中国科学技术大学：《正电子物理》课程教学讲稿（正电子在材料科学中的应用）04 正电子技术及其发展（2/2）

正电子概况IV 正电子技术及其发展 叶邦角 N P 核固体物理研究室 Laboratory of Nuclear Solid State Physics,USTC

ℷ⬉ᄤᡔᴃঞ݊থሩ ৊䙺㾦 Ḍ೎ԧ⠽⧚ⷨおᅸ L a b o r a t o r y o f N u c l e a r S o l i d S t a t e P h y s i c s , U S T C ℷ⬉ᄤὖމ I V

5正电子角关联

5 .ℷ⬉ᄤ㾦݇㘨

e+e-湮没产生的2y的夹角与180°有一微小的 偏离。实验同时测量e+e湮没产生的2y关联信 号，可以获得电子动量分布信息，并且可进 步得到费米面形貌，研究能带结构等 。 同CDB相似，二维角关联(2D-ACAR)可以由 e+-e-湮灭的动量分布来获得电子结构的信息， 特别对单晶材料。 ny Camera 1 Camera 2

e + e -⑂≵ѻ⫳ⱘ 2 ?ⱘ།㾦Ϣ 1 8 0 e᳝ϔᖂᇣⱘ 行أ DŽᅲ偠ৠᯊ⌟䞣 e + e -⑂≵ѻ⫳ⱘ 2 ?݇㘨ֵ ো ˈৃҹ㦋ᕫ⬉ᄤࡼ䞣ߚᏗֵᙃ ৃҹ㦋ᕫ⬉ᄤࡼ䞣ߚᏗֵᙃ ˈᑊϨৃ䖯ϔ ℹᕫࠄ䌍㉇䴶ᔶ䉠 ℹᕫࠄ䌍㉇䴶ᔶ䉠 ˈⷨお㛑ᏺ㒧ᵘㄝ ⷨお㛑ᏺ㒧ᵘㄝ DŽ
ৠ C D BⳌԐ , Ѡ㓈㾦݇㘨 ˄ 2 D - A C A R ˅ৃҹ⬅ e + - e -ޤ♁ⱘࡼ䞣ߚᏗᴹ㦋ᕫ⬉ᄤ㒧ᵘⱘֵᙃ ޤ♁ⱘࡼ䞣ߚᏗᴹ㦋ᕫ⬉ᄤ㒧ᵘⱘֵᙃ ˈ ⡍߿ᇍऩ᱊ᴤ᭭ ⡍߿ᇍऩ᱊ᴤ᭭ DŽ

比之CDB技术，2D-ACAR技术具有以下两个 优点： (1)可以获得更多的信息，因为是二维探测， 故动量密度仅仅积分一次，即： N(p..P,)=Jp-7(P)dp. 而多普勒展宽技术主要是一维探测，故取的 是两次积分后的信息，即： D(p:)=可丁p'(p)dp,dp

↨ПCDBᡔᴃˈ2D-ACARᡔᴃ݋᳝ҹϟϸϾ ᡔᴃ݋᳝ҹϟϸϾ Ӭ⚍˖ N px py p dpz ( , ) = ( )
ρ2γ
˄1˅ৃҹ㦋ᕫ᳈໮ⱘֵᙃˈ಴ЎᰃѠ㓈᥶⌟ˈ ᬙࡼ䞣ᆚᑺҙҙ⿃ߚϔ⃵ˈे˖ 㗠໮᱂ࢦሩᆑᡔᴃЏ㽕ᰃϔ㓈᥶⌟ 㗠໮᱂ࢦሩᆑᡔᴃЏ㽕ᰃϔ㓈᥶⌟ˈᬙপⱘ ᰃϸ⃵⿃ߚৢⱘֵᙃ ᰃϸ⃵⿃ߚৢⱘֵᙃˈे˖ z y x D( p ) ( p)dp dp 2


= γ ρ

(2)2D-ACAR比多普勒展宽技术具有更高的分辨。 通常2D-ACAR技术具有0.5×10-3m.c量级的 分辨，而CDB的分辨为4×10-3mc。 2D-ACAR技术的主要缺点是必须有较多的计 数，因而需要较强的正电子源强并且需要较长 的测量时间，此外它经常要与寿命谱仪和多普 勒展宽技术联合使用

