精确测定中低能区弱束缚核12,14Be + 12C, 27Al核反应总截面并提取其核物质密度分布 许杭华1， 徐望1，M. Fukuda2，蔡晓鹭1 1中国科学院上海应用物理研究所 2 Faculty of Science, Osaka University

内容 12,14Be的研究背景及现状 实验概况

12Be 一、12，14Be的研究背景及现状 ☆ large neutron asymmetry Halo/skin like structure Breakdown of the N =8 Shell Closure (Ground state structure) Huge deformation (cluster structure) Few-body system …… 12Be is a key isotope in the beryllium chain, as it is located between the one-neutron halo 11Be and the twoneutron halo 14Be. Phys. Rev. Lett. 108 (2012) 142501

1. Non-Borromean neutron halo candidate SAMBA type nucleus? 10Be n The existence of such a structure (2 neutron halo structure) in a non-Borromean nucleus is not yet established and investigating this in 12Be is of particular interest. Phys. Lett. B 682 (2010) 391

Evidence suggest the halo structure of 12Be Spectroscopic factor |12Beg.s.:0+> =32% (1s1p)8+68%(1s1p) 6(2s,1d) 2 Confirms that the N=8 gap has collapsed The most direct way to measure the ground-state structure of 12Be is to determine the spectroscopic factors for the removal of a neutron. For example, the neutron closed shell configuration (0p)8 would give spectroscopic factors of 0 and about 2 for the knockout reactions to the ½+and ½-states, respectively. References: Navin et al., Phys. Rev. Lett. 85, 266 (2000). 9Be(12Be, 11Be +n) S.D.Pain et al., Phys. Rev. Lett. 96,032502 (2006). 12C(12Be, 11Be +n) 这说明,处于基态的12Be的外层价中子占据了2s1/2 and/or 1d5/2,3/2,1/2的单粒子轨道, 12Be的基态具备了晕结构的必要条件(low angular momentum motion for halo particles , (2s - intruder level) and few-body dynamics)。尽管 12Be具有相当高的双中子分离能S2n= 3.76 MeV ，早期的相互作用截面的测量也没有发现它具有晕结构性质，但是已经有的两家实验表明了12Beg.s.存在三体结构的晕核的迹象 (Toshio Suzuki et al., Phys. Rev. C 56(1997)847) Log ft = 3.834 ± 0.017 (F. Ajzenberg-Selove, Nucl. Phys. A506 (1990) 1) (2) Effects on to GT transitions 35% Configuration

12Be基态核物质密度分布的实验研究 Lab. Halo Experimental methods Brief description 几家典型的实验 Lab. Halo Experimental methods Brief description LBL MSU GANIL No interaction cross section（I ）[1] RMSmatter= 2.59 ±0.06 fm RMSneutron = 2.65 ±0.06 fm Includes only those reactions which destroy the projectile. Excludes target reactions which leave the projectile intact. 790MeV/nucleon Fragments’s momentum distributions[2] =92.22.7MeV/c Halo structure? Naïve, not meaningful. 56.8,64.8MeV/nucleon Neutron-removal cross sections, -xn[5] RMSmatter = 2.85±0.07 fm 060MeV/nucleon Total reaction cross section （ R ）[3] RMSmatter = 2.622 ±0.073 fm RMSneutron = 2.75 ±0.11 fm 25-65MeV/nucleon, Kox, S. et al.,Phys. Rev. C35, 1678 (1987) GSI Halo-like Elastic Scattering (four momentum transfer) [4] The study of proton scattering at small momentum transfers is an efficient tool to study nuclear matter distributions and allows one to determine both sizes of the core and halo. Halo configuration:Core(10Be)+2n RMSmatter = 2.71 ± 0.06fm RMShalo=4.00 ± 0.28fm [1] I.Tanihata et al., Phys.Lett.B206(1988)592. [2] M. Zahar et al., Phys. Rev. C48 (1993) R1484. [3] E.Liatard et al., Europhys.Lett. 13 (1990)401. [4] S. Ilieva, Nucl. Phys. A 875 (2012) 8. [5] R. E. Warner et al., Phys. Rev. C64 (2001) 044611.

