Intense source of positron using channeling effect in crystals

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Submitted on 20 Jun 2012

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Intense source of positron using channeling effect in

crystals

Chenghai Xu

To cite this version:

Chenghai Xu. Intense source of positron using channeling effect in crystals. Accelerator Physics [physics.acc-ph]. Université Paris Sud - Paris XI, 2012. English. �tel-00710353�

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*QMbB/2` M 2H2+i`QM rBi? p2HQ+Biv Q7 v ∼ c TbbBM;  Mm+H2mbX 6`QK i?2 `2bi 7`K2 Q7 BM+B/2Mi 2H2+i`QM- i?2 Mm+H2mb KQp2b iQr`/b i?2 2H2+i`QM rBi? p2HQ+Biv Q7 vX h?2 T2F 2H2+i`B+ }2H/ E Q7 Mm+H2mb Bb +QMi`+i2/ BM i?2 /B`2+iBQM Q7 KQiBQM- i?2 bbQ+Bi2/ K;M2iB+ }2H/ B Bb T2`T2M/B+mH` iQ E M/ ?b i?2 bK2 K;MBim/2 b

E #2+mb2 Q7 GQ`2Mix i`Mb7Q`KX Ai HQQFb HBF2  THM2 2H2+i`QK;M2iB+ rp2 r?B+?

`2T`2b2Mi i?2 pB`imH T?QiQMb M/ KQpBM; iQr`/ i?2 2H2+i`QMX h?2 pB`imH T?QiQMb bmz2` *QKTiQM b+ii2`BM; #v i?2 BM+B/2Mi 2@X h?2 b+ii2`2/ [mMi TT2`b b #`2Kbbi`?HmM; 2KBii2/ #v i?2 BM+B/2Mi 2H2+i`QM r?2M pB2r2/ 7`QK i?2 H#Q`iQ`v 7`K2X

bbmKBM; i?i i?2 /BbiM+2 #2ir22M i?2 T`BK`v T`iB+H2 M/ i?2 Mm+H2B Bb H`;2` i?M i?2 Mm+H2` `/Bmb- i?2 Mm+H2mb +M #2 i`2i2/ b  TQBMi +?`;2X avK#QH rBi? bi2`BbF BM/B+i2b Bi Bb  [mMiBiv BM 2H2+i`QM 7`K2X

h?2 2H2+i`B+ }2H/ Q7 i?2 Mm+H2B BM i?2 H#Q`iQ`v 7`K2 Bb

E_⊥ = Ze

b2 UkXRV

r?2`2 b Bb i?2 BKT+i T`K2i2`- Z Bb i?2 iQKB+ MmK#2` M/ bvK#QH ⊥ K2Mb i?2 [mMiBiv Bb T2`T2M/B+mH` iQ vX h`Mb72` iQ 2H2+i`QM 7`K2,

E_⊥∗ = E_⊥γ, Hϕ∗ = E⊥βγ UkXkV

H∗

ϕ Bb i?2 K;M2iB+ }2H/ BM i?2 /B`2+iBQM T2`T2M/B+mH` iQ v M/ E∗X AM i?2

`2HiBpBbiB+ +QM/BiBQM- β ∼ 1- bQ E∗

⊥= Hϕ∗- r2 ?p2  THM2 rp2X h?2 2H2+i`QK;@

M2iB+ }2H/ BM 2H2+i`QM 7`K2 Bb +QM+2Mi`i2/ BM i?2 iBK2 BMi2`pH, tef f = b/γcX h?2

/2T2M/2M+2 Q7 E M/ H QM iBK2 +M #2 TT`QtBKi2/ #v :mbbBM /Bbi`B#miBQM rBi?  rB/i? b/γcX

E∗ = H∗ = γZe

b2 e

−c2_γ2_t2_/2b2

UkXjV h?2 6Qm`B2` i`Mb7Q`K Bb HbQ  :mbbBM rBi?  rB/i? γc/b- r2 +M HbQ TT`QtB@ Ki2 Bi #v  `2+iM;H2 rBi?  rB/i? γc/bX

h?2 2H2+i`QK;M2iB+ 2M2`;v T2` mMBi pQHmK2 Bb ;Bp2M #v

E∗2+ H∗2

8π #

Z2e2γ2

b4 UkX9V

h?2 T?QiQM +HQm/ TM+F2 ?b  iBK2 rB/i? Q7 b/γc r?B+? +Q``2bTQM/b iQ  H2M;i? Q7 b/γ- bQ i?2 2M2`;v T2` mMBi `2 Bb Z2e2γ2 b4 b γ # Z2e2γ b3 UkX8V

b bB/ #27Q`2- i?2 6Qm`B2` i`Mb7Q`K Bb  :mbbBM rBi?  rB/i? γc/b- +M #2 TT`QtBKi2/ #v  `2+iM;H2 Q7 rB/i? γc/b M/ ?b M mTT2` HBKBi 7`2[m2M+v

ν_max∗ = γc/bX lM/2` bm+? M bbmKTiBQM i?2 2M2`;v T2` mMBi `2 ;Bp2M #v 1[X

UkX8V Bb /Bbi`B#mi2/ Qp2` i?2 `2+iM;H2 7`2[m2M+v bT2+i`mKX aQ i?2 iQiH MmK#2` Q7 T?QiQMb +Q``2bTQM/BM; iQ i?2 2M2`;v T2` mMBi `2 i  /BbiM+2 b +M #2 ;Bp2M #v

Z2e2γ b3 1 hν∗ max = Z 2_e2_γ b3 b hγc UkXeV Re

t -4 -2 0 2 4 0 0.2 0.4 0.6 0.8 1 2 Ze/b γ c γ b/ E (a) ν -4 -2 0 2 4 0 0.2 0.4 0.6 0.8 1 Ze/bc c/b γ c/b γ = max ν (b)

6B;m`2 kXk, 1H2+i`QK;M2iB+ TmHb2 BM i?2 2H2+i`QM 7`K2 M/ Bib 6Qm`B2` i`Mb7Q`K, UV TmHb2- U#V bT2+i`mK

aQ i?2 MmK#2` Q7 T?QiQMb rBi?  7`2[m2M+v ν∗BM i?2 BMi2`pH ∆ν∗M/ i  /BbiM+2

b Bb T`QTQ`iBQMH iQ ∆ν∗/ν∗ Z2e2γ b3 b γc ∆ν∗ hν∗ UkXdV h?Bb 2[miBQM Bb pHB/ QMHv r?2M ∆ν∗ < γc/bX h?2 K2M MmK#2` Q7 b+ii2`2/ T?QiQMb Q7 7`2[m2M+v ν i  /BbiM+2 b Bb

σT × UT?QiQM /2MbBiv T2` `2 rBi? 7`2[m2M+v ν∗V =

Z2e2 b2_hc

∆ν∗

ν∗ σT UkX3V

r?2`2 σT Bb i?2 +`Qbb b2+iBQM Q7 *QKTiQM b+ii2`BM;X

h?2 iQiH +`Qbb b2+iBQM T2` Mm+H2mb #2 !(ν∗_)∆ν∗ r?B+? 2[mH iQ i?2 BMi2;`H

Q7 1[X UkX3V Qp2` i?2 `2 Q7 i?2 T?QiQM +HQm/X " (ν∗)∆ν∗ = ∆ν∗ ν∗ σT Z2_e2 hc # 2πbdb b2 UkXNV = σT Z2e2 !_c ∆ν∗ ν∗ ln bmax bmin UkXRyV h?2 BMi2;`iBQM `M;2 bmax = a0/Z1/3U a0Bb i?2 "Q?` `/Bmb V- bmin = λeU*QKTiQM

2H2+i`QM rp2H2M;i? V M/ σT = 8π/3r2eX 6BMHHv i?2 7QHHQrBM; `2bmHi +M #2 ;Bp2M

r?2M `2im`M iQ H#Q`iQ`v 7`K2 M/ iF2 BMiQ ++QmMi i?2 M2;H2+i2/ MmK2`B+ 7+iQ`b " (ν)∆ν = 4 137Z 2∆ν ν r 2 eln 183 Z1/3 UkXRRV r?2`2 re Bb i?2 2H2+i`QM `/BmbX

h?2 iQiH 2M2`;v HQbi iQ T?QiQMb Q7 7`2[m2M+v ν T2` Ti? H2M;i? dx Bb

(T?QiQM 2M2`;v) × (Mm+H2B /2MbBiv) × ("(ν)∆ν) × dx UkXRkV

h?2 BMi2;`iBQM Q7 i?2 7`2[m2M+v ν ;Bp2b i?2 iQiH p2`;2 2M2`;v HQbb T2` Ti? H2M;i? dx #v BM+B/2Mi 2H2+i`QM

−$ dE_dx % rad = E4Z2 N 137r 2 eln 183 Z1/3 UkXRjV

r?2`2 E = hνmax- r?B+? Bb 2H2+i`QM 2M2`;v- L Bb Mm+H2B /2MbBivX 6`QK 1[X UkXRjV

Bi +M #2 b22M i?2 `/BiBQM HQbb Bb T`QTQ`iBQMH iQ i?2 BM+B/2Mi 2M2`;v M/ i?2 b[m`2 Q7 iQKB+ MmK#2`X aQ BM Q`/2` iQ ;2i KQ`2 T?QiQMb Bi M22/b iQ BM+`2b2 i?2 BM+B/2Mi 2M2`;v M/ mb2 ?B;? iQKB+ MmK#2` Ki2`BHX

.2}M2 `/BiBQM H2M;i? X0 1 X0 = 4 N 137Z 2<sub>r</sub>2 eln&183Z−1/3 ' UkXR9V aQ i?2 `/BiBQM HQbb 2pQHmiBQM Bb

E = E0e−t UkXR8V

r?2`2 t = x/X0X h?2 1[X UkXR8V K2Mb i?2 `/BiBQM HQbb Bb i?2 bK2 7Q` HH

Ki2`BH B7 BM i2`Kb Q7 `/BiBQM H2M;i?X

>Qr2p2`- i?2 #Qp2 +H+mHiBQM /Q2b MQi +QMbB/2` i?2 2z2+i Q7 iQKB+ 2H2+i`QMb QM i?2 Mm+H2B- b+`22M 2z2+iX a+`22M 2z2+i Bb M BKTQ`iMi 7+iQ` BM #`2Kbbi`?HmM; r?2`2 i?2 Mm+H2B 2H2+i`B+ }2H/ Bb b+`22M2/ #v iQKB+ 2H2+i`QMb- r?B+? +M `2/m+2 i?2 BMi2`+iBQM 7Q`+2 M/ Bb MQi M2;HB;B#H2 BM ?B;? 2M2`;v `2;BQMX h?2 b+`22M 2z2+i +M #2 /2b+`B#2/ b #2HQr(R8- Rd), ξ= 100mec 2 U µ 1 − µZ −1/3 _UkXReV

r?2`2 U = E + mec2 Bb i?2 iQiH 2M2`;v Q7 BM+B/2Mi 2H2+i`QM- µ = E

!

