Polarised Compton Scattering and Annihilation in Flight · Total Cross Section Asymmerties (Annihilation) 2 4 6 8 10 En 0 m e-0.2 0.2 0.4 0.6 0.8 1 A Annih Annihilation total XSasymmetry

Polarised Compton Scattering and Annihilation inFlight

Pavel Starovoitov

NC PHEP, Minsk

August 3, 2006

Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 1 / 18

Outline

1 Total Cross SectionAnnihilationCompton

2 Differential Cross SectionAnnihilation

AsymmetriesCross SectionPolