Neutron-rich10Be and 14C nuclei were studied via resonant α scattering of radioactive 6He and 10Be beams, respectively, produced by the TwinSol facility at the University of Notre Dame. The Prototype Active-Target Time-Projection Chamber (pAT-TPC) was used as a thick gaseous α target to induce resonant scattering and as a device to track reacted particles inside the target, providing continuous excitation functions and angular distributions over a wide range of energies and angles. The experimental results indicate a melting phenomenon of α clusters in the 4+ rotational member of the 10Be ground state and a linear chain alignment of three α clusters in 14C excited states, as recently predicted by an anti-symmetrized molecular dynamics calculation

Ahn, T.

Bazin, D.

Becchetti, F. D.

Beceiro-Novo, S.

Fritsch, A.

Kolata, J. J.

Mittig, W.

Suzuki, D.

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DOI 10.1393/ncc/i2016-16372-0Colloquia: SEA2016IL NUOVO CIMENTO 39 C (2016) 372Cluster structure of neutron-rich 10Be and 14C via resonantalpha scatteringD. Suzuki(1), T. Ahn(2), D. Bazin(3), F. D. Becchetti(4), S. Beceiro-Novo(3),A. Fritsch(5), J. J. Kolata(2) and W. Mittig(3) for the AT-TPC Collaboration(1) RIKEN Nishina Center - Wako, Saitama, Japan(2) Department of Physics, University of Notre Dame - Notre Dame, IN, USA(3) National Superconducting Cyclotron Laboratory, Michigan State UniversityEast Lansing, MI, USA(4) Department of Physics, Randall Laboratory, University of MichiganAnn Arbor, MI, USA(5) Gonzaga University, Department of Physics - Spokane, WA, USAreceived 28 November 2016Summary. — Neutron-rich 10Be and 14C nuclei were studied via resonant α scatter-ing of radioactive 6He and 10Be beams, respectively, produced by the TwinSol facil-ity at the University of Notre Dame. The Prototype Active-Target Time-ProjectionChamber (pAT-TPC) was used as a thick gaseous α target to induce resonant scat-tering and as a device to track reacted particles inside the target, providing continu-ous excitation functions and angular distributions over a wide range of energies andangles. The experimental results indicate a melting phenomenon of α clusters inthe 4+ rotational member of the 10Be ground state and a linear chain alignment ofthree α clusters in 14C excited states, as recently predicted by an anti-symmetrizedmolecular dynamics calculation.1. – IntroductionStudies of α clustering, dated back to as far as the 1930s [1], still constitute theforefront in modern nuclear physics. Neutron-rich nuclei have increasingly attracted at-tention in recent years. If clustering occurs, these nuclei represent a hybrid system, whereexcess neutrons around α clusters add another degree of freedom, prompting questionson whether α clusters in stable nuclei with equal numbers of protons (Z) and neutrons(N) persist as they are, or change their cluster properties such as geometrical alignment,or even dissolve into a shell-model-like state. Neutron-rich 10Be and 14C are very im-portant nuclei to answer these questions since their N = Z isotopes, 8Be and 12C, havearguably the best established cluster states, that are even reproduced by ab initio cal-culations using bare nuclear forces [2, 3]. Previous theoretical studies by the molecularCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 D. SUZUKI et al. for the AT-TPC COLLABORATIONorbital model [4], the anti-symmetrized molecular dynamics (AMD) approach [5-7], themulticluster generator coordinate method [8], and full [9,10] or semi microscopic clustermodels [11] show that the two valence neutrons of 10Be and 14C significantly impact theα clustering, predicting molecular neutron orbitals [4], or linear chain alignment of αclusters [7], the phenomenon that was first conjectured for the N = Z nuclei [12], butremains unidentified even for the simplest 3α case in 12C [13, 14]. While a number ofexperiments have been carried out [15-22], most of the predicted cluster states remainunknown or to be studied.We studied 10Be [23] and 14C [24] via α resonant scattering off radioactive 6He and10Be beams, respectively. The active target and time-projection chamber, PrototypeAT-TPC (pAT-TPC) [25] containing He and CO2 gas mixture was used as a reactiontarget as well as tracking medium of charged particles. The thick target method [26],where excitation functions are measured by decelerating beam particles over the lengthof a thick target, was used. Measuring reaction trajectories inside the target, commonlycalled active target technique [27], allows one to directly determine the reaction ver-tex and unambiguously deduce the beam energy, which translates into the resonanceenergy [23, 24, 28]. This would otherwise be limited with the widely-used multiple sili-con detector setup that indirectly determines the reaction vertex, by assuming reactionkinematics energetically allowed, from the energy and angle of an α particle after leav-ing the target. The active target method enables the measurement of wide-ranging andcontinuous excitation functions and angular distributions, facilitating the identificationof unknown resonances and oscillatory diffraction patterns, which are the most reliableinformation in determining the spin and parity.2. – ExperimentThese measurements were performed as the first series of experiments of the pAT-TPCusing TwinSol [29] radioactive-ion beams at the FN tandem accelerator facility of theUniversity of Notre Dame [30]. 6He ions were produced via the (d,3He) reaction using adeuterium target at 1200 mm-Hg and 29.2 MeV 7Li (3+) primary beam. To produce 10Beions, a stack of four 0.1 mg/cm2 thick 13C targets were bombarded by a 46 MeV 11B(5+)primary beam. Radioactive ions thus produced were collected and purified in flight bythe TwinSol device [29] consisting of a pair of solenoidal magnets. The secondary beamwas delivered to the cylindrical target volume of He:CO2 90:10 mixture gas at 1 atm ofthe pAT-TPC [25], measuring 50 cm along the beam axis and 27 cm in diameter. Thebeam energies of 6He and 10Be were 15 and 40 MeV, respectively. The correspondingcenter-of-mass energies Ec.m. (6 MeV for 6He and 11.3 MeV for 10Be) decreased to zerowhile travelling the length of the gas volume. The average rate of 6He that entered thevolume was 2 × 103 ions per second with a purity of 90%. The main impurity was 4He.The average rate of 10Be was 103 ions per second. The beam purity was about 35%with main contaminants of 4He(2+) (50%), 9Be(4+) (5%), and 10B(4+) (3%). Electronsfrom reaction trajectories are guided toward the Micromegas amplifier [31] by an electricfield of 0.8 kV/cm parallel to the beam axis. The Micromegas consists of 2 mm wideradial strips separated into quadrants. A waveform digitizer [32] records the charge as afunction of drift time over 40μs by using an array of 511 switching capacitors.CLUSTER STRUCTURE OF NEUTRON-RICH 10Be AND 14C VIA RESONANT α SCATTERING 3+1)J(J0 10 20 [MeV]xE051015(C)Fig. 1. – (A) Excitation function for 6He + α elastic scattering. The data are integrated overθc.m. = 65◦–135◦. The observed 4+ resonance at around Ec.m. = 2.7 MeV and the missing 4+resonance expected from a 10Be state at Ex = 11.8 MeV are denoted by the lines. (B) Dif-ferential cross sections of 6He + α elastic scattering for the 4+ resonance at Ec.m. = 2.7 MeV(filled circles). Off-resonance data at 3.3 MeV (open circles) are also shown for reference. Theoscillatory pattern of the 2.7 MeV data agrees with that of the squared Legendre function withL = 4 (dashed line), for which an arbitrary scaling factor was adopted for presentation purposes.(C) Excitation energies vs. J(J + 1) plot for rotational band members of the ground (circles)and second (squares) 0+ states of 10Be. The ground-state band members of 8Be (triangles) arealso shown for comparison.3. – ResultsThe angle-integrated excitation function for 6He elastic scattering is shownin fig. 1(A). While elastic scattering was previously measured at several beamenergies [15-17,19], this is the first differential cross section data taken continuously overa finite range of energy. The resonance visible at Ec.m. = 2.56(15)MeV is assigned aspin and parity of 4+ from the diffraction seen in the angular distribution of fig. 1(B),which excellently agrees with the oscillatory pattern of the squared Legendre functionfor an angular momentum L = 4. The partial α decay width was estimated to beΓα/Γ = 0.49(5) from the resonance cross sections. These results are in line with theprevious measurement with a narrower energy range, but with better statistics [19]. Thelarge partial width of this 4+ state, widely considered as the 4+ member of the second0+ rotational band, supports the predicted σ-type molecular orbital structure aroundthe two α clusters [4, 5]. Another 4+ state of the ground state 0+ band, often discussedas a π-type partner of the second 0+ band, is predicted at Ec.m. = 3 to 6 MeV by severalcalculations [4-6, 8, 10, 11]. This state has been associated with a 10Be level found atan excitation energy (Ex) of 11.76 MeV [20], or Ec.m. = 4.36MeV, given the α emissionthreshold at Ex = 7.4MeV. However, our result that allowed us to survey a wide rangeof excitation energies up to Ec.m. = 6MeV rules out resonances at predicted energies,with an upper limit of Γα = 20 keV. This is almost one order of magnitude small thanthat of the 2.56 MeV resonance with Γα = 145(15) keV. The missing resonance strengthand the hindered branching for α emission indicate that the degree of clusterization isreduced in the 4+ state of the ground state 0+ rotational band. The weakening of clus-tering is pointed out by an early AMD study of 10Be [5], predicting that the α clustersin the 0+ ground state gradually dissolve in the rotational band members as the totalspin increases. It is interesting to note that the ground state band of 10Be has almost thesame level spacing as 8Be (fig. 1(C)), while the α clustering in 8Be appears to be robustin 0+, 2+, and 4+ states. The α spectroscopic factors of 8Be are equally large in all of4 D. SUZUKI et al. for the AT-TPC COLLABORATION4+2+ 0+2+4+Exp.2468-2E c.m.