/U- E! Bb 2M2`;v Q7 2KBii2/ T?QiQMX h?2 bKHH2` ξ- i?2 ;`2i2` b+`22MBM; 2z2+iX 6Q` ?B;? BM+B/2Mi 2M2`;v r?2`2 ξ ∼ 0 r2 +M i`2i Bi b +QKTH2i2 b+`22MBM;X

AM i?2 +QKTH2i2 b+`22MBM; +b2- i?2 /Bz2`2MiBH `/BiBQM T`Q##BHBiv T2` Ti? H2M;i? dx Bb ;Bp2M #v(R8) 7Q` mec2 & U & 137mec2Z−1/3, −$ dE_dx % rad = 4Z2 N 137Ar 2 eEln ( 2E mec2 − 1 3 ) UkXRdV 7Q` U ' 137mec2Z−1/3, −$ dE_dx % rad = 4Z2 N 137Ar 2 eE ( ln(183Z−1/3) + 1 18 ) UkXR3V

6B;m`2 kXj, .Bz2`2MiBH `/BiBQM T`Q##BHBiv T2` `/BiBQM H2M;i? Q7 H2/ 7Q` 2H2+@ i`QMb Q7 p`BQmb 2M2`;v(R8)X

*QKT`BM; 1[X UkXR3V M/ 1[X UkXRjV- i?2`2 Bb  /Bz2`2M+2 Q7 QM2 7+iQ`X AMi`Q/m+2 i?2 p2`;2 7`+iBQMH 2M2`;v HQbb T2` `/BiBQM H2M;i?X

−_U1 dE_dt = −$ dE_dx % rad X0 U UkXRNV RN

r?2`2 t = x/X0X

AM +QKTH2i2 b+`22MBM; +b2- i?2 i?2 p2`;2 7`+iBQMH 2M2`;v HQbb ?b i?2 7QH@ HQrBM; pHm2,

−_U1 dE_dt = 1 + b UkXkyV

r?2`2 b = 1/[18ln(183Z−1/3)]X b bHB;?iHv /2T2M/b QM Z- iQKB+ MmK#2`X 6`QK 6B;X

kX9 Bi b?Qrb i?i i?2 7`+iBQMH 2M2`;v HQbb #v +QHHBbBQM /2+`2b2b b i?2 BM+B/2Mi 2M2`;v BM+`2b2b- #mi BM+`2b2b #v `/BiBQM HQbb b i?2 BM+B/2Mi 2M2`;v BM+`2b2bX 6Q` G2/ rBi? M BM+B/2Mi 2M2`;v Q7 #Qmi 10MeV i?2 7`+iBQMH 2M2`;v HQbb #v i?2 +QHHBbBQM Bb 2[mH iQ i?2 `/BiBQMX h?Bb /2}M2b  [mMiBiv- +`BiB+H 2M2`;vX

kXkXk avM+?`Qi`QM `/BiBQM

>B;? BMi2MbBiv TQbBi`QM bQm`+2b rBi? TQH`BxiBQM `2 M22/2/ BM 7mim`2 +QHHB/2`bX PM2 bQHmiBQM Bb iQ mb2 +B`+mH`Hv TQH`Bx2/ T?QiQMb T`Q/m+2/ BM  ?2HB+H mM/mHiQ` #v ?B;? 2M2`;v MQM@TQH`Bx2/ 2H2+i`QMbX h?Bb bvbi2K +M T`Q/m+2 H`;2 KQmMi Q7 T?QiQMb M/ ?b  HQr2` i?2`KH /2TQbBiBQM BM i?2 2@2Y +QMp2`i2` #2+mb2 i?2 2H2+i`QMb /Q MQi BKTBM;2 QM i?2 +QMp2`i2`X

6B;m`2 kX8,  KQ/2H ?2HB+H mM/mHiQ`- r?2`2 λ Bb i?2 T2`BQ/ H2M;i?- r0 i?2 BMM2`

`/Bmb Q7 i?2 +QBH-  M/ # i?2 +QBH /BK2MbBQM- M/ j i?2 +QBH +m``2Mi /2MbBivX h?2 2KTiv ǴB` bT+2Ǵ #2ir22M i?2 +QBHb Kv #2 `2TH+2/ rBi? ?B;?@T2`K2#BHBiv bi22H TQH2bX(R3)

lM/mHiQ` Bb M BMb2`iBQM /2pB+2 r?B+? +QMbBbib Q7  T2`BQ/B+ bi`m+im`2 Q7 /BTQH2 K;M2ibX h?2 biiB+ K;M2iB+ }2H/ Bb Hi2`MiBM; HQM; i?2 H2M;i? Q7 i?2 mM/mH@

iQ` rBi?  T2`BQ/ λwX >2HB+H mM/mHiQ`b `2 K/2 Q7  /Qm#H2@?2HBt@rQmM/ #B}H`

6B;m`2 kX9, 6`+iBQMH 2M2`;v HQbb #v +QHHBbBQM M/ `/BiBQM 7Q` 2H2+i`QMb BM B` M/ H2/(R8)X

+m``2Mib rBi? QTTQbBi2 /B`2+iBQM `QmM/  im#2(RN)X h?2 +m``2Mib T`Q/m+2 i`Mb@ p2`b2 T2`BQ/B+ ?2HB+H K;M2iB+ }2H/ Q7 +QMbiMi K;MBim/2X 1H2+i`QMb i`p2`bBM; i?2 T2`BQ/B+ K;M2i rBHH mM/2`;Q Qb+BHHiBQM M/ 2KBi T?QiQMbX h?2 Q`#Bi Q7 i?2

2H2+i`QMb BM i?2 ?2HB+H K;M2iB+ }2H/ B Bb  ?2HBt ?pBM; i?2 bK2 T2`BQ/ λw b

i?2 }2H/X h?2 `/Bmb Bb, b=$ λw 2πρ %2 ρ * 1 −$ λ_2πρw %2+−1/2 UkXkRV

r?2`2 ρ = γβmc2/eB- β M/ γ `2 i?2 MQ`KHBx2/ p2HQ+Biv M/ 2M2`;vX

avM+?`Qi`QM `/BiBQM rBi? +B`+mH` TQH`BxiBQM Bb 2KBii2/ BM  +QMB+H M;H2

θ _{∼ 1/γ `QmM/ i?2 2H2+i`QM KQiBQM /B`2+iBQMX 1H2+i`QMb rBi? p2`v ?B;? 2M2`;v}

M/ H`;2 MmK#2` Q7 T2`BQ/b BM i?2 mM/mHiQ` rBHH T`Q/m+2 T?QiQMb rBi?  M``Qr bT2+i`mKX h?2 rp2H2M;i? Bb λ= λw 2γ2 &1 + K 2₎' UkXkkV M/ K = λweB 2πmc UkXkjV

6Q` K << 1- i?2 Qb+BHHiBQM KTHBim/2 Q7 i?2 KQiBQM Bb bKHH M/ i?2 BM@ i2`72`2M+2 Tii2`M Q++m`b- r?B+? H2/b iQ  M``Qr 2M2`;v #M/bX A7 K >> 1-i?2 Qb+BHHiBQM KTHBim/2 Bb H`;2` M/ 1-i?2 `/BiBQM 7`QK /Bz2`2Mi T2`BQ/ Bb MQM@ +Q``2Hi2/- r?B+? H2/b iQ  #`Q/ 2M2`;v bT2+i`mKX AM i?2 b2+QM/ +b2 Bi Bb  rB;;H2`X

h?2 2M2`;v #M/rB/i? 7Q` i?2 T?QiQMb Bb ∼ 1/N M/ /2T2M/b QM i?2 M;mH` /Bp2`;2M+2 Q7 i?2 2H2+i`QM #2K r?B+? Kmbi #2 H2bb i?M,

θmax =

,

γ√N-−1 UkXk9V

6`QK 1[X UkXkkV r2 +M +H+mHi2 i?2 T2F 2M2`;v Q7 i?2 T?QiQMb,

Eγ = 4π!cγ2 λw(1 + K2) UkXk8V M/ i?2 T2F 2M2`;v Bb Q#iBM2/ r?2M K = 1 Eγ = 2π!cγ2 λw UkXkeV kk

h?2 `i2 Q7 2M2`;v HQbb #v `/BiBQM Bb Pγ = 2 3 rec (mc2₎3E 2_F2 ⊥ UkXkdV

r?2`2 F<sub>⊥</sub> = ecB M/ E Bb i?2 2M2`;v Q7 2H2+i`QMX aQ i?2 iQiH `/Bi2/ 2M2`;v Q7

M 2H2+i`QM Bb ∆W = 8 3π 2<sub>r</sub> emc2 γ2K2N λw UkXk3V h?2 MmK#2` Q7 `/Bi2/ T?QiQMb Bb, Nγ = 2 3παK 2_{&1 + K}2_{' N} UkXkNV

r?2`2 α = 1/137 Bb i?2 }M2 bi`m+im`2 MmK#2`X >2`2 r2 +M b22 i?2 vB2H/ Q7 T?QiQM /2T2M/b QM K M/ NX M 2H2+i`QM Q7 100GeV ;QBM; i?`Qm;?  100m HQM; mM/mHiQ` rBi?  T2`BQ/ Q7 1cm rBHH T`Q/m+2 250 T?QiQMb rBi? 2M2`;v Q7 5.3MeV

kXkXj *QKTiQM b+ii2`BM;

*QKTiQM 2z2+i T`Q+2bb Q++m`b r?2M i?2 T?QiQM +QHHB/2b rBi? `2bi 2H2+i`QM M/ i`Mb72`b bQK2 2M2`;v iQ 2H2+i`QMX A7 i?2 2H2+i`QM KQiBQM Bb BM `2HiBpBbiB+ `2;BQM-i?2 T?QiQM rBHH ;BM 2M2`;v M/ `2;BQM-i?2 2H2+i`QM rBHH HQQb2 2M2`;vX h?Bb Bb +HH2/ *QKTiQM #+F@b+ii2`BM; Q` BMp2`b2@*QKTiQM b+ii2`BM;X  b+?2K2 #b2/ QM i?Bb T?2MQK2MQM rb T`QTQb2/ b  bQHmiBQM 7Q` AG* TQH`Bx2/ TQbBi`QM bQm`+2(ky)X  R iQ k :2o 2H2+i`QM #2K +QHHB/2b rBi?  Hb2` #2K BM pBbB#H2 Q` BM7``2/ HB;?iX h?2 Hb2` Bb +B`+mH`Hv TQH`Bx2/- i?2M i?2 T`Q/m+2/ T?QiQMb #v *QKTiQM b+ii2`BM; `2 HbQ +B`+mH`Hv TQH`Bx2/X S?QiQMb ?p2 i2Mb Q7 MeV 2M2`;vX h?2M T?QiQMb `2 b2Mi iQ i?BM 2@2Y TB` +QMp2`i2`X 6BMHHv HQib Q7 HQM;Bim/BMHHv TQH`Bx2/ 2@2Y TB`b `2 Q#iBM2/X

AiǶb +QMp2MB2Mi iQ +H+mHi2 BM i?2 2H2+i`QM `2bi 7`K2X AM i?Bb 7`K2- i?2 Hb2` T?QiQM 2M2`;v ?b M BM+`2b2 #v γX ++Q`/BM; iQ i?2 +QMb2`piBQM Q7 2M2`;v M/ KQK2Mi- r2 ?p2 Ee = Ephoton− E ! photon+ Eo UkXjyV Pe = Pphoton− P ! photon UkXjRV

r?2`2 Ee M/ Eo +Q``2bTQM/ iQ }MH M/ BMBiBH 2M2`;B2b Q7 2H2+i`QMX Ephoton M/

E_photon! `2 i?2 BMBiBH M/ }MH T?QiQM 2M2`;B2bX Pe Bb }MH 2H2+i`QM KQK2MimKX

Pphoton M/ P

!

photon `2 BMBiBH M/ }MH T?QiQM KQK2MimKX

// i?2 +QMb2`piBQM Q7 `2HiBpBbiB+ BMp`BMi,

(E/c)2_{− P}2 = m2₀c2 UkXjkV

q2 ;2i i?2 rp2H2M;i? b?B7i,

∆λ = λe[1 − cosθ] UkXjjV

r?2`2 λeBb i?2 *QKTiQM rp2H2M;i? Q7 2H2+i`QM M/ θ Bb i?2 M;H2 Q7 i?2 b+ii2`2/

T?QiQM rBi? `2bT2+i iQ i?2 BMBiBH /B`2+iBQMX

*QKBM; #+F iQ i?2 H#Q`iQ`v 7`K2- i?2 T?QiQM 7`2[m2M+v rBHH #2 bB;MB}+MiHv BM+`2b2/ #2+mb2 Q7 .QTTH2` b?B7iX h?2 M;mH` /Bbi`B#miBQM rBHH #2 +QM+2Mi`i2/ BM  bKHH M;H2- ∼ 1/γX h?2 2M2`;v Q7 i?2 *QKTiQM T?QiQM T`Q/m+2/ BM Hb2` M/ 2H2+i`QM BMi2`+iBQM Bb,

ω2 = (1 − βcosθ1

)ω1

1 − βcosθ + [1 − cos(θ − θ1)]ω1/E

UkXj9V

r?2`2 ω1 M/ ω2 `2 2M2`;B2b 7Q` Hb2` M/ *QKTiQM T?QiQMX E Bb 2H2+i`QM 2M2`;vX

6Q` ?B;? E iFBM; i?2 }`bi TT`QtBKiBQM r2 ?p2 β = 1 − 1/2γ2X 6Q` bKHH

θ-cosθ _{= 1 − θ}2/2X *QMbB/2`BM; ?2/@QM +QHHBbBQM- +QKTH2i2 #+F b+ii2`BM;- r?2`2

θ1 = π- BMb2`i #Qp2 TT`QtBKiBQM r2 ?p2 ω2 = . 2 − 2γ12 / ω1 1 2γ2 + θ2 2 + [2 − θ2 2]ω1/E UkXj8V L2;H2+i bKHH [mMiBiB2b-ω2 = 4γ2_ω 1 1 + γ2_θ2_{+ 4γ}2_ω 1/E UkXjeV q2 +M b22 i?i i?2 *QKTiQM T?QiQM 2M2`;v Bb /2T2M/BM; QM i?2 b+ii2`2/ M;H2 M/ 2H2+i`QM 2M2`;vX 6Q` bKHH2` b+ii2`2/ M;H2 r2 ?p2 H`;2` 2M2`;v Q7 i?2 *QKTiQM T?QiQMX

6B;m`2 kXe b?Qrb i?2 2M2`;v bT2+i`mK Q7 b+ii2`2/ T?QiQMb 7`QK bBKmHiBQM #v *ALX h?2 Hb2` rp2H2M;i? Bb 1064nm- r?B+? K2Mb T?QiQM 2M2`;v 1.164eV X

1M2`;v Q7 2H2+i`QM #2K Bb 1.28GeV X *QMbB/2` /Bz2`2Mi BM+B/2Mi M;H2 0o-12o M/

90oX q2 +M b22 i?i bKHH BM+B/2Mi M;H2 +M T`Q/m+2 KQ`2 T?QiQMb rBi? H`;2

2M2`;v(kR)X

6B;m`2 kXd Bb i?2 2M2`;v bT2+i`mK Q7 T`Q/m+2/ T?QiQMbX q?2`2 i?2 BM+B/2Mi Hb2` Bb iQiHHv `B;?i +B`+mH` TQH`Bx2/X Gb2` rp2H2M;i? Bb 1064nm M/ BM+B/2Mi 2H2+i`QM 2M2`;v Bb 1.28GeV X

6B;m`2 kXe, aT2+i`mK 7Q` T`Q/m+2/ γ BM *QKTiQM #+F@b+ii2`BM;X AM+B/2Mi Hb2` rp2H2M;i?, 1064nmX AM+B/2Mi 2H2+i`QM 2M2`;v, 1.28GeV X(kR)

6B;m`2 kXd, aT2+i`mK 7Q` T`Q/m+2/ γ BM *QKTiQM #+F@b+ii2`BM; rBi? `B;?i TQH`@ Bx2/ Hb2`X AM+B/2Mi Hb2` rp2H2M;i?, 1064nmX AM+B/2Mi 2H2+i`QM 2M2`;v, 1.28GeV X _ K2Mb `B;?i TQH`BxiBQM- G K2Mb H27i TQH`BxiBQMX(kR)

kXkX9 *?MM2HBM; `/BiBQM

AM +`vbiHb- `2;mH` ``M;2K2Mi Q7 iQKb +QMbiBimi2  HiiB+2 r?B+? #2?p2b `Qm;?Hv HBF2  rB;;H2`(kk)X q?2M +?`;2/ T`iB+H2b `2 BM+B/2Mi QM  +`vbiH Q`B2Mi2/ iQ HQr@BM/2t +`vbiHHQ;`T?B+ /B`2+iBQM- i?i Bb- +HQb2 iQ HQr@BM/2t t2b M/ THM2b-+QHH2+iBp2 M/ +Q?2`2Mi 2z2+ib `2 2tT2+i2/ rBi? `2bT2+i iQ KQ`T?Qmb i`;2iX AM i?2 BMi2`+iBQM rBi? +`vbiH i?2 +?`;2/ T`iB+H2b r?B+? `2 +QKTH2i2Hv ;Qp2`M2/ #v KMv +Q``2Hi2/ +QHHBbBQMb rBi? HiiB+2 iQKb `2 +?MM2H2/X

6B;m`2 kX3, tBH +?MM2HBM; /2KQMbi`iBQM

AM tBH +?MM2HBM;- i?2 T`iB+H2b rBHH /2p2HQT  [mbB T2`BQ/B+ i`D2+iQ`v `QmM/ i?2 iQKB+ bi`BM;b r?i Bb bQ +HH2/ Ǵ`Qb2ii2 KQiBQMǴ- BM r?B+? i?2 T`iB+H2b `2 `mMMBM; M2`Hv T`HH2H iQ i?2 iQKB+ bi`BM; BM z /B`2+iBQM mM/2` i?2 }`bi TT`QtBKiBQM(kj)X Ai +M #2 TT`QtBKi2/ #v /Bbi`B#miBM; i?2 iQKB+ +?`;2b mMB7Q`KHv HQM; i?2 bi`BM; /B`2+iBQMX h?2 BMi2`+iBQM rBi? iQKB+ bi`BM; +M #2 i`2i2/ b i?2 KQp2K2Mi BM M p2`;2/ TQi2MiBHX

G2i ¯V (,r_⊥) #2 i?2 p2`;2/ i`Mbp2`b2 TQi2MiBH

¯ V(,r_⊥) = 1 d # ∞ −∞ dzV(,r_⊥, z). UkXjdV

r?2`2 d Bb i?2 bT+2 #2ir22M iQKb QM i?2 bi`BM;X h?2 i`Mbp2`b2

2M2`;v-ET = 1 2Ev 2 T + U (,r⊥) UkXj3V ke

r?2`2 U(,r⊥) = e,V(,r⊥)c ,r⊥ Bb  `/Bmb@p2+iQ`c vT = P⊥/E Bb i?2 M;H2 Q7 i?2

i`D2+iQ`v rBi? i?2 T`QT;iBQM tBbX

A7 ET > 0 i?2 iQKB+ bi`BM; +M MQi +Tim`2 i?2 +?`;2/ T`iB+H2b(kj)X h?Bb

/2i2`KBM2b i?2 +?MM2HBM; +QM/BiBQM ET <0- r?B+? ;Bp2b i?2 +`BiB+H M;H2

ψc =

0 2U0

E UkXjNV

r?2`2 U0 Bb i?2 /2Ti? Q7 i?2 TQi2MiBH r2HHX

Crystal Entries 92776 Mean 363 RMS 766.5 Eenergy (MeV) 0 2000 4000 6000 8000 10000 1 10 2 10 3 10 4 10 5 10 Crystal Entries 92776 Mean 363 RMS 766.5 Amorphous Entries 16630 Mean 693.8 RMS 1552 Amorphous Entries 16630 Mean 693.8 RMS 1552 Amorphous Entries 16630 Mean 693.8 RMS 1552 Crystal v.s Amouphous Crystal Amorphous