Halo-like structure of 12Be: In ground state or excited state? proton-scattering experiments in inverse inematics revealed a low-density tail in the matter distribution, indicating a slight halolike character of the neutron distribution. 11Be (d, p) reactions, which indicats that the ground state has a small s-wave contribution (spectroscopic factor of 0.28 +0.03 -0.07), whereas the long-lived excited 0t 2 state may exhibit an extended density tail corresponding to a much larger s-wave spectroscopic factor (0.73 +0.27 -0.40)…provides some indication that the long-lived 02+ state in 12Be may have a neutron halo-like structure. Nucl. Phys. A 875 (2012) 8-28 Phys. Lett. B 682 (2010) 391 …additional information about the structure of 12Be is important. Phys. Rev. Lett. 108 (2012) 142501

三体束缚态 Efimov态 10，11，12Be分离能比较 目前Be核半径的测量结果 Sn S2n 10Be 6.8 MeV - 11Be …this nucleus is well bound…one should not expect it to be well described by the two-neutron and inert-core model when the core is 10Be. 10Be n Nucl. Phys. A 609 (1996) 43

2. Huge deformation (molecular/cluster structure) ------通过破裂反应研究12Be的集团结构 原子核分子集团结构会出现在形变壳模型框架下的超形变和巨形变的极端情况下 6He+6He, 4He+8He,t+9Li,…… an -4n- cluster configuration Excited state band Ground state band M. Freer et al., Phys. Rev. Lett. 82 (1999) 1383

3. Brief Overview of Experimental Results In the case of 12Be, no definite conclusion about the ground state structure of the nucleus can be made based on the comparison of the theoretical calculation with the experimental data.

4. Brief Overview of Study in 12Be Author References Breakdown of the shell structure (Ground state structure of 12Be) N.A. Orr and M. Freer Nucl. Phys. A 654 (1999) 710c. A. Navin et al. Phys. Rev. Lett. 85 (2000) 266. S. D. Pain et al. Phys. Rev. Lett. 96 (2006) 032502. H. Iwasaki et al. Phys. Lett. B 481 (2000) 7. R. Kanungo et al. Phys. Lett. B 682 (2010) 391. Radius of 12Be I. Tanihata et al. Phys. Lett. B 206 (1988) 592. E. Liatard et al. Europhys. Lett. 13 (1990) 401. M. Zahar et al. Phys. Rev. C 48 (1993) R1484. S. Ilieva et al. Nucl. Phys. A 875 (2012) 8. Charge radius of 12Be A. Krieger et al. Phys. Rev. Lett. 108 (2012) 142501 Clustering structure (Deformation) M. Freer et al. Phys. Rev. Lett. 82 (1999) 1383 Y. Kanada-En’yo et al. Phys. Rev. C 52 (1995) 628. Phys. Rev. C 68 (2003) 014319. T. Neff et al. Nucl. Phys. A 752 (2005) 321c. Few-body structure J.S. Al-Khalili et al. Phys. Rev. C 54 (1996) 1843. I.J. Thompson et al. Phys. Rev. C 53 (1996) 708. Efimov states A. E. A. Amorim et al. Phys. Rev. C 56 (1997) R2378

14Be 5. Studies on 14Be First observation Halo structure [15] the two-neutron separation energy (MeV) a pion double charge-exchange measurement 1.12 ± 0.16[16] a time-of-flight experiment 1.48 ± 0.14[17] the weighted average of them 1.34 ± 0.11 Halo structure Discovery interaction cross section（ I ） [19] Fragments’s momentum distributions [20] Confirmation Total reaction cross section （ R ） [21] [22] Elastic Scattering (Measurement in inverse kinematics) (four momentum transfer) [28] Halo configuration: Core(12Be)+2n accepted Core(10Be)+4n Cannot be excluded tetraneutron in coincidence with 10Be [27] Experimental results of the amount of mixing[30,31,32,33] controversial Theoretical calculation Wave functions of the valence neutrons ν1s1/2,ν0d5/2 [23,24,25,29] Clustering effects [23,26] References: [15] J. D. Bowman et al., Phys. Rev. Lett. 31 (1973) 614. [16] J. M. Wouters, et al., Z. Phys. A 331 (1988) 229. [17] G. Audi and A. H. Wapstra, Nucl. Phys. A565 (1993) p1. and p66. [19] I.Tanihata et al., Phys. Lett. B 206 (1988) 592. [20] M. Zahar, et al., Phys. Rev. 48 (1993) R1484. [21] E.Liatard et al., Europhys.Lett. 13(1990)401 [22] T.Suzuki et al., Nucl.Phys. A658(1999)313 [23] Y.Kanada-Eu’yo et al., Phys.Rev.C52(1995)628 [24] J.S.Al-Khalili et al., Phys.Rev. C54(1996)1843 14Be [25] I.J.Thompson and M.V.Zhukov, Phys.Rev. C53(1996)708 [26] T.Neff, H.Feldmeier and R.Roth, Nucl.Phys.A752(2005)321c [27] F. M. Marqués et al., Phys.Rev. C65(2000)044006 [28] S. Ilieva et al. Nucl. Phys. A 875 (2012) 8. [29] Zhongzhou Ren et al., Phys. Lett. B351 (1995) 11; J. Phys. G20 (1994) 1185; Phys. Lett. B 252 (1990) 311 [30] P.Deseuvemont, Phys.Rev. C52(1995)704 [31] M.Labiche et al., Phys.Rev. C60(1999)027303; M.Labiche et al., Phys. Rev. Lett. 86 (2001) 600; [32] T.Sugimoto et al., Jour.Phys. C849(2006)43 [33] N.A.Orr and M. Freer, Nucl.Phys.A654(1999)710c

