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
一、12，14Be的研究背景及现状
☆ large neutron asymmetry
( N  Z ) 0.33 (12 Be)


0.43 (14 Be)
A
① Halo/skin like structure
② Breakdown of the N =8 Shell Closure
(Ground state structure)
③ Huge deformation (cluster structure)
④ Few-body system
⑤ ……
12Be
12Be
is a key isotope in the beryllium
chain, as it is located between the oneneutron 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.
n
Phys. Lett. B 682 (2010) 391
Evidence suggest the halo structure of 12Be
(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)
n
|12Beg.s.:0+> =32% (1s1p)8+68%(1s1p) 6(2s,1d) 2
Confirms that the N=8 gap has collapsed
(2) Effects on to GT transitions
angular momentum
motion for halo particles ,
(2s - intruder level) and
few-body dynamics)。尽
35%
12
transition
Be(0g.s. ) GT


12 B(1g.s. )
(Toshio Suzuki et al., Phys. Rev. C
56(1997)847)
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
Log ft = 3.834 ± 0.017
(F. Ajzenberg-Selove, Nucl. Phys.
A506 (1990) 1)
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
几家典型的实验
Lab.
LBL
MSU
GANIL
GSI
Halo
No
Experimental methods
Brief description
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]
Halo structure? Naïve, not meaningful.
56.8,64.8MeV/nucleon
=92.22.7MeV/c
Neutron-removal cross sections, -xn[5] 060MeV/nucleon
RMSmatter = 2.85±0.07 fm
Halolike
Total reaction cross section （ R ）[3]
RMSmatter = 2.622 ±0.073 fm
RMSneutron = 2.75 ±0.11 fm
Elastic Scattering
(four momentum transfer) [4]
Halo configuration:Core(10Be)+2n
RMSmatter = 2.71 ± 0.06fm
RMShalo=4.00 ± 0.28fm
25-65MeV/nucleon, Kox, S. et al.,Phys. Rev. C35, 1678 (1987)
 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.
[1] I.Tanihata et al., Phys.Lett.B206(1988)592.
[4] S. Ilieva, Nucl. Phys. A 875 (2012) 8.
[2] M. Zahar et al., Phys. Rev. C48 (1993) R1484. [5] R. E. Warner et al., Phys. Rev. C64 (2001) 044611.
[3] E.Liatard et al., Europhys.Lett. 13 (1990)401.
6
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.
Nucl. Phys. A 875 (2012) 8-28
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.
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
目前Be核半径的测量结果
10，11，12Be分离能比较
10Be
Sn
6.8 MeV
S2n
-
11Be
0.504 MeV
12Be 3.169 MeV 3.76 MeV
n
10Be
n
n
10Be
n
…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
an -4n- cluster configuration
6He+6He, 4He+8He,t+9Li,……
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
Breakdown of the shell
structure
(Ground state
structure of 12Be)
Radius of 12Be
Charge radius
of 12Be
Clustering structure
(Deformation)
Few-body structure
Efimov states
Author
References
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.
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.
A. Krieger et al.
Phys. Rev. Lett. 108 (2012) 142501
M. Freer et al.
Phys. Rev. Lett. 82 (1999) 1383
Y. 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.
J.S. Al-Khalili et al.
Phys. Rev. C 54 (1996) 1843.
I.J. Thompson et al.
Phys. Rev. C 53 (1996) 708.
A. E. A. Amorim et al.
Phys. Rev. C 56 (1997) R2378
5. Studies on 14Be
First observation
[15]
1.12 ± 0.16[16]
1.48 ± 0.14[17]
1.34 ± 0.11
[19]
[20]
[21]
[22]
a pion double charge-exchange measurement
a time-of-flight experiment
the weighted average of them
interaction cross section（ I ）
Fragments’s momentum distributions
Total reaction cross section （ R ）
interaction cross section（ I ）
Elastic Scattering (Measurement in inverse kinematics)
(four momentum transfer)
the two-neutron separation energy
(MeV)
Discovery
Halo
structure
Confirmation
Halo configuration:
tetraneutron in coincidence with 10Be
Experimental results of the amount of mixing[30,31,32,33]
Wave functions of the valence neutrons ν1s1/2,ν0d5/2
Theoretical
calculation
Clustering effects
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
[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
(1988) 592.
[28]
Core(12Be)+2n accepted
Core(10Be)+4n
Cannot be excluded
[27]
controversial
[23,24,25,29]
[23,26]
[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.
14Be
[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
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)?
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
Carbon target
With thickness t
N1(AZ)
透射法测量截面的原理图
N2(AZ)
（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
   ln( R / R )
t
in
out
R = I + inela
I = -1/t ln(N2/N1)
（2）靶后出射子散射出靶后探
测器（0.1%）

R
1 
   ln 
t  R (1  P) 
in
I
out
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.
3. 实验靶的选取
同位素靶材料
次级靶
(透射率R:90%)
12C
厚度
27Al
4-14 mm
4-14 mm
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
机时估算
能量
主束能量、
次级束
流强
(MeV/u)
12Be
80 MeV/u
100 enA
14Be
12C
LISE++模
拟流强
(pps)
束流时间（小时）
靶
（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）
62.7
3940
C、Al、CH2 0.5 (=2.5*105/3940*10*3/3600)
42.4
1910
24.0
56.4
40.3
24.0
789
93
49
24
C、Al、CH2 1.1
0.9
空
C、Al、CH2 22
C、Al、CH2 43
29
空
53.1
1650
25.2
2070
(=2.5*105/1910*10*3/3600)
(=2.5*105/789*10/3600)
(=2.5*105/93*10*3/3600)
(=2.5*105/49*10*3/3600)
(=2.5*105/24*10/3600)
C、Al、CH2 1.3 (=2.5*105/1650*10/3600)
0.3 (=2.5*105/2070*10/3600)
空
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
靶前
需要探测器
探测器尺寸与厚度
作用
PPAC
--
束流监测
E SSD
--
TOF (T1, T2)
--
靶前粒子
鉴别
3块E SSD
靶后
CsI(Tl)
来源
RIBLL提供
高能端：64×64 mm2×1500 m 1块
北大叶沿林老
低能端：50×50 mm2×300 m
2块 靶后粒子 师课题组提供
鉴别
上海应物所
76.2 mm×30 mm
（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。