(2) 2D-ACAR↨໮᱂ࢦሩᆑᡔᴃ݋᳈᳝催ⱘߚ䕼DŽ 䗮ᐌ2D-ACARᡔᴃ݋᳝0.5×10-3mec䞣㑻ⱘ ߚ䕼ˈ㗠CDBⱘߚ䕼Ў4×10-3 mecDŽ 2D-ACARᡔᴃⱘЏ㽕㔎⚍ᰃᖙ乏᳝䕗໮ⱘ䅵 ᭄ˈ಴㗠䳔㽕䕗ᔎⱘℷ⬉ᄤ⑤ᔎᑊϨ䳔㽕䕗䭓 ⱘ⌟䞣ᯊ䯈ˈℸ໪ᅗ㒣ᐌ㽕Ϣᇓੑ䈅Ҿ੠໮᱂ ࢦሩᆑᡔᴃ㘨ড়Փ⫼DŽ

Principle of the Momentum Distribution Techniques The momentum components py perpendicular to the propagation direction lead to angular deviations of the collinearity of the annihilation y-rays according to moc These equations hold for small angles.Ox,y can be egistered simultaneously in both x and y directions by a coincidence measurement using position-sensitive detection of the y-quanta

The momentum components px,y perpendicular to the propagation direction lead to angular deviations Θx,y of the collinearity of the annihilation γ-rays according to These equations hold for small angles. Θx,y can be egistered simultaneously in both x and y directions by a coincidence measurement using position-sensitive detection of the γ-quanta. Principle of the Momentum Distribution Techniques

Due to the limited energy resolution of Doppler- broadening spectroscopy,electron structure investigations are carried out mainly by angular correlation of annihilation radiation. Because the momentum of valence electrons is significantly lower,the momentum distribution of annihilating electrons shifts to smaller values.This means a smaller angular deviation for ACAR and a smaller Doppler broadening for DOBS. The curve of defect-rich material is thus higher and narrower than that of defect-free reference material,when both curves are normalized to equal area

D u e t o t h e l i m i t e d e n e r g y r e s o l u t i o n o f D o p p l e r - b r o a d e n i n g s p e c t r o s c o p y, e l e c t r o n s t r u c t u r e i n v e s t i g a t i o n s a r e c a r r i e d o u t m a i n l y b y a n g u l a r c o r r e l a t i o n o f a n n i h i l a t i o n r a d i a t i o n.
B e c a u s e t h e m o m e n t u m o f v a l e n c e e l e c t r o n s i s s i g n i fi c a n t l y l o w e r, t h e m o m e n t u m d i s t r i b u t i o n o f a n n i h i l a t i n g e l e c t r o n s s h i ft s t o s m a l l e r v a l u e s. T h i s m e a n s a s m a l l e r a n g u l a r d e v i a t i o n fo r A C A R a n d a s m a l l e r D o p p l e r b r o a d e n i n g fo r D O B S.
T h e c u r v e o f d e fe c t - r i c h m a t e r i a l i s t h u s h i g h e r a n d n a r r o w e r t h a n t h a t o f d e fe c t - fr e e r e fe r e n c e m a t e r i a l, w h e n b o t h c u r v e s a r e n o r m a l i z e d t o e q u a l a r e a

ID-ACAR The first ACAR measurements in one dimension were realized with Geiger counters by Behringer and Montgomery (1942).A position-sensitive detection can be realized in the simplest way in one dimension (1D-ACAR)by the mechanical movement of a long scintillation detector (Hautojarvi and Vehanen 1979;Mijnarends 1979). The integration in one more dimension compared with (6)results in a counting rate of N(⊙)=A∫∫σ（⊙mc,P,P:)p,dp

1D-ACAR
The first ACAR measurements in one dimension were realized with Geiger counters by Behringer and Montgomery (1942). A position-sensitive detection can be realized in the simplest way in one dimension (1D-ACAR) by the mechanical movement of a long scintillation detector (Hautojärvi and Vehanen 1979; Mijnarends 1979). The integration in one more dimension compared with (6) results in a counting rate of

Magnet Sample ⊙ Slit ●e+ Slit S1 Magnet S2 Coincidence Memory The angular resolution is realized by lead slits.It can be adjusted in the range 0.2 to 5 mrad.The energy resolution of a corresponding Doppler broadening experiment would range from 0.05 to 1.3 keV.Thus,ACAR has a much better momentum resolution than the Doppler-broadening technique

The angular resolution is realized by lead slits . It can be adjusted in the range 0.2 to 5 mrad. The energy resolution of a corresponding Doppler broadening experiment would range from 0.05 to 1.3 keV. Thus, ACAR has a much better momentum resolution than the Doppler-broadening technique

2D-ACAR & 2D-detector array 2D-detector array Sample p. Coincidence 2D-Memory Coincidence counting rate N: N.(⊙，日，)=A∫o(⊙，mc,O,mc,p,)p ⑧x,y-px,y/moc Resolution:0.2~5mrad (0.05~1.2keV)

2D-ACAR Θ ￾✂✁ ✄ ￾✂✁ ✄☎