精确测定中低能区弱束缚核精确测定中低能区弱束缚核 12,1412,14Be + Be + 1212C, C, 2727AlAl 核反应核反应总截面并提取其核物质密度分布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

一、一、 1212 ，， 1414BeBe 的的研究背景及研究背景及现状现状

☆ large neutron asymmetry

( )N Z

A

12

140.33 ( Be)0.43 ( Be)

① Halo/skin like structure② Breakdown of the N =8 Shell Closure (Ground state structure)③ Huge deformation (cluster structure)④ Few-body system⑤ ……

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

12Be

1. Non-Borromean neutron halo candidate

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

10Be

n n

SAMBA type nucleus?

Evidence suggest the halo structure of 12Be

n

Spectroscopic factor |12Beg.s.:0+> =32% (1s1p)8+68%(1s1p) 6(2s,1d) 2

Confirms that the N=8 gap has collapsed

(1) 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:① Navin et al., Phys. Rev. Lett. 85, 266 (2000). 9Be(12Be, 11Be +n) ② S.D.Pain et al., Phys. Rev. Lett. 96,032502 (2006). 12C(12Be, 11Be +n)

(Toshio Suzuki et al., Phys. Rev. C 56(1997)847)

)1()0( ..12

..12 sg

transitionGTsg BBe Log ft = 3.834 ± 0.017

(F. Ajzenberg-Selove, Nucl. Phys. A506 (1990) 1)

(2) Effects on to GT transitions

35%

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

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

Configuration

12Be基态核物质密度分布的实验研究

Lab. Halo Experimental methods Brief description

LBLMSU

GANILNo

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] =92.22.7MeV/c

Halo structure? Naïve, not meaningful.56.8,64.8MeV/nucleon

Neutron-removal cross sections, -

xn[5]RMS

matter = 2.85±0.07 fm

060MeV/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)

GSIHalo-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)+2nRMS

matter = 2.71 ± 0.06fm

RMShalo=4.00 ± 0.28fm

几家典型的实验

[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.

6

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

Halo-like structure of 12Be: In ground state or excited state?

Phys. Lett. B 682 (2010) 391

…additional information about the structure of 12Be is important.Phys. Rev. Lett. 108 (2012) 142501

…additional information about the structure of 12Be is important.Phys. Rev. Lett. 108 (2012) 142501

10 ， 11 ， 12Be 分离能比较Sn S2n

10Be 6.8 MeV -11Be 0.504 MeV -12Be 3.169 MeV 3.76 MeV

10Be

n

n

10Be

n

n

三体束缚态 Efimov态

目前 Be 核半径的测量结果

…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. 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

Excited state band

Ground state band

M. Freer et al., Phys. Rev. Lett. 82 (1999) 1383

6He+6He, 4He+8He,t+9Li,……

an -4n- cluster configuration

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.

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.

3. Brief Overview of Experimental Results

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 radiusof 12Be

A. Krieger et al. Phys. Rev. Lett. 108 (2012) 142501

Clustering structure(Deformation)

M. Freer et al. Phys. Rev. Lett. 82 (1999) 1383Y. Kanada-En’yo et al. Phys. Rev. C 52 (1995) 628.

Y. Kanada-En’yo et al. Phys. Rev. C 68 (2003) 014319.

T. Neff et al. Nucl. Phys. A 752 (2005) 321c.

Few-body structureJ.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

4. Brief Overview of Study in 12Be

5. Studies on 14Be

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

[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

14Be

Until now, no final conclusions about the structure of 14Be can be made on the basis of the existed experimental data.

6. 14Be Motivations

12Be

n

n

1. 作为 14Be 的” core” 的 12Be的所具有的结构与自由的 12Be不同 .

2. ”Four neutron halo”的结构还没有排除 .3. 10Be+4n(tetraneutron)?

二、 实验设想二、 实验设想

)/ln(1

outinRR

t

（ 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

)1(

ln1

PR

R

tout

in

I

（ 2 ）靶后出射子散射出靶后探测器（ 0.1%）

I = -1/t ln(N2/N1)N1(AZ) N2(AZ)

Carbon target With thickness t

R = I + inela

透射法测量截面的原理图透射法测量截面的原理图

1. 实验方法

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)

1. includes only those reactions which destroy the projectile

2. excludes target reactions which leave the projectile intact.

1. 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)]

2. 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 厚度次级靶

( 透射率 R:90%)

12C 4-14 mm27Al 4-14 mmCH2 5-20 mm

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

• 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

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 C 、 Al 、 CH2 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 C 、 Al 、 CH2 22 (=2.5*105/93*10*3/3600)

40.3 49 C 、 Al 、 CH2 43 (=2.5*105/49*10*3/3600)

24.0 24 空 29 (=2.5*105/24*10/3600)

12C 53.1 1650 C 、 Al 、 CH2 1.3 (=2.5*105/1650*10/3600)

25.2 2070 空 0.3 (=2.5*105/2070*10/3600) 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。

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。

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）

4. 实验探测器情况探测器布局示意图探测器布局示意图

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。