Ne [28], were not observed in this Coulomb-excitation experiment. An accumulation of γ-ray events at around 925(4) keV could be interpreted as a possible candidate for the deexcitation of a proposed (4+) state in 30Na (cf. Fig. 9). MCSM calculations predicted a strong 4+→3+ transition with B(M1,4+→3+)=0.43 μ2 N[31]. Thus, an additional branching to the (3+) state with a transition energy of 501(4) keV should be observed. With the high γ-ray efficiency of the MINIBALL array a verification of this prediction should be feasible by the measured coincidence relations. Taking into account the measured yields in the γ-ray singles spectrum and the γ-ray efficiency of the MINIBALL array, one detected event with coincident 501-keV and 424-keV γrays could be expected. Experimental data—taken with both targets (Sn and Pd)—were sorted into a prompt particle-γγ coincidence matrix. Coincidence gates were set on the (3+)→ 2+transition at 424 keV and on the proposed (4+)→(3+) transition at 501 keV to investigate γ-ray transitions feeding the (3+) state. The cut spectrum showed γ-ray events at 501 and 424 keV, respectively, as shown in Fig. 8. This would be perfectly in line with the results deduced from the γ-ray singles spectra, which favored an excited state at 925(5) keV with about 67(10)% γ-ray decay branching to the 2+ground state and about 33(10)% branching to the (3+) state at 424 keV. This state at 925 keV is a possible candidate for the proposed 4+state in 30Na [26]. The known decay branches of the nearby 1+ 2state at 926(2) keV, which was observed by β-decay studies [28], were not observed in the present Coulomb-excitation experiment. The reduced excitation probabilities of the excited states in 30Na, which are of further interest, were determined by means of the measured intensities of the depopulating γ-ray transitions, relative to the well-known cross section for the Coulomb excitation of the target nuclei. The electromagnetic transition matrix elements were fitted using the GOSIA code [44,45]. The spin and parity of the 424-keV level in 30Na are not fixed experimentally, but recent shell-model calculations favored a deformed 3+state at this energy [26,31]. Furthermore, shell-model calculations favored a deformed 4+ state at around 800 keV [26], which could be assigned to the newly observed 925-keV state. The quadrupole moment of the 2+ground state was predicted to be Q(2+)=16 efm 024309-7 M. SEIDLITZ et al. PHYSICAL REVIEW C 89, 024309 (2014) 0 1 2 3 Counts / 10 keV 0 200 400 600 800 1000 Energy [keV] 0 1 2 3 Counts / 10 keV 501 keV 424 keV Gate 424 keV Gate 501 keV FIG. 8. Prompt particle-γγ coincidence spectrum of the Coulomb excitation of 30Na, gated on the 424-keV transition (top) and on the newly observed 501-keV transition (bottom), for the sum of both targets (Sn and Pd). Coincident γ-ray transitions were observed at 501 keV, feeding the 424-keV level. Doppler correction was performed for the detected 30Na nucleus. γrays with a detected energy between 508 and 514 keV were excluded from the analysis to eliminate random coincidences with 511-keV γrays. [26]. Within a rotational model applied to the K=2 yrast band, values for the diagonal matrix elements were included in the GOSIA calculations. Predictions within the MCSM expect a rather large M1 contribution for the 2+→3+transition with a transition strength of B(M1)↑=0.268 μ2 N[31]. All additional information on low-lying levels up to 1 MeV, e.g., energy, spin, parity, branching ratio, etc., which were determined by β-decay studies [28], was taken into account. For the excitation of the 424-keV level in 30Na the GOSIA calculations yielded excitation strengths of B(E2,2+→ (3+)) =230(40) e2fm4and B(E2,2+→(3+)) =320(100) e2fm4for the measurement with the 104Pd and 120Sn target, respectively. Furthermore, the possible (4+) state at 925 keV was calculated to be populated with a value of B(E2,2+→(4+)) =125(45) e2fm4and B(E2,2+→ (4+)) =96(50) e2fm4for the two different targets. Deexcitation of the (4+) state had to proceed via an E2 transition to the ground state, competing with a mixed E2+M1 transition to the (3+) state. To reproduce the measured branching ratios the M1 component of the (4+)→(3+) transition had to be much smaller than the value of 0.43 μ2 N, predicted by MCSM calculations [31]. Assuming a moderate E2 strength of B(E2) =80 e2fm4for the 501 keV transition, the GOSIA calculation yielded a M1 strength of B(M1,(4+)→(3+)) = 0.027(14) μ2 N. All quoted errors are mainly dominated by the statistical errors of the measured deexcitation yields of the relevant projectile and target excitations, respectively. Systematic errors arising from uncertainties of the deduced beam composition and of the calculated target excitation cross section were minor and were taken into account with about 5% and 3%, respectively. IV. DISCUSSION A. 29Na The measured reduced transition probabilities of the N= 18 nucleus 29Na are compared to recently published experimental values [29] and MCSM predictions [26]. The transition strength of the 5/2+ 1→3/2+transition at 72 keV deduced in this work yielded B(E2,3/2+→5/2+ 1)=150(20) e2fm4. This value is in good agreement with the value of B(E2)↑= 140(25) e2fm4published by Hurst and collaborators [29]. Recent shell-model calculations using the USD interaction and the SDPF-M interaction predict an excitation strength of 111 and 135 e2fm4, respectively, for the 5/2+ 1state [26]. Thus, the experimental results are consistent with the predictions by the MCSM calculations using the SDPF-M interaction, which yielded a mixing of intruder configurations by 42% and 32% for the wave function of the 3/2+ground state and the first excited 5/2+ 1state, respectively [26,28], confirming the onset of large intruder admixtures in the ground-state wave function already for the N=18 isotope 29Na. Within a simple rotational model the measured transition strengths yielded Q0=0.542(36) eb for the intrinsic electric quadrupole moment of the ground state of 29Na, assuming a prolate deformation. This gives a quadrupole deformation parameter of β2=0.48(3), using the equation given in Ref. [46]. However, this simple model overestimates the quadrupole deformation of 29Na due to the different static and dynamic nuclear properties, arising from differences in the underlying single-particle configurations of the ground and first excited states. An earlier, precise β-NMR measurement pointed to slightly less deformation: Q0=0.430(15) eb and β2=0.38(2) [25]. To further investigate the mechanism of intrusion in the neutron-rich Na isotopes, the experiment searched for collective properties of possible higher-lying 3/2+ 2,5/2+ 2, and 7/2+ 1states dominated by intruder configuration, which were predicted by MCSM calculations [26]. A possible candidate for a weak transition might be observed at 1518(4) keV, de-exciting a known level at 1588 keV, which was assigned as (5/2+ 2) state by new β-decay studies [28]. An upper limit for the reduced transition probability was deduced, yielding B(E2,3/2+→(5/2+ 2)) <70 e2fm4. This value is consistent with the moderately large B(E2)↑values predicted by theory for the intruder dominated states around 1.5–2.5 MeV [26]. Additionally, the measured B(E2) value implies a large 2p2h admixture in the wave function of the 1588-keV state and a significant coupling to the ground state due to the large intruder mixing. Indeed MCSM calculations predicted 77% intruder admixture for the 5/2+ 2state [28]. Other transitions of intruder-dominated higher-lying states predicted by theory were not observed. However, conclusive results of transition probabilities of higher-lying deformed states were not possible due to the experimental limitation and low count rates. 024309-8