Structure of 11 Be studied in β-delayed neutron- and γ- decay from polarized 11 Li

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Nuclear Physics A 46 (4) c c Structure of Be studied in β-delayed neutron- and γ- decay from olarized Li Y. Hirayama a, T. Shimoda a,h.izumi a,h.yano a,m.yagi a, A. Hatakeyama b, C.D.P. Levy c,k.p.

Miyatake d a Deartment of Physics, Graduate School of Science, Osaka University b Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo c TRIUMF d High Energy Accelerator

1 Nuclear Physics A 46 (4) c c Structure of Be studied in β-delayed neutron- and γ- decay from olarized Li Y. Hirayama a, T. Shimoda a,h.izumi a,h.yano a,m.yagi a, A. Hatakeyama b, C.D.P. Levy c,k.p.jackson c and H. Miyatake d a Deartment of Physics, Graduate School of Science, Osaka University b Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo c TRIUMF d High Energy Accelerator Research Organization (KEK) The detailed level scheme of Be, including sin-arity assignments, has been established from a β-delayed decay sectroscoy of sin-olarized Li ( Li β Be n Be γ Be ). From the decay scheme of Be, neutron sectroscoic factors of the levels in Be have been determined. The resent results have been comared with the redictions by the Anti-symmetrized Molecular Dynamics (AMD) theory, where various tyes of -cluster states have been redicted for the excited states both in Be and Be. Some of the levels in Be show good accord with the -cluster states in the rotational bands and with a single -cluster state.. INTRODUCTION In a light neutron-rich nucleus Be, which has been regarded as a bench-mark nucleus to test the nuclear models for neutron-rich nuclei, the sins and arities have been assigned only for a few low-lying states. This situation limits comarisons between exeriment and theory level by level. In order to establish the level scheme, in articular the firm sin-arity assignments, and the decay scheme of Be, we have alied a new method of β-delayed decay sectroscoy [] for a sin-olarized Li. This method takes advantage of the fact that the allowed β-decay from a olarized nucleus shows an angular distribution of W (θ) (+AP cos θ). Here, θ, A and P are the emission angle from the olarization axis, the asymmetry arameter of β-transition and the olarization of the arent nucleus, resectively. The AP value is measured in coincidence with the delayed neutrons and/or γ-rays. In the case of allowed decay of Li (I π = ), the asymmetry arameter A takes discrete values of.,.4 or+.6, deending on the ossible sin-arity of /, or of the daughter state in Be, resectively. The olarization P, which is common for all the β-transitions, is determined from the exerimental β-decay asymmetry AP in coincidence with the delayed decay from the state with known sin-arity; in the resent case the γ-decay from the first excited state (.3 MeV, / ). Therefore, in addition to the level energies determined from the discrete energies of delayed articles and/or γ-rays, sins and arities of the resective levels can be determined unambiguously from the β-decay asymmetry coincident with the delayed radiations /$ see front matter 4 Elsevier B.V. All rights reserved. doi:.6/j.nuclhysa.4.9.8

2 c Y. Hirayama et al. / Nuclear Physics A 46 (4) c c. EXPERIMENT The exeriment was erformed at the radioactive nuclear beam facility ISAC of TRI- UMF, where highly olarized Li beam is available by means of collinear otical uming technique []. The olarized Li ( s, P 48%) was transorted in vacuum and was stoed on a Pt stoer foil where an external magnetic field was alied to reserve the nuclear olarization. The Pt foil was surrounded by an assembly of radiation detectors laced in the atmoshere. The β-decay asymmetry AP was measured by thin lastic scintillation detector telescoes laced along the olarization axis (θ= and π). The γ-rays were detected by two HPGe detectors. The delayed neutrons were detected by two tyes of scintillation detectors; six large area lastic scintillators for high energy neutrons (E n =. - 9 MeV, flight length =. m) and two 6 Li-doed glass scintillators for low energy neutrons ( - kev, 3 mm). The neutron energies were measured by the time-of-flight (TOF) technique in β-neutron coincidence. The resent detector system allowed us to make β(a)-γ, β(a)-n, γ-γ and β(a)-n-γ coincidence measurements. The total number of Li was determined to be (4.9±.) by normalizing the γ-decay intensity of the Be (.3) Be transition to the well-established intensity [3,4]. 3. RESULTS Figure shows the high-energy neutron TOF sectrum (uer) and the β-decay asymmetry arameter A in coincidence with the neutrons (lower) as a function of the neutron flight time. The exected values of A for the Li β-decay are shown by horizontal lines in the lower anel. It is clearly seen that the asymmetry arameter drastically changes at the neutron eak osition and is consistent with the exected value. From the asymmetry arameters corresonding to the neutron eaks, the sins and arities of the neutron emitting states in Be were definitely determined to be for the neutron eaks # and #3b, and for #, # and #4. From the β-n-γ coincidence relations, the level energies and their sins and arities in Be were assigned as E x =.6 MeV ( ), 8. ( ), 3.89 ( ) and.69 ( ). The resence of the weak neutron transition # ( Be (8.8) Be (6.63)) was confirmed by analyzing the Doler-broadened line shae of the.89 MeV γ-ray ( Be (6.63) Be (3.368)), affected by the neutron recoil. The very low-energy neutron transitions Be () Be (3.368) and Be (3.89) Be (3.368) were clearly observed by the low-energy neutron detectors. In the TOF and asymmetry sectra in Fig., it seems that many eaks are overlaing. In order to examine the hidden eaks and to determine the intensity of the above established neutron decays, both the sectra were fitted based on the arameters of the above-determined level scheme in Be. Each neutron eak was calculated by taking into account the level width, the neutron detection efficiency and the time-resonse of detectors. Figure shows examles of the eak rofile of the β-n-γ coincidence associated with the 8. MeV level in Be; Be(8.) # Be(6.9).9 γ Be(.96) and Be(8.) # Be(.98).9 γ Be(3.368). The reroduction of the TOF and asymmetry sectra was fair in the region of the rominent eaks. However, significant discreancy was observed around TOF and 8 ns, and TOF > ns. In order to imrove the reroduction, the neutron decays from the known levels in Be were assumed; #, #3, # and #9 (see Fig 3). This effectively imroved the reroduction of both the sectra around and ns. This fit allowed sin-arity

3 Y. Hirayama et al. / Nuclear Physics A 46 (4) c c 3c assignments for the 3.4,.3 and.6 MeV levels in Be to be, and, resectively. Further imrovement of the fit around 8 ns was made by incororating neutron decays from tentatively assumed levels at.6, 9. and. MeV. The thin curves in the TOF sectrum of Fig. are thus resolved eaks and the thick solid lines are the results of the reroduction. The overall reroduction is good, in articular for the TOF sectrum. However, we still can not reroduce some structures in the asymmetry sectrum. The level scheme and the decay scheme of Be established in the resent work are shown in Fig. 3, together with the decay scheme of Be. From the assigned sins and arities, the observed neutron decay intensities and the level widths, the neutron-sectroscoic factors (S-factors) for the decays Be Be + n were estimated [] by assuming the lowest ossible angular momenta of the neutron emission. counts / ns A Neutron energy En ( MeV ) b 4 I = :+.6 I = :.4 Summation 3a MeV /.6 I = :+.6 counts / 3 ns counts / ns 3 coincident with 9 kev γ-ray coincident with 9 kev γ-ray.. I = :.4 I = / : TOF ( ns ) Figure. Neutron TOF sectrum (uer) and β- asymmetry arameter sectrum (lower) as a function of the neutron flight time TOF ( ns ) Figure. Neutron TOF sectra in coincidence with the γ- ray emitted from Be. 4. DISCUSSION The resent results were comared with the redictions by the Anti-symmetrized Molecular Dynamics (AMD) theory which redicts three kinds of -cluster states both in Be [] and Be [6], and a single -cluster state in Be []. The -cluster structures are characterized by the configuration of the neutrons outside the clusters: The cluster structure develos with increasing number of neutrons in the sd-shell, as schematically shown in Figs. 4(a) and 4(b).