[MeV](C)0ρpρnΔρAMD[1/fm3]0.4250.3250.2250.1250.025-0.075Fig. 2. – (A) Excitation function for 10Be + α elastic scattering. Resonances of 14C and theirspins and parities from the present analysis are shown. (B) Differential cross sections of 10Be + αelastic scattering for the resonance at Ec.m. = 7.0 MeV (filled circles). The oscillatory patternagrees with that of the squared Legendre function with L = 4 (dashed line), for which anarbitrary scaling factor was used. (C) Comparison of the 2+ and 4+ resonance energies to thelinear 3α chain states predicted in a β-γ constraint AMD study [7]. The proton (ρp) and neutron(ρn) density distributions and their differential (Δρ = ρp − ρn) for the predicted linear chainstates are displayed.these states according to the folding-model potential calculation that well describes thelevel energies and widths of these states [33]. In one ab initio Quantum Monte Carlocalculation of 8Be [2], the density distribution of the 4+ state shows the two α clustersas clearly as in the 0+ ground state. The dissociation of α clusters in 10Be, which thusstands in stark contrast with 8Be, may be due to the two excess neutrons that completethe filling of the 1p3/2 orbital. The large energy gap relative to the higher 1p1/2 orbitalthat gives rise to the subshell closure at N = 6 may favour shell-model-like structureover the α clustering.The excitation function for elastic α scattering of 10Be is shown in fig. 2(A). Amongseveral resonances of 14C identified, there are two positive-parity states, one being a2+ state at Ec.m. = 3.0MeV, the other a 4+ state at 7.0 MeV. These spin and parityassignments were made again from the oscillation patterns of differential cross sections(fig. 2(B)). These levels are compared to a β-γ constraint AMD calculation using thegenerator coordinator method [7] in fig. 2(C). The experimental resonance energies wellagree with the 2+ and 4+ states of one of the rotational bands predicted. As seen in theintrinsic density distributions, three α clusters are aligned in a linear arrangement in thisband. This supports the presence of a linear 3α chain structure in excited states of 14C.CLUSTER STRUCTURE OF NEUTRON-RICH 10Be AND 14C VIA RESONANT α SCATTERING 54. – SummaryTo study the cluster structure of 10Be and 14C, resonant α scattering of radioactive6He and 10Be beams was measured at the TwinSol facility using the pAT-TPC. Thehindered branching for α emission observed for the 4+ rotational member of the 10Beground state indicates that the α clustering of the ground state, consistently predicted bydifferent theoretical studies, fades away in the 4+ rotational member. The newly-found2+ and 4+ states of 14C agree with linear chain states predicted by the recent AMDwork. The α clustering is robust against dissociation in 8Be and the linear chain struc-ture is predicted to be manifested very weakly in 12C. The present results suggestingthese phenomena realized in 10Be and 14C indicate that two valence neutrons alone candrastically and essentially evolve the α cluster structure.∗ ∗ ∗This work was supported by the National Science Foundation under GrantNos. PHY09-69456, PHY14-01343, PHY14-19765, PHY14-30152, and MRI09-23087.REFERENCES[1] Wheeler J. A., Phys. Rev., 52 (1937) 1083.[2] Wiringa R. B., Phys. Rev. C, 62 (2000) 014001.[3] Epelbaum E. et al., Phys. Rev. Lett., 109 (2012) 252501.[4] Itagaki N. and Okabe S., Phys. Rev. C, 61 (2000) 044306.[5] Kanada-En’yo Y. et al., Phys. Rev. C, 60 (1999) 064304.[6] Suhara T. and Kanada-En’yo Y., Prog. Theor. Phys., 123 (2010) 303.[7] Suhara T. and Kanada-En’yo Y., Phys. Rev. C, 82 (2010) 044301.[8] Descouvemont P., Nucl. Phys. A, 699 (2002) 463.[9] Ito M. et al., Phys. Lett. B, 588 (2004) 43.[10] Hernández de la Peña L. et al., J. Phys. G, 27 (2001) 2019.[11] Arai K., Phys. Rev. C, 69 (2004) 014309.[12] Morinaga H., Phys. 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Cluster structure of neutron-rich 10Be and 14C via resonant alpha scattering

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Cluster structure of neutron-rich 10Be and 14C via resonant alpha scattering

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