Measurement of electric polarizabilities of 3 He and 4 He

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Measurement of electric polarizabilities of 3He and 4He

范功涛 1 徐望 1 潘强岩 1 罗文 1 杨利峰 1 李永江 1 蔡晓鹭 1 徐

本基 1

林承键 2 贾会明 2 徐新星 2 吴振东 2 杨峰 2 张焕乔 2

1 中科院上海应用物理研究所2 中国原子能科学研究院

PART Ⅰ Background & Motivation

PART II Experimental details

PART III Data analysis

PART IV Extract α by Fresco

PART V Summary

第十三届全国核结构研讨会暨第九次全国“核结构与量子力学”专题讨论会 2010/07/26

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1.1 物质极化的物理图象

极化率 (polarizability) 描述了原子或分子，因感受到外电场的作用，而改变其正常子云形狀的程度。

P= αE α 为电极化率， E 是外电场， P 为感应电偶极矩。

51 10 /E N m

分子的极化 : 原子的极化 :

122 10 /E N m

原子核的极化 :

223 10 /E N m

核子的极化 :

224 10 /E N m

I Background & Motivation

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处在重核的库仑场中的轻核极化的物理过程

靶核的电激化率 =0

炮弹的电极化率 =0炮弹的电极化率 =αP

靶核的电激化率 =αT

炮弹的电极化率 =0

靶核的电激化率 =0

原子核在强外电场中同样也会被极化，感应产生的感应电偶极矩为 P= αE 。如果处在重核的库仑场中，产生的极化势为： 2 2

4

1

2pol

Z eV

R

Rmin

E~2*10 -21N/m4He

208Pb

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A

1.2 理论上研究核子或核电磁极化率的现状

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To measure electric and magnetic polarizability of nucleon through Compton quasielastic scattering of gamma from a nucleon.

To measure electric polarizability of light nucleus through elastic scattering of the nucleus from a heavy and spherical nucleus (e.g. Pb). or elastic scattering of a heavy and spherical nucleus (e.g. Pb) from the nucleus.

Total potential between two nucleus is given:

we have measured the cross section ratio

2 2

4

1( )

2coul pol coul

Z eU r V V V

R

),(

),(

),(

),(),(

refref

ref

ref E

E

E

EER

1.3 Experimental methods

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Compton scattering

PRC, 64 （ 2001 ） 025203 PRC 78, 021601(R) (2008)

Elastic scattering

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1.4 实验上研究核子或核电磁极化率的现状

A

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实验上测量电磁极化率的意义

电极化率（ α ）和磁极化率（ β ）是用于描述处于外加电场、磁场中的原子核 & 核子的基本物理量 [1] ；

精确测量原子核 & 核子的电磁极化率可以用于检验关于基本夸克和胶子以及一些核子的机制计算与模型（例如手征微扰理论等） [1][2] ；

精确测量原子核 & 核子的电磁极化率可以为理解更复杂系统提供根据[1] ；

精确测量原子核 & 核子的电磁极化率可以用于修正原子能级的精确计算 [3] ；

[1] B.E.MacGibbon et.al Phys. Rev. C 52(1995)2097

[2] J.Schmiedmayer et.al Phys. Rev. Lett 66(1991)1015

[3] K.Pachucki et.al Phys. Rev. A 75(2007)032521

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0.10

0.15

0.20

0.25

0.30

0.35

3He

E

(fm

3 )

Pachucki.2007( Electromagnetic momentum

+ dipole approximation) Leidemann.2003 ( Few-body) Rinker.1976 ( Compton scattering) Goeckner. 1991 ( Elastic scattering)

3He 电极化率数据

1.5 为什么测量 3He 和 4He 的电极化率？

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.094He

E

(fm

3 )

Pachucki.2007( Electromagnetic momentum

+ dipole approximation)Leidemann 2003 ( Few-body)Gazit. 2006( Sum rules)

Friar.1977( Compton scattering)

4He 电极化率数据

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测量 3He 和 4He 的电极化率的意义

♣ 3He 4He 是连接少体系统和更复杂系统的中介 [1] ；♣ 精确测量的 3He 4He 的电极化率可以用于修正原子能级的精确计算 [2] ；♣ 解决用不同的方法（ Elastic scattering and Compton scattering ）测量的 3He 电极化率数据不一致的问题；♣ 第一次用弹散的方法得到 4He 的电极化率；♣ 国内少有的高精度（ R(E) 的精度为 0.1% ）核物理实验；♣ 对 3He ， 4He 分别用了两个靶（ 208Pb 和 144Sm ）保证了测量的可靠性 ;♣ 为以后在ＳＬＥＧＳ上用 Compton scattering 测量他核或核子的电磁极化率打下基础。

[1] Doron Gazit et.al Phys. Rev. Lett 96(2006)112301[2] K.Pachucki et.al Phys. Rev. A 75(2007)032521

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What we have measured At low energy, the effects of strong

interactions between the two nuclei can be neglected. The cross-section therefore is approximately given by the Rutherford formula, while other deviations may arise from several sources. One of the most important of these deviations is due to electric polarization of each nucleus.

Therefore, total potential between two nucleus is given:Vtotal = Vcoul +Vpol+……,

where

. So we will measure the cross section ratio between one energy point and the referenced energy point: .