4 4c Y. Hirayama et al. / Nuclear Physics A 46 (4) c c ~ Li Τ / =8. ms Q β =.6 MeV 8.8()% 3.9(8)% 4.4(9)% 8.9(4)%.(3)% logft=4.3(8).4()%.4()% 6.8(4) % logft=4.3() logft=4.6(9) logft=4.(9) logft=4.46() logft=.(8) logft=.(8) + logft= ()% logft=.(9).(4) % +. logft=4.8..9()% logft=6.() (4)% logft=.6() /, (, ) b 3.()% 8.()% 4 3.4()%.4()% a ()%.(3)% 4.9(6)%.(3)%.86()% % (8)% 4.4(9)% -4. % (4)%.(4)%.4(8)%.8()% 6.(3)%.(3)% 9.(4)%.8(6)% () + (4 ) 3 9.3(4) % ( ) +3.8 % 3.()% ()% () %.38(9) %.46(9)%.(4)% 3.4()% 6.()% { 6 He+ +n.9(3)%.(6)% Be + 3n.36 9 Be + n.(8)% logft=.6(8) /.3 / Be ( +.3 ) Be + n Figure 3. Level scheme of Be and decay scheme of Li Be Be Be, established in the resent work. In Fig. 4(a), the redicted energy levels of Be are shown together with the exerimental levels established in the resent work. The tentatively assumed levels are not shown. The rotational band with K π =/, where the -cluster structure is less develoed than the others, is characterized by small log ft-values. The level energies, assigned sins and arities, and the log ft-values of the three levels at.3 (/ ),.69 ( ) and 3.89 ( ) MeV show good agreement with those of the redicted band members. The levels at 3.4 and MeV, and the levels at.4 and.3 MeV seem to be the candidates for the K π = band members. The 8. ( ) and 8.8 ( ) MeV levels associated with small log ft-values are the candidates for the single -cluster state redicted at around 9 MeV. In Fig. 4(a), the candidate exerimental levels are connected with the redicted ones by the dotted lines. The exerimental S-factors give another insights into the structure of Be. Figure 4(b) shows the neutron-decay aths, and their S-factors are dislayed along each ath. The 8.8 MeV level shows a large S-factor for the decay channel to the Be (.3) state which is redicted to be of -cluster nature. On the contrary, the 8. MeV level shows small S-factors for any of the decay channels. These facts suggest that the 8. MeV level is of the redicted single -cluster structure. One of the candidates for the K π = band members, the.3 MeV level does not decay to the states characterized by the well-develoed -cluster structure. Therefore, the.4 MeV level may be the K π β n γ

5 Y. Hirayama et al. / Nuclear Physics A 46 (4) c c c = band member. As for the two candidates for the lowest state in the K π = band, these levels are not energetically allowed to decay to the well-develoed -cluster states in Be. From the S-factors it is thus not ossible to determine which level is the band member. It is to be noted that the 8.8 ( ) and.6 ( ) MeV levels have large overlas with the Be states where the distinctive -cluster structures are redicted. This suggests that these levels are of -cluster nature, although these levels are not redicted by the AMD theory. (a) Be (, ) / Exeriment a cluster disaears 3.89 logft=4.3 logft=. logft=. / logft=. hω : K = / 9/ / / ~ logft=6. / 9/ / n in -shell n in sd-shell hω : K = hω : K = / AMD (b) New cluster states??? (, ) +.8 / / Be ( Be(d,) Be ).49, L=.44, L=.3, L=.36, L=., L=., L=.43, L=.6, L=.3, L= () + (4 ) Be + n MeV AMD theory Figure 4. (a) Predicted energy levels by the AMD theory and the exerimental levels. The redicted -cluster structures are schematically shown. (b) Exerimental energy levels of Be and Be, the observed neutron-decay aths and the S-factors (along the aths) for the resective decay channels. For each Be level, only a decay channel associated with the largest S-factor is shown.. SUMMARY We have alied a new method of β-delayed decay sectroscoy for a sin-olarized Li to establish the level scheme and decay scheme of Be. The sins and arities of 8 levels were firmly assigned for the first time. Some of the levels are in accord with the redictions by the AMD theory, where various tyes of -cluster states are redicted. REFERENCES. H. Miyatake et al., Phys.Rev.C6 (3) C.D.P Levy et al., Nucl. Instr. and Meth. B4 (3) N. Aoi et al., Nucl. Phys. A66 (99) 8c. 4. D.J. Morrissey et al., Nucl. Phys. A6 (99).. Y. Kanada-En yo et al., Phys. Rev. C66 () Y. Kanada-En yo et al., Phys. Rev. C6 (999) M.H. Macfarlane and J.B. French, Rev. Mod. Phys. 3 (96) 6.

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