6B;m`2 kXN, S?QiQM bT2+i`mK 7`QK 2@ #2K BKTBM;BM; QM imM;bi2M +`vbiHUrBi? IRRR= /B`2+iBQMV M/ KQ`T?Qmb i`;2iX AM+B/2Mi 2M2`;v, 10GeV X AM+B/2Mi MmK@ #2`, 8yyyX h`;2i i?B+FM2bb, 1mm

AM i?2 `Qb2ii2 KQiBQM Q7 +?`;2/ T`iB+H2b- i?2 2H2+i`QMb rBHH `/Bi2X h?2 +QHH2+iBp2 M/ +Q?2`2Mi 2z2+ib rBHH TT2` #2+mb2 Q7 i?2 `2;mH` bi`m+im`2 Q7 i?2 i`;2i- KQ`2 T?QiQMb rBHH #2 2KBii2/ +QKT`2/ rBi? KQ`T?Qmb i`;2iX "2+mb2 Q7 i?2 p2`v bi`QM; }2H/b M/ p2`v b?Q`i T2`BQ/b Q7 +?MM2HBM; r?B+? T`2b2Mi  72r i?QmbM/ BMi2`@iQKB+ /BbiM+2- i?2 2KBii2/ T?QiQM ?b  7`2[m2M+v Km+? ?B;?2` i?M  MQ`KH K;M2iB+ rB;;H2` rBi? i?2 bK2 BM+B/2Mi 2H2+i`QMbX h?2 7`2[m2M+v +M #2 r`Bii2M b

ω = 2γ2∆ET UkX9yV

r?2`2 γ Bb i?2 GQ`2Mix 7+iQ`- ∆ET Bb  72r 2o r?B+? Bb i?2 i`Mbp2`b2 2M2`;v HQbb

#2ir22M +?MM2H2/ bii2bX b i?2 +?`;2/ T`iB+H2b 2M2`;v BM+`2b2- i?2 TQi2MiBH kd

r2HH Bb /22T2`- BM i?2 2H2+i`QM 7`K2- #v i?2 7+iQ` γ #2+mb2 Q7 `2HiBpBbiB+ 2z2+i r?B+? 2M+`2b2 i?2 7`2[m2M+v Q7 2KBii2/ T?QiQM(kk)X

6B;m`2 kXN b?Qrb  bT2+i`mK +QKT`BbQM Q7 `/Bi2/ T?QiQMb #2ir22M KQ`@ T?Qmb M/ +`vbiH i`;2i mM/2` i?2 bK2 i?B+FM2bbX Ai +M #2 b22M i?i i?2 vB2H/ 7Q` i?2 +`vbiH Bb ?B;?2` i?M KQ`T?Qmb rBi?  ?B;? KQmMi Q7 bQ7i T?QiQMbX h?Bb Bb #2+mb2 BM +?MM2HBM; 2z2+i- i?2 2H2+i`QM 2M+QmMi2`b  b2[m2M+2 Q7 bQ7i +QHHB@ bBQMb rBi? iQKB+ bi`BM; BM r?B+? H`;2 KQmMi Q7 bQ7i T?QiQM `2 `/Bi2/X Ai +M #2 BHHmbi`i2/ #v bvBM; i?i i?2 p2`;2 `/Bmb Q7 +m`pim`2 Q7 i?2 2H2+i`QM i`D2+iQ`v M2` M BM/BpB/mH iQK ?b  bKHH +m`pim`2 `/Bmb- r?2`2b rBi? +?MM2HBM; +QM/BiBQM BM  +`vbiH i?2 2H2+i`QM i`D2+iQ`v BM~m2M+2/ #v L Mm+H2B ?b Km+? H`;2` +m`pim`2 `/Bmb M/ b BM bvM+?`Qi`QM `/BiBQM- H`;2 `/Bmb H2/b iQ bQ7i2` T?QiQMbX q?BH2 BM i?2 KQ`T?Qmb i`;2i i?2 `M/QK ``M;2K2Mi Q7 iQKb KF2 i?2 2H2+i`QMb ?p2  ?B;? TQbbB#BHBiv Q7 2M+QmMi2`BM; BM/BpB/mH iQKb rBi?  bKHH BKT+i T`K2i2`X aQ i?2 T?QiQMb BM KQ`T?Qmb `2 KQ`2 ?`/2` i?M BM +`vbiHX

b i?2 +QHH2+iBp2 2z2+i- i?2 MmK#2` Q7 `/Bi2/ T?QiQMb Bb +QMbB/2`#Hv L iBK2b ?B;?2` rBi? `2bT2+i iQ M KQ`T?Qmb i`;2i- r?2`2 L `2T`2b2Mib i?2 MmK#2` Q7 iQKb rBi?BM Ǵ+Q?2`2Mi H2M;i?Ǵ,

lcoh=

E_{(E − ω)}

m2_ω2 UkX9RV

q?2M i?2 BM+B/2Mi M;H2 Bb Km+? ?B;?2` i?M +`BiB+H M;H2- MQi?2` T?2MQK@ 2M Kv ?TT2M, +Q?2`2Mi #`2Kbbi`?HmM;- BM r?B+? i?2 BM+B/2Mi T`iB+H2b +`Qbb `2;mH`Hv THM2b Q` bi`BM;b Q7 iQKbX "2+mb2 Q7 i?2 `2;mH` bi`m+im`2 Q7 +`vbiH-Qb+BHHiBQMb rBi? BMi2`72`2M+2 2z2+ib Q++m`Ub22 6B;X kXRyVX

kXj a+?2K2b 7Q` TQH`Bx2/ T?QiQMb

kXjXR >2HB+H mM/mHiQ` b+?2K2

6B;m`2 kXRR Bb i?2 HvQmi 7Q` i?2 ?2HB+H mM/mHiQ`X h?2 R8y :2o 2H2+i`QM KBM HBM+ #2Kb Tbb2b i?`Qm;?  HQM; ?2HB+H mM/mHiQ` iQ ;2M2`i2  KmHiB@J2o T?QiQM #2KX h?2 T?QiQM #2K BKTBM;BM; QM  i?BM K2iH i`;2i iQ ;2M2`i2 TQbBi`QMb BM M 2H2+i`QK;M2iB+ b?Qr2`X h?2 TQbBi`QMb `2 +Tim`2/- ++2H2`i2/ M/ i`Mb@ TQ`i2/ iQ i?2 .KTBM; _BM;(k9)X

h?2 ?2HB+H mM/mHiQ` 7Q` AG* Kmbi #2 bmT2`+QM/m+iBM; iQ +?B2p2 i?2 `2[mB`2/ T`K2i2`b Q7 ?B;? }2H/X h?2 lM/mHiQ` T2`BQ/ Bb 11.5mmX hrQ BMi2`H2p2/ ?2HB+H

λ

e-ψ

6B;m`2 kXRy, *Q?2`2Mi #`2Kbbi`?HmM; BM +`vbiH K2/BmKX

rBM/BM;b Q7 L#hB bT+2/ ?H7  T2`BQ/ T`i ;2M2`i2 i?2 i`Mbp2`b2 ?2HB+H }2H/ r?i Bb 0.86T X h?2 +iBp2 mM/mHiQ` H2M;i? Bb 147m HQM; r?B+? Bb +QMbiBimi2/ #v 7Q`iv@irQ 4m HQM; +`vQKQ/mH2- 2+? +`vQKm/mH2 ?b M +iBp2 H2M;i? Q7 3.5mX AMD2+iBM; M 2H2+i`QM #2K rBi? 2M2`;v Q7 150GeV rBHH T`Q/m+2 T?QiQM #2K rBi? +B`+mH` TQH`BxiBQMX h?2 }`bi ?`KQMB+ Q7 i?2 T?QiQM bT2+i`mK Bb 10MeV M/ i?2 T?QiQM #2K TQr2` Bb 131kW X

h?2 mM/mHiQ` p+mmK +?K#2` ?b  MQKBMH BMM2` /BK2i2` Q7 5.85mm M/ Bb K/2 Q7 +QTT2`X h?2 bmTT2` +QM/m+iBpBiv Q7 +QTT2` i +`vQ;2MB+ i2KT2`im`2b rBHH KBiB;i2 `2bBbiBp2 rHH 2z2+ibXh?2 Ki2`BH #2ir22M i?2 bmT2`+QM/m+iBM; rBM/BM;b Bb bQ7i K;M2iB+ B`QM r?B+? +M BM+`2b2 i?2 }2H/X 1+? +`vQKQ/mH2 +QMiBMb  HB[mB/ ?2HBmK #i?X AM@bBim +`vQ+QQH2`b `2 mb2/ iQ +?B2p2 x2`Q HB[mB/ #QBH QzX

kXjXk *QKTiQM #+F@b+ii2`BM; b+?2K2

:2o 2H2+i`QM +QHHB/2b rBi? +B`+mH`Hv TQH`Bx2/ Hb2` #2K +M T`Q/m+2 J2o T?Q@ iQMbX h?Bb Bb #b2/ QM AMp2`b2 *QKTiQM b+ii2`BM;X 6B;X kXRk b?Qrb i?2 E1E@h6 /2KQMbi`iBQMX Ai Bb +QMbBbi2/ #v i?2 BMD2+iBQM HBM+ M/ 2[mBTT2/ rBi?  T?QiQ@ +i?Q/2 _6 ;mM-  /KTBM; `BM; M/ M 2ti`+iBQM HBM2(k8)X h?2 2M2`;v Q7 2H2+i`QM

6B;m`2 kXRR, Pp2`HH HvQmi Q7 i?2 SQbBi`QM aQm`+2 mbBM; mM/mHiQ`(k9) #2K Bb 1.28GeV X h?2 +B`+mK72`2M+2 Q7 i?2 /KTBM; `BM; Bb #Qmi R9y KX