6. 14Be Motivations 12Be n 作为14Be的”core”的12Be的所具有的结构与自由的12Be不同. ”Four neutron halo”的结构还没有排除. 10Be+4n(tetraneutron)? Until now, no final conclusions about the structure of 14Be can be made on the basis of the existed experimental data.

二、 实验设想 1. 实验方法 R = sI + sinela I = -1/t ln(N2/N1) N1(AZ) N2(AZ) Carbon target With thickness t R = sI + sinela 透射法测量截面的原理图 （2）靶后出射子散射出靶后探测器（0.1%） （1）截面误差和靶前、后探测器中的反应 事件和探测器测量效率的稳定性的关系

interaction cross section (I) total reaction cross section (R) 2. 实验能区的选取 高能(800 A MeV) interaction cross section (I) 中（低）能 total reaction cross section (R) includes only those reactions which destroy the projectile excludes target reactions which leave the projectile intact. R more sensitive to the nuclear matter distribution in the tail region of the nucleus [R. E. Warner et al., Phys. Rev. C 52, R1166(1995). (8B)] Nuclear and Coulomb effects (T. Kobayashi et al., Phys. Lett. B 232, 51,1989) also are more easily separated at low energies. R measurements now seem to be a necessary complement to the high-energy I data.

同位素靶材料 厚度 3. 实验靶的选取 C、Al靶较以往的Si、Cu、Pb靶轻，与12Be的碰撞截面更有利于反映12Be的核外层结构 次级靶 (透射率R:90%) 12C 4-14 mm 27Al CH2 5-20 mm C、Al靶较以往的Si、Cu、Pb靶轻，与12Be的碰撞截面更有利于反映12Be的核外层结构 Glauber模型的计算需要输入靶核的物质密度分布，而C、Al核物质密度分布较为清楚

（考虑到靶前加光阑，流强按模拟 值1/10算，统计量按2.5*105计） 机时估算 主束能量、 流强 次级束 能量 (MeV/u) LISE++模 拟流强 (pps) 靶 束流时间（小时） （考虑到靶前加光阑，流强按模拟 值1/10算，统计量按2.5*105计） 80 MeV/u 100 enA 12Be 62.7 3940 C、Al、CH2 0.5 (=2.5*105/3940*10*3/3600) 42.4 1910 1.1 (=2.5*105/1910*10*3/3600) 24.0 789 空 0.9 (=2.5*105/789*10/3600) 14Be 56.4 93 22 (=2.5*105/93*10*3/3600) 40.3 49 43 (=2.5*105/49*10*3/3600) 24 29 (=2.5*105/24*10/3600) 12C 53.1 1650 1.3 (=2.5*105/1650*10/3600) 25.2 2070 0.3 (=2.5*105/2070*10/3600) 实验预期精度2-3%，统计误差应小于0.2%（与靶厚造成的系统误差相当），一个能量点至少需要250，000个事件。 根据上表的结果，实验内容需要约100小时束流时间。另外，调节次级束12Be、12C所需要时间共15h*3=45小时，调节束流能量5次所需要时间8h*5=40小时。再考虑到换靶及抽真空的时间，我们一共需要机时200小时。

4. 实验探测器情况 探测器布局示意图 位置 需要探测器 探测器尺寸与厚度 作用 来源 靶前 PPAC -- 束流监测 RIBLL提供 E SSD 靶前粒子鉴别 TOF (T1, T2) 靶后 3块E SSD 高能端：64×64 mm2×1500 m 1块 低能端：50×50 mm2×300 m 2块 靶后粒子鉴别 北大叶沿林老师课题组提供 CsI(Tl) 76.2 mm×30 mm 上海应物所（制作中）

总结 12，14Be核结构有丰富的研究内容。 精确测量12，14Be的总反应截面，进而提取其核物质密度分布，可以帮助解决其核结构方面的许多问题。 希望得到RIBLL的支持，明年能尽快安排机时完成我们的实验。如果今年有额外的机时我们也非常希望能在今年做。