2 2

4

1

2pol

Z eV

R

2 2

coul

zZ eV

R

),(

),(

),(

),(),(

refref

ref

ref E

E

E

EER

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II Experimental details

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What we have measured

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Calibration+144Sm at 18MeV Left60o

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III Data analysis

3.1 Check our data by a simple cut method

prelim

inary re

sults

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3.2 Signal overlap and overflow correction

3He+208Pb at 8MeV Left60o

1300 2600

Ncre=T*V*Ns T: gate widthV: signal rateNs: signal counts

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(1) Get the length of the “tail” : mean*2=2572(2) Get the mean counts per channel : M ， M=848/300=2.83(3) Extract the correction: Ncre= （ mean*2-n ） *M= （ 2572-

2000 ） *2.83=1619


3.3 High-energy tails of the scattering peak correction

Ncre’=1952

A simple method for this correction

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3.4 Low-energy tails of the scattering peak correction

通过调节延长时起始点的位置，比较“延长”部分加上 C 谱的计数和实际谱的计数。并作 Χ2 。以此确定延长时起始点的位置。

C 谱延伸部分比较


A simple method for this correction

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3.5 Check the corrections by R(60o/30o) and R(140o/165o) 4He+208Pb

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3.6 Other corrections we will consider

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4.1 About Fresco

IV Extract the polarizabilitis by Fresco

2 2 2 2

4

1( )

2coul pol

zZ e Z eU r V V

r r

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4.2 Simulate the possible situation of our experimentE(MeV) ( 140, 60)Dvi % (140, 30)Dvi %(165, 60)Dvi % (165, 30)Dvi %8. 00 0. 0027 0. 0028 0. 0082 0. 00698. 50 0. 0028 0. 0016 0. 0081 0. 00519. 00 0. 0027 0. 0025 0. 0082 0. 00639. 50 0. 0027 0. 0022 0. 0082 0. 007210. 00 0. 0027 0. 0021 0. 0082 0. 006910. 50 0. 0029 0. 0020 0. 0082 0. 006811. 00 0. 0030 0. 0023 0. 0082 0. 007111. 50 0. 0028 0. 0023 0. 0082 0. 007112. 00 0. 0029 0. 0034 0. 0082 0. 008012. 50 0. 0032 0. 0026 0. 0083 0. 007913. 00 0. 0033 0. 0011 0. 0084 0. 006513. 50 0. 0036 0. 0017 0. 0083 0. 006714. 00 0. 0043 0. 0035 0. 0083 0. 008414. 50 0. 0054 0. 0029 0. 0087 0. 008415. 00 0. 0069 0. 0042 0. 0094 0. 009215. 50 0. 0100 0. 0084 0. 0104 0. 011716. 00 0. 0149 0. 0131 0. 0121 0. 013916. 50 0. 0223 0. 0196 0. 0153 0. 017117. 00 0. 0338 0. 0298 0. 0207 0. 022417. 50 0. 0505 0. 0453 0. 0290 0. 030318. 00 0. 0824 0. 0661 0. 0406 0. 041019. 00 0. 1734 0. 1356 0. 0754 0. 077320. 00 0. 2863 0. 2406 0. 1268 0. 1288

The situation we considered ：A: Axes of the detectors deviated 5o B: Beam pass though the collision point but deviated 5o C: Beam deviated collision point 1mmD: Detectors deviated 2.5o

Total deviation ：

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4.3 Target polarization effect and other effect we should consider

2 22

4

1( )

2P T T P

Pol

Z ZU r e

r

Other effect we should consider A: Inelastic scatteringB: Existence of nuclear reactionsC: Several other effects includes atomic screening, vacuum polarization and relativistic corrections

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4.4 Try to extract the polarizability by Fresco

prelim

inary re

sults

prelim

inary re

sults

prelim

inary re

sults

prelim

inary re

sults

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Some improvement should be considered

数据分析方面 : A: 扣除 12C 衬底的影响； B: 靶内能损的影响； C: RUN by RUN 检查 cut ； D: 做相应的模拟； E: 等等 ;

理论方面 : A: 仔细检查修改后的 Fresco 程序； B: 研究其他反应道的影响，如散射过程中 208Pb 被激发到 3- 态； 3He+208Pb-> d+209Bi 等； C: 研究其他效应的影响，如： atomic screening, vacuum polarization and relativistic corrections ； D: 独立用 ECIS 提取电极化率以检查用 Fresco 提取的结果 ; E: 等等 .

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In this work, using the method-the light nucleus scattered by the heavy nucleus at energies below the Coulomb barrier, we precisely and systematically measured the electric polarizabilities of 3He and 4He in Aug.2008 and Sep.2008 on HI-13 tandem accelerator in China Institute of Atomic Energy. We hope we can solve the problem of inconsistency among the results of the 3He’s electric polarizability and extract the 4He’s electric polarizability by our experiment. Detail analyses are still in progress.

V Summary

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I would like to thank Prof Wang Xu, Dr Wen Luo, Prof Qiang-yan Pan, DrYong-jiang Li and other fellows of our group for their help during the data analysis. I also would like to thank Prof Cheng-jian Lin, Prof Huan-qiao Zhang,Xin-xing Xu, Huimin Jia, Fei Jia and Feng Yang of China Institute of Atomic Energy for their help during the experiment.

Thank you ！

Measurement of electric polarizabilities of 3 He and 4 He

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