AM Q`/2` iQ BM+`2b2 i?2 Hb2` TQr2`-  Hb2` TmHb2 bi+FBM; bvbi2K rBi? i?2 QTiB+H `2bQMMi +pBiv Bb M22/2/X h?2 Hb2` Qb+BHHiQ` T`Q/m+2b Hb2` TmHb2b Q7 k3 MCfTmHb2 rBi?  `2T2iBiBQM `i2 Q7 375MHzX h?2 rp2H2M;i? Bb 1064nm M/ TmHb2 rB/i? Bb 4psX h?2 QTiB+H `2bQMMi +pBiv Bb  6#`v@S2`Qi +pBiv rBi? bT?2`B+H KB``Q`b Q7 99.6W `2~2+iBpBiv M/ 210.5mm +m`pim`2 i #Qi? 2M/bX

h?2 QTiB+H `2bQMMi +pBiv Bb /2bB;M2/ iQ bi+F TQr2` #v #Qmi i?QmbM/ iBK2b M/ iQ 7Q+mb i?2 Hb2` TmHb2b #v i?2 bT?2`B+H KB``Q`bX h?2 rBbi bBx2 Q7 i?2 Hb2` i i?2 7Q+mb TQBMi BMbB/2 i?2 +pBiv Bb #Qmi 30µmX h?2 QTiB+H `2bQMMi +pBiv 7Q` Hb2`@*QKTiQM b+ii2`BM; Bb BMbiHH2/ QM KQp#H2 i#H2 iQ KF2 bm`2 i?i i?2 Hb2` TQbBiBQM +M #2 KQp2/ rBi? `2bT2+i iQ i?2 2H2+i`QM #2KX h?2 ++m`+B2b `2 yX3 M/ 9 µm BM p2`iB+H M/ ?Q`BxQMiH /B`2+iBQMbX

h?2 2H2+i`QM #2K M/ Hb2` TmHb2b rBHH #2 bvM+?`QMBx2/ iQ +QHHB/2 rBi? M M;H2 Q7 3 /2;`22X J2o T?QiQMb rBi? +B`+mH` TQH`BxiBQM rBHH #2 T`Q/m+2/ #2+mb2 Q7 *QKTiQM #+F b+ii2`BM;X

kXjXj SQH`Bx2/ #`2Kbbi`?HmM; b+?2K2

6mim`2 ?B;? 2M2`;v 2@2Y +QHHB/2`b M22/ ?B;? HmKBMQbBiv M/ T?vbB+b +T#BHBivX >B;? HmKBMQbBiv `2[mB`2b HQr #2K 2KBiiM+2 M/ mbBM; TQH`Bx2/ #2K +M 2tTM/ i?2 T?vbB+b +T#BHBiB2bX

h?2 T`Q/m+iBQM Q7 TQH`Bx2/ 2H2+i`QMb Bb r2HH mM/2`biQQ/X  T?QiQ@2KBbbBQM BM  b2KB+QM/m+iQ` T?QiQ+i?Q/2 HBF2 b: +M T`Q/m+2 M 2H2+i`QM #2K rBi?  /2;`22 Q7 75 − 80W 7Q` HQM;Bim/BMHHv TQH`BxiBQMX >Qr2p2` i?2 T`Q/m+iBQM Q7

6B;m`2 kXRk, E1E@h6 ++2H2`iQ` +QKTH2t UHQr2` };m`2VX h?2 mTT2` };m`2 b?Qrb  K;MB}2/ pB2r Q7 TQbBiBQM BM i?2 QTiB+H `2bQMMi +pBiv M/ T?QiQM /2i2+iQ`(k8)X

BMi2Mb2 TQH`Bx2/ TQbBi`QM #2K M22/ KQ`2 bB;MB}+Mi _. v2iX

MQi?2` b+?2K2 7Q` i?2 TQH`Bx2/ T?QiQM Bb mbBM; HQr 2M2`;v TQH`Bx2/ 2H2+i`QM #2K iQ bi`BF2  i?BM K2iH i`;2i(ke)X b oXJXai`FMQp2MFQ K2MiBQM2/- r?2M +B`+mH`Hv TQH`Bx2/ T?QiQM TbbBM; i?`Qm;? i?2 +QMp2`i2`- i?2 T`Q/m+2/ TQbBi`QMb Kv /2TQH`Bx2 KBMHv /m2 iQ i?`22 2z2+ib,

RX "`2Kbbi`?HmM; 2z2+ic

kX "?#? b+ii2`BM; QM i?2 i`;2i 2H2+i`QMbc

jX JmHiBTH2 b+ii2`BM; BM i?2 *QmHQK# }2H/ Q7 Mm+H2BX

hQ HBKBi i?2 /2TQH`BxiBQM-  HQr 2M2`;v(∼ 50MeV ) 2H2+i`QM #2K rBi? HQM;Bim@

/BMH TQH`BxiBQM Bb mb2/ iQ BKTBM;2 QM i?BM i`;2i∼ 0.2X0X h?2 HQr 2M2`;v Q7 BM@

+B/2Mi T`iB+H2b M/ i?BM i`;2i i?B+FM2bb +M HBKBi i?2 /2TQH`BxiBQM Q7 TQbBi`QMbX

6B;m`2 kXRj, *B`+mH` TQH`BxiBQM 7Q` i?2 T`Q/m+2/ T?QiQMbX AM+B/2M+2, 2H2+i`QMX AM+B/2Mi 2M2`;v, 50MeV X AM+B/2Mi MmK#2`, R KBHHBQMX *QMp2`i2`, imM;bi2MX

h`;2i i?B+FM2bb, 0.2X0X G27i, JQMi2@+`HQ `2bmHibX _B;?i, MmK2`B+ `2bmHi 7`QK

SQivHBibBM(ke)X

>2`2 r2 ;Bp2 bQK2 bBKmHiBQM `2bmHib #Qmi i?Bb b+?2K2 Ub22 6B;bX kXRj M/ kXR9VX M 2H2+i`QM #2K rBi? iQiHHv HQM;Bim/BMH TQH`BxiBQM BKTBM;BM; QM 

0.2X0 i?B+FM2bb imM;bi2M KQ`T?Qmb i`;2iX h?2 BM+B/2Mi 2M2`;v Bb 50MeV r?B+?

rBHH `2/m+2 i?2 /2TQH`BxiBQM 7`QK #`2Kbbi`?HmM;X h?2 i?BM i`;2i i?B+FM2bb +M +QMi`QH i?2 b+ii2`BM; iBK2b HbQX h?2 6B;X kXRj M/ kXR9 b?Qr i?2 +B`+mH` TQH`BxiBQM 7Q` T`Q/m+2/ T?QiQMb M/ HQM;Bim/BMH TQH`BxiBQM 7Q` TQbBi`QMbX

6Q` T`Q/m+2/ TQbBi`QMb- i?2 iQiH vB2H/ Bb 0.95(Ne+_/Ne₋)- r?B+? K2Mb HQM;B@

im/BMH TQH`BxiBQM Bb 0.28X 6Q` T?QiQMb- i?2 K2M +B`+mH` TQH`BxiBQM Bb 0.15X Pm` `2bmHib ;`22 r2HH rBi? MmK2`B+ +H+mHiBQM 7`QK XS SQivHBibBMX

6B;m`2 kXR9, HQM;Bim/BMH TQH`BxiBQM 7Q` i?2 T`Q/m+2/ TQbBi`QMbX AM+B/2M+2, 2H2+@ i`QMX AM+B/2Mi 2M2`;v, 50MeV X AM+B/2Mi MmK#2`, R KBHHBQMX *QMp2`i2`, imM;bi2MX

h`;2i i?B+FM2bb, 0.2X0X G27i, JQMi2@+`HQ `2bmHibX _B;?i, MmK2`B+ `2bmHi 7`QK

SQivHBibBM(ke)X

kX9 SB` T`Q/m+iBQM

kX9XR SB` T`Q/m+iBQM BM KQ`T?Qmb K2/BmK

q?2M  T?QiQM rBi? 2MQm;? ?B;? 2M2`;v Tbb2b #v Mm+H2B- i?Bb T?QiQM Kv Ki2`B@ HBb2 BMiQ M 2@2Y TB`X h?Bb T`Q+2bb Bb +HH2/ TB` T`Q/m+iBQM- r?B+? Bb  [mMimK T?2MQK2MQM M/ /Q2b MQi ?p2  +HbbB+H /2b+`BTiBQMX

AM Q`/2` iQ /2b+`B#2 i?2 /vMKB+b Q7 `2HiBpBbiB+ 2H2+i`QM- .B`+ /2p2HQT2/ 

i?2Q`vX ++Q`/BM; iQ ?Bb i?2Q`v  7`22 2H2+i`QM ?b 2M2`;v ±1(mc2₎2_{+ p}2_c2X A7

i?2 2H2+i`QM Bb i `2bi- r2 ?p2 ±mc2X h?Bb bQHmiBQM T2`KBib M2;iBp2 pHm2bX Ai

HQQFb bi`M;2- #mi .B`+ T`2/B+i2/ i?i i?2`2 2tBbib  ivT2 Q7 T`iB+H2 rBi? i?2 bK2 T`QT2`iB2b b 2H2+i`QM 2t+2Ti BMp2`b2 +?`;2X h?2 Q#b2`piBQM Q7 TQbBi`QMU"v *XM/2`bQMV T`Qp2/ .B`+Ƕb T`2/B+iBQMX

b TQBMi2/ Qmi #v KMv mi?Q`b- r2 +M `2K`F i?i B7 M2;iBp2 2H2+i`QMb bii2b 2tBbi- i?2 SmHB 1t+HmbBQM S`BM+BTH2 `2[mB`2b i?i HH i?2 M2;iBp2 bii2b #2 }HH2/X Ai rQmH/ #2- i?2M- TQbbB#H2 iQ BK;BM2 M BM}MBi2 b2 Q7 M2;iBp2 2M2`;v 2H2+i`QMbX h?Bb b2 Bb `272``2/ b i?2 .B`+ b2X A7 M BKTBM;BM; T?QiQM Bb ;BpBM; 2MQm;? 2M2`;v iQ M 2H2K2Mi Q7 i?Bb M2;iBp2 2M2`;v b2- Bi rQmH/ #2 HHQr2/ iQ `Bb2 BMiQ i?2 TQbBiBp2 2M2`;v bii2 U6B;X kXR8VX Ai `2bmHib  ?QH2 BM i?2 M2;iBp2 2M2`;v b2X h?Bb ?QH2 +Q``2bTQM/b iQ M #b2M+2 Q7 M2;iBp2 +?`;2- ?2M+27Q`i?-Bi TT2`b b TQb?2M+27Q`i?-BiBp2Hv +?`;2/X h?Bb ?QH2 ?b i?2 bK2 Kbb b i?2 2H2+i`QM #mi rBi? TQbBiBp2 +?`;2X

"2+mb2 Q7 2M2`;v M/ KQK2MimK +QMb2`piBQM- TB` T`Q/m+iBQM +M QMHv iF2 TH+2 r?2M  T?QiQM TbbBM; i?2 2H2+i`B+ }2H/ Q7 i?2 Mm+H2BX h?2 2H2+i`QM M/

TQbBi`QM ?b `2bi 2M2`;v Q7 mec2X aQ ++Q`/BM; iQ i?2 2M2`;v +QMb2`piBQM- i?2

T?QiQM Kmbi ?p2 2M2`;v KQ`2 i?M i?2 bmK Q7 2@2Y TB`, 1MeV X

2 c e m 2 c e -m 0 ∞ + ∞ -γ γ E e+

e-6B;m`2 kXR8, 1t+BiiBQM Q7 2H2+i`QM 7`QK M2;iBp2@2M2`;v bii2 iQ TQbBiBp2@bii2 #v ?B;? 2M2`;v T?QiQM

"2i?2@>2BiH2` /2p2HQT2/ i?2 +`Qbb b2+iBQM 7Q` TB` T`Q/m+iBQM #v  p2`v ?B;? 2M2`;v T?QiQM TbbBM;  Mm+H2mb M/ iFBM; BMiQ ++QmMi i?2 b+`22MBM; 2z2+i(Rd-kd), 7Q` mec2 & E & 137mec2Z−1/3, σpair = Z2 137r 2 e $ 28 9 ln 2E mec2 − 218 27 % UkX9kV 7Q` E ' 137mec2Z−1/3, σpair = Z2 137r 2 e $ 28 9 ln 183 Z1/3 − 2 27 % UkX9jV 1[bX UkX9jV M/ UkXR3V b?Qr i?i i p2`v ?B;? 2M2`;v `2;BQM i?2 +`Qbb b2+iBQM Q7 TB` T`Q/m+iBQM Bb bBKBH` iQ #`2Kbbi`?HmM;X

h?2 TB` T`Q/m+iBQM +M #2 bBKTHv T`Q+2bb2/ #v 62`KBǶb i`2iK2Mi iQ i?2 #`2Kbbi`?HmM; Ub22 ȜkXkXRV BM r?B+?  7bi 2H2+i`QM b+ii2` i?2 pB`imH T?QiQMb Q7 Mm+H2BX *QMbB/2`  p2`v ?B;? 2M2`;v T?QiQM Tbb2b M2`  Mm+H2mbX h`Mb7Q`K iQ  M2r 7`K2 r?2`2 i?2 Mm+H2B KQp2 iQr`/ T?QiQM rBi?  p2HQ+Biv p2`v M2` c-r?2`2 i?2 Mm+H2B HQQFb HBF2  rp2 Q7 T?QiQMbX h?2 BM+B/2Mi T?QiQM BM i?Bb 7`K2 rBHH `2/m+2 Bib 7`2[m2M+vX h?2 T`Q+2bb +M #2 bBKTHv i`2i2/ b  +QHHBbBQM #2ir22M

BM+B/2M+2 rBi? pB`imH T?QiQMb, (hν + hν → e−_{+ e}+)X

6Q` p2`v ?B;? 2M2`;v T?QiQMb- i?2 +`Qbb b2+iBQM +M #2 TT`QtBKi2/ b σpair ∼ Z2 137r 2 e 28 9 ln 183 Z1/3 UkX99V

6Q` TB` T`Q/m+iBQM i?2 K2M 7`22 Ti? +M #2 /2}M2/, lp =

1 N σpair

UkX98V r?2`2 N `2T`2b2Mib i?2 Mm+H2B /2MbBivX h?2 /2+`2b2 Q7 T?QiQM #2K /2MbBiv Bb,

dn n = − dx lp UkX9eV q?B+? ;Bp2 i?2 bQHmiBQM n= n0e−x/lp UkX9dV

*QKT`BM; rBi? `/BiBQM H2M;i? 1[X UkXR9V- r2 }M/ i?i lp =

7

9X0 UkX93V

h?2 #`2Kbbi`?HmM; M/ TB` T`Q/m+iBQM `2 i?2 KBM T`Q+2bb2b 7Q`  b?Qr2` T?2MQK2MQMX h?2 b?Qr2` +M #2 BMBiBi2/ #v M 2H2+i`QM Q`  T?QiQMX "v  T?QiQM 7Q` 2tKTH2- i?2 T?QiQM /BbTT2`b M/ M 2@2Y TB` rBHH #2 +`2i2/ r?2M i?2 T?QiQM Tbb #v  Mm+H2mbX h?2 ?B;? 2M2`;v 2H2+i`QM Q` TQbBi`QM 2KBib T?QiQMb-i?2M i?2 T?QiQMb +`2i 2@2Y TB`XXX b i?2 T`Q+2bb +QMiBMm2- i?2 BM+B/2Mi 2M2`;v bQQM /BbbBTi2b KQM; i?2 b2+QM/`B2b- M/ i?2 MmK#2` Q7 b2+QM/`v T`iB+H2b BM+`2b2 [mB+FHvX b i?2 2KBii2/ T?QiQMb ?p2 MQi 2MQm;? 2M2`;v iQ +`2i2 2@2Y TB`- i?2 MmK#2` Q7 2H2+i`QM- TQbBi`QM M/ ?B;? 2M2`;v T?QiQM /2+`2b2 M/ HH i?2 2M2`;v rBHH /BbbBTi2 BM 2t+BiiBQM M/ BQMBxiBQM Q7 i?2 iQKb(R8)X

h?2 2t+i T`Q+2bb Bb p2`v +QKTH2tX >2`2 `2 bQK2 `2bmHib 7`QK JQMi2 *`HQ bBKmHiBQMX h?2 6B;X kXRe Bb i?2 iQiH vB2H/ ULmK#2` Q7 T`iB+H2b T2` BM+B/2Mi 2H2+i`QMV Q7 2H2+i`QMb M/ TQbBi`QMb BM  b?Qr2` BMBiBi2/ #v Ryyy 2H2+i`QMbX h?2 Ki2`BH Bb imM;bi2M- M/ i?2 BM+B/2Mi 2M2`;v Bb 1GeV 7Q` i?2 H27i };m`2 M/ 10GeV

target thickness (mm) 0 10 20 30 40 50 )i / N_o yield ( N 0 1 2 3 4 5 e- Energy: 1 GeV e-e+ target thickness (mm) 0 10 20 30 40 50 )i / N_o yield ( N 0 5 10 15 20 25 30 35 40 _{e- Energy: 10 GeV} e-e+

6B;m`2 kXRe, h?2 iQiH vB2H/ Q7 2H2+i`QMb M/ TQbBi`QMb BM  b?Qr2` BMBiBi2/ #v Ryyy

2H2+i`QMb Q7 2M2`;v E0- bm#biM+2 imM;bi2MX #b+Bbb, i`;2i i?B+FM2bbX P`/BMi2,

vB2H/X G27i E0 = 1GeVX _B;?i E0 = 10GeV(:2Mi9)

electron Entries 5101 Mean 25.28 RMS 46.84 Energy (MeV) 0 100 200 300 400 500 600 700 800 1 10 2 10 3 10 electron Entries 5101 Mean 25.28 RMS 46.84

Incident e- Energy: 1 GeV

positron Entries 3136 Mean 33.76 RMS 55.7 positron Entries 3136 Mean 33.76 RMS 55.7 positron Entries 3136 Mean 33.76 RMS 55.7 e+ e-electron Entries 38433 Mean 47.27 RMS 108.3 Energy (MeV) 0 1000 2000 3000 4000 5000 1 10 2 10 3 10 4 10 electron Entries 38433 Mean 47.27 RMS 108.3

Incident e- Energy: 10 GeV

positron Entries 25618 Mean 56.57 RMS 121.6 positron Entries 25618 Mean 56.57 RMS 121.6 positron Entries 25618 Mean 56.57 RMS 121.6 e+

e-6B;m`2 kXRd, h?2 bT2+i`mK Q7 2H2+i`QMb M/ TQbBi`QMb i QTiBKmK i?B+FM2bbX #@

b+Bbb, 1M2`;vX G27i, E0 = 1GeVX _B;?i E0 = 10GeV

7Q` `B;?iX Ai b?Qrb i?i i?2 2H2+i`QM vB2H/ Bb H`;2` i?M i?2 TQbBi`QM vB2H/ rBi? i?2 bK2 +QM/BiBQMX i #2;BMMBM; i?2 vB2H/ BM+`2b2b b i?2 i?B+FM2bb BM+`2b2b- i?2M 7i2`  KtBKmK Bi /2+2b2bbX h?2 QTiBKmK i?B+FM2bb Bb 12mm 7Q` H27i };m`2 M/

19mm 7Q` i?2 `B;?i };m`2X

h?2 b?Qr2` QTiBKmK TQbBiBQM +M #2 +H+mHi2/ i?2Q`2iB+HHv rBi? bQK2 T@ T`QtBKiBQM- BM r?B+? i?2 *QKTiQM 2z2+i M/ i?2 +QHHBbBQM HQbb `2 M2;H2+i2/- i?2 bvKTiQiB+ 7Q`KmHb 7Q` `/BiBQM M/ TB` T`Q/m+iBQM `2 mb2/X h?2 `2bmHib `2,

S`BK`v 2H2+i`QM Q7 2M2`;v E0(R8) TII(π)(E0,0) = 1.01 ( lnE0 ε0 − 1 ) UkX9NV S`BK`v T?QiQM Q7 2M2`;v E0 TII(γ)(E0,0) = 1.01 ( lnE0 ε0 − 1 2 ) UkX8yV

ε0 Bb i?2 +`BiB+H 2M2`;v- r?B+? Bb /2}M2/ b i?2 T`iB+H2 2M2`;v 7Q` r?B+? `/BiBQM

HQbb 2[mHb iQ i?2 BQMBxiBQM HQbbX

kX9Xk SB` T`Q/m+iBQM BM +`vbiHb i p2`v ?B;? 2M2`;v

MQi?2` TB` T`Q/m+iBQM T`Q+2bb Q++m`b i p2`v ?B;? T?QiQM 2M2`;B2b rBi?  p2`v bKHH BM+B/2M+2 M;H2 QM i?2 +`vbiH tBb- r?B+? Bb /Bz2`2Mi 7`QK i?2 +HbbB+H QM2 /2b+`B#2/ #v "2i?2@>2BiH2`X am+?  T`Q+2bb #2+QK2b BKTQ`iMi 2MQm;? i KmHiB@ :2o 2M2`;B2b M/ ?B;? +`vbiH }2H/bX h?2 i?`2b?QH/ Q7 i?2 TB` T`Q/m+iBQM #2+QK2b KQ`2 BKTQ`iMi i?M i?2 "2i?2@>2BiH2` T`2pBbBQMb- r?B+? Bb /2}M2/ #v,

ω= m

3_c4_ρd

!2_Zα UkX8RV

r?2`2 ω Bb i?2 BM+B/2Mi T?QiQM 7`2[m2M+vc ρ Bb i?2 i?2`KH pB#`iBQM KTHBim/2 c d Bb i?2 BMi2`iQKB+ /BbiM+2c ! = h/2πc h Bb i?2 SHM+F +QMbiMic Z Bb i?2 iQKB+ MmK#2` M/ α Bb i?2 }M2 bi`m+im`2 +QMbiMiX

h?Bb i?`2b?QH/ /2T2M/b QM i?2 +`vbiH bi`m+im`2 M/ KF2b Ki2`BHb rBi? H`;2 Z M/ bKHH ρ U+QQH2/ Ki2`BHbV #2+QK2b KQ`2 BMi2`2biBM;X b M

2tKTH2-i?2 imM;bi2M +`vbiH ?b  i?`2b?QH/ Q7 Rj :2o i 100◦_C M/ ky :2o i `QQK

i2KT2`im`2c r?2`2b i?2 :2`KMBmK +`vbiH ?b  i?`2b?QH/ Q7 8y :2o i 100◦_C

M/ Ryy :2o i `QQK i2KT2`im`2 (k3)X M 2tT2`BK2Mi K/2 i *1_L rBi? 

;2`KMBmK +`vbiH HB;M2/ QM Bib IRRy= tBb M/ +QQH2/ i 100◦ E +QM}`K2/

i?2 i?`2b?QH/ pHm2 M/ i?2 2M?M+2K2Mi QM TB` T`Q/m+iBQMX h?i 2M?M+2K2Mi `2T`2b2Mi2/ #Qmi QM2 Q`/2` Q7 K;MBim/2 rBi? `2bT2+i iQ "2i?2@>2BiH2` pHm2 rBi?  T?QiQM #2K Q7 R8y :2o(kN)X

kX8 AQMBxiBQM

*?`;2/ T`iB+H2b KQpBM; i?`Qm;? Kii2` HQb2 2M2`;v #v BMi2`+iBQMb rBi? iQKB+ 2H2+i`QMb- BM r?B+? i?2 iQKB+ 2H2+i`QMb rBHH +[mB`2 bQK2 2M2`;v M/ #2 `Bb2/ iQ ?B;? H2p2H bii2bX A7 i?2 }MH bii2 Bb  +QMiBMmmK H2p2H Bi Bb M BQMBxiBQM T`Q+2bb- Pi?2`rBb2 Bi Bb M 2t+BiiBQM T`Q+2bbX >2`2 ǴBQMBxiBQMǴ `272`b iQ #Qi? Q7 i?2 2`Q+bbb2bX AQMBxiBQM HQbb BM i`;2i Bb ?`K7mH- M/ Bi rBHH ?2i i?2 i`;2i M/ BM/m+2b i?2 b?Q+F rp2 r?B+? Kv /2bi`Qv i?2 i`;2iX AiǶb  F2v T`Q#H2K BM ?B;? BMi2MbBiv TQbBi`QM bQm`+2X

hQ +H+mHi2 i?2 BQMBxiBQM HQbb #v  ?2pB2` T`iB+H2 Q7 +?`;2 ze T`QT;iBM; i?`Qm;?  K2/BmK- }`bi bbmK2 i?2 BM+B/2Mi T`iB+H2b /Q MQi +?M;2 Bib KQp2K2Mi /B`2+iBQMX *QMbB/2` i?2 iQKB+ 2H2+i`QMb b 7`22 M/ i `2bi- i?2 +QHHBbBQM b HbiBM; bm+?  b?Q`i iBK2 i?i i?2 2H2+i`QM +[mB`2b M BKTmHb2 rBi?Qmi +?M;BM; Bib TQ@ bBiBQM /m`BM; i?2 +QHHBbBQM(jy)X "v i?Bb ?vTQi?2bBb i?2 2M2`;v HQbb T2` Ti? H2M;i? Bb, −dE_dx = 4πNz 2_e4 mv2ln bmax bmin UkX8kV

r?2`2 N Bb i?2 2H2+i`QM /2MbBiv- bmax Bb i?2 KtBKmK BKT+i T`K2i2` M/ bmin

Bb i?2 KBMBKmK BKT+i T`K2i2`- m M/ v +Q``2bTQM/ iQ i?2 BM+B/2Mi Kbb M/ p2HQ+BivX

A7 i?2 BM+B/2Mi T`iB+H2b `2 2H2+i`QMb- i?2 bBimiBQM Bb +QKTHB+i2/ M/ i?2 T`2pBQmb bbmKTiBQM Bb BMpHB/X h?2`2 `2 KBMHv irQ `2bQMbX h?2 }`bi QM2 Bb i?2 i`D2+iQ`v +?M;2 Q7 i?2 BM+B/2Mi 2H2+i`QM Bb MQi M2;HB;B#H2 r?2M +QHHB/2b rBi? iQKB+ 2H2+i`QMbX "2+mb2 i?2 BM+B/2Mi 2H2+i`QM rBHH +[mB`2  i`Mbp2`b2 KQK2MimK r?B+? Bb 2[mH iQ i?2 2D2+i2/ 2H2+i`QMX h?2 b2+QM/ QM2 Bb 7Q` i?2 +QHHBbBQM #2ir22M B/2MiB+H T`iB+H2b i?2 2t+?M;2 T?2MQK2M rBHH Q++m` M/ b?QmH/ #2 iF2M BMiQ ++QmMiX "2i?2 M/ b?FBM /2`Bp2/ i?2 2[miBQMb Q7 +QHHBbBQM HQbb #v 2H2+i`QMb- r?B+? ;Bp2b(jy),

6Q` MQM@`2HiBpBbiB+ 2H2+i`QM i?2 2M2`;v HQbb T2` Ti? H2M;i? dx Bb, −dE_dx = 4πe 4_N mv2 $ lnmv 2 2I − 1 2ln2 + 1 2 % UkX8jV j3

6Q` ?B;? `2HiBpBbiB+ p2HQ+BiB2b i?2 2M2`;v HQbb Q7 2H2+i`QMb Bb −dE_dx = 4πe 4_N mc2 $ lnmc 2 2I − 3 2ln&1 − β 2'1/2 − 1₂ln8 + 1 16 % UkX89V thickness (mm) 0 10 20 30 40 50

Energy deposition per mm (MeV/mm/e-)

0 5 10 15 20 25 30 35 40 10 GeV 1 GeV 6B;m`2 kXR3, 1M2`;v /2TQbBiBQM T2` KK 7Q` 2H2+i`QMb BKTBM;BM; QM KQ`T?Qmb imM;bi2M- irQ FBM/b Q7 2M2`;v `2 mb2/, 1GeV M/ 10GeV X #b+Bbb, i`;2i i?B+FM2bb UKKVX P`/BMi2, 1M2`;v /2TQbBiBQM T2` BM+B/2Mi 2@ T2` KKX

6`QK i?2 #Qp2 irQ 7Q`KmHb- BM i?2 MQM@`2HiBpBbiB+ `2;BQM i?2 BQMBxiBQM HQbb /2+`2b2b [mB+FHv b i?2 BM+B/2Mi 2M2`;v BM+`2b2bX "2+mb2 Bi Bb TT`QtBKi2Hv

T`QTQ`iBQMH iQ 1/mv2X AM `2HiBpBbiB+ +QM/BiBQM i?2 2M2`;v HQbb BM+`2b2b bHQrHv

b i?2 BM+B/2Mi 2M2`;v BM+`2b2bX h?2`2 `2 irQ bT2+ib, h?2 BM+`2b2 Q7 bmax M/

/2+`2b2 Q7 bminX h?2 }`bi Bb- BM [mMimK i?2Q`v- i?2 T2`im`#iBQM Kmbi #2 bKHH

/m`BM; i?2 T2`BQ/b b/v < τ = 1/ν r?B+? /2i2`KBM2b bmax = v/¯νX q?2`2 ¯ν Bb M

TT`QT`Bi2 p2`;2 Q7 i?2 7`2[m2M+B2b Q7 i?2 iQKX q?2M BM+B/2Mi 2H2+i`QM 2M2`;v

BM+`2b2b- i?2 KtBKmK BKT+i T`K2i2` BM+`2b2b b bmax = v/¯ν(1−β2)1/2X h?2

b2+QM/ TQBMi- BM [mMimK K2+?MB+b i?2 KBMBKmK BKT+i T`K2i2` b?QmH/ #2 H2bb i?M /2 "`Q;HB2 rp2H2M;i? Q7 T`iB+H2bX b 2M2`;v BM+`2b2b- i?2 /2 "`Q;HB2 rp2H2M;i? Q7 BM+B/2Mi T`iB+H2 /2+`2b2b- bQ i?2 KBMBKmK BKT+i T`K2i2` /2@ +`2b2bX

6B;m`2 kXR3 b?Qrb i?2 2M2`;v /2TQbBiBQM T2` BM+B/2M+2 T2` KK rBi? Ryyy 2H2+@ i`QMb BKTBM;BM; QM  imM;bi2M i`;2iX h?2 BM+B/2Mi 2M2`;v Q7 1GeV M/ 10GeV `2 +QMbB/2`2/X 6B;m`2 b?Qrb i?i- i }`bi i?2 `/BiBQM HQbb Bb /QKBMMi b T`@ iB+H2bǶ p2`;2 2M2`;v Bb ?B;?X h?2M rBi? i?B+FM2bb BM+`2b2b- i?2 p2`;2 2M2`;v

/2+`2b2b bQ i?2 +QHHBbBQM HQbb #2+QK2 /QKBMMi ;`/mHHvX >2`2 r2 +M /2}M2 i?2

+`BiB+H 2M2`;v ε0(R8), T`iB+H2b rBi? i?2 2M2`;v ε0 i?i i?2 `/BiBQM HQbb T2` `@

/BiBQM H2M;i? Bb 2[mH iQ i?2 +QHHBbBQM HQbb T2` `/BiBQM H2M;i?X ε0 Bb i?2 bQHmiBQM

Q7 i?2 7QHHQrBM; 2[miBQMX 6Q` imM;bi2M- ε0 ?b  pHm2 Q7 ∼ 8MeV X

−$ dE_dt % col = −$ dE_dt % rad UkX88V

r?2`2 t = x/X0- Bb BM i2`Kb Q7 `/BiBQM H2M;i? X0X

kXe *QmHQK# b+ii2`BM; QM +`vbiH Mm+H2B

h?2 `2HB#BHBiv Q7 i?2 +`vbiH bQm`+2b Bb #b2/ QM i?2B` HQM;@i2`K `2bBbiM+2 iQ `/BiBQM /K;2bX h?2 KBM bQm`+2 Q7 /K;2 Bb *QmHQK# b+ii2`BM; Q7 i?2 #2K QM i?2 Mm+H2B Q7 i?2 +`vbiH- r?2`2 7bi +?`;2/ T`iB+H2b Kv ?p2 2HbiB+ +QHHBbBQMb rBi? i?2 Mm+H2B Q7 i?2 +`vbiHX 6Q` i?2 Mm+H2mb rBi? +2`iBM H2p2Hb Q7 i?2 `2+QBH 2M2`;v - i?2 Hii2` Kv #2 /BbHQ/;2/ 7`QK Bib HiiB+2 bBi2 Q` +M BMBiBi2  +b+/2 Q7 /BbTH+2K2Mib KQM; i?2 M2B;?#Qm`BM; iQKbX

h?2 `2+QBH 2M2`;v i`Mb72`2/ iQ i?2 Mm+H2mb Bb r`Bi2M b,

T = Q

2

2M UkX8eV

r?2`2 Q Bb i?2 i`Mb72` KQK2MimK- M Bb i?2 Kbb Q7 i?2 Mm+H2mbX hF2 imM;bi2M

b M 2tKTH2- B7 i?2 `2+QBH 2M2`;v T Bb #Qp2 bQK2 i?`2b?QH/ Ed- #Qmi k8

2o-i?2 Mm+H2mb rBHH #2 /BbHQ/;2/ 7`QK Bib HiiB+2 bBi2(jR)X A7 T > 2Ed- i?2 /BbHQ/;2/

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r?2`2 Lc = A × 1keV - A Bb i?2 iQKB+ Kbb Q7 i?2 Mm+H2mbX

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UV h`;2i, hmM;bi2MX AM+B/2Mi 2@

0 2 4 6 8 10 12 14 0.5 1 1.5 2 2.5 3 3.5 4 Positron yield (N o /N i ) Thickness(X0) 100MeV 200MeV 300MeV 1GeV 5GeV 10GeV 10GeV 5GeV 1GeV 300MeV 200MeV 100MeV

U#V h`;2i, hmM;bi2MX AM+B/2Mi γ

0 2 4 6 8 10 12 0.5 1 1.5 2 2.5 3 3.5 4 Positron yield (N o /Ni ) Thickness(X0) 100MeV 200MeV 300MeV 1GeV 5GeV 10GeV 10GeV 5GeV 1GeV 300MeV 200MeV 100MeV

U+V h`;2i, hBiMBmKX AM+B/2Mi 2@

0 1 2 3 4 5 6 7 8 9 10 0.5 1 1.5 2 2.5 3 3.5 4 Positron yield (N o /Ni ) Thickness(X0) 100MeV 200MeV 300MeV 1GeV 5GeV 10GeV 10GeV 5GeV 1GeV 300MeV 200MeV 100MeV

U/V h`;2i, hBiMBmKX AM+B/2Mi γ

6B;m`2 jXR, hQiH vB2H/ Q7 TQbBi`QM

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0 2 4 6 8 10 12 14 16 18 20 0.5 1 1.5 2 2.5 3 3.5 4 Electron yield (N o /Ni ) Thickness(X0) 100MeV 200MeV 300MeV 1GeV 5GeV 10GeV 10GeV 5GeV 1GeV 300MeV 100MeV 200MeV

UV h`;2i, hmM;bi2MX S`Q/m+2/ T`@ iB+H2b, 2@ 0 2 4 6 8 10 12 14 16 0.5 1 1.5 2 2.5 3 3.5 4 Electron yield (N o /Ni ) Thickness(X0) 100MeV 200MeV 300MeV 1GeV 5GeV 10GeV 10GeV 5GeV 1GeV 300MeV 100MeV 200MeV

U#V h`;2i, hBiMBmKX S`Q/m+2/ T`@ iB+H2b, 2@ 0 50 100 150 200 250 300 0.5 1 1.5 2 2.5 3 3.5 4 Photon yield (N o /Ni ) Thickness(X0) 100MeV 200MeV 300MeV 1GeV 5GeV 10GeV 10GeV 5GeV 1GeV 300MeV 200MeV 100MeV

U+V h`;2i, hmM;bi2MX S`Q/m+2/ T`@ iB+H2b, γ 0 20 40 60 80 100 120 140 160 180 0.5 1 1.5 2 2.5 3 3.5 4 Photon yield (N o /Ni ) Thickness(X0) 100MeV 200MeV 300MeV 1GeV 5GeV 10GeV 10GeV 5GeV 1GeV 300MeV 100MeV 200MeV

U/V h`;2i, hBiMBmKX S`Q/m+2/ T`@ iB+H2b, γ

6B;m`2 jXk, hQiH vB2H/ Q7 2H2+i`QM M/ γX AM+B/2Mi T`iB+H2b, 2H2+i`QM

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jXy R9Xye k9XyR k9X3R 9dXRd N8Xek RjjX9k

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h?B+FM2bbUX0V RyyJ2o kyyJ2o jyyJ2o R:2o 8:2o Ry:2o

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9Xy NX3R kRXje k9X39 eyX3R RekXR9 kj9X9e

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h#H2 jXj, J2M 1M2`;v 7Q` T`Q/m+2/ TQbBi`QMbX h`;2i Ki2`BH, hmM;bi2MX AM@ +B/2M+2, γX AM+B/2Mi bBx2, kX8 KKX 1M2`;v mMBi, J2oX h`;2i i?B+FM2bb mMBi, X0

h?B+FM2bbUX0V RyyJ2o kyyJ2o jyyJ2o R:2o 8:2o Ry:2o

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kX9 kdXyd jNXe8 93X33 NjXjj kkNXe3 j88Xdj

jXy k9X98 jjXyd 9RX99 dRXN9 RekXj8 kjRX88

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9Xy k9X83 kNXkk j8Xdj 8RXe8 RykXy3 Rj8Xyd

h#H2 jX9, _Ja Q7 1M2`;v 7Q` T`Q/m+2/ TQbBi`QMbX h`;2i Ki2`BH, hmM;bi2MX AM+B/2M+2, γX AM+B/2Mi bBx2, kX8 KKX 1M2`;v mMBi, J2oX h`;2i i?B+FM2bb mMBi, X0

h?B+FM2bbUX0V RyyJ2o kyyJ2o jyyJ2o R:2o 8:2o Ry:2o

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BM+B/2M+2b `2 2H2+i`QM Q` T?QiQMX Ai b?Qrb i?i b i?2 i`;2i i?B+FM2bb BM+`2b2b i?2 K2M TQH`BxiBQM /2+`2b2b B7 Qi?2` +QM/BiBQMb `2 }t2/X h?Bb Bb #2+mb2 b i?2 i?B+FM2bb BM+`2b2b i?2 #`2Kbbi`?HmM; M/ KmHiBTH2 b+ii2`BM; T`Q+2bb2b rBHH H2/ iQ /2TQH`BxiBQMX qBi? i?2 BM+B/2Mi 2M2`;v BM+`2b2b- i?2 p2`;2 TQH`BxiBQM Q7 i?2 T`Q/m+2/ T`iB+H2b /2+`2b2bX h?Bb Bb /m2 iQ i?2 7+i i?i ?B;? 2M2`;v T`iB+H2 ?b  ?B;?2` TQbbB#BHBiv iQ 2M+QmMi2` #`2Kbbi`?HmM;X hQ +QMi`QH i?2 TQH`BxiBQM Q7 T`Q/m+2/ T`iB+H2b- r2 b?QmH/ HBKBi i?2 i`;2i i?B+FM2bb M/ mb2 HQr 2M2`;v BM+B/2M+2bX 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1 1.5 2 2.5 3 3.5 4 Electron longitu de polarization Thickness(X0) 10GeV _5GeV 1GeV 300MeV 200MeV 100MeV UV 2@ TQH`BxiBQM 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.5 1 1.5 2 2.5 3 3.5 4 Positron longitu de polarization Thickness(X0) 10GeV 5GeV 1GeV 300MeV 200MeV 100MeV U#V 2Y TQH`BxiBQM 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.5 1 1.5 2 2.5 3 3.5 4 Photon circular p olarization Thickness(X0) 10GeV 5GeV 1GeV 300MeV 200MeV 100MeV U+V γ TQH`BxiBQM 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.5 1 1.5 2 2.5 3 3.5 4 Electron longitu de polarization Thickness(X0) 10GeV 5GeV 1GeV 300MeV 200MeV <sub>100MeV</sub> U/V 2@ TQH`BxiBQM 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.5 1 1.5 2 2.5 3 3.5 4 Positron longitu de polarization Thickness(X0) 10GeV 5GeV 1GeV 100MeV 300MeV 200MeV U2V 2Y TQH`BxiBQM 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.5 1 1.5 2 2.5 3 3.5 4 Photon circular p olarization Thickness(X0) 100MeV 200MeV 300MeV 10GeV 5GeV 1GeV U7V γ TQH`BxiBQM

6B;m`2 jXj, SQH`BxiBQM 7Q` T`Q/m+2/ T`iB+H2bX h`;2i Ki2`BH, hmM;bi2MX UV@ U+V, AM+B/2Mi 2@X U/V@U7V, BM+B/2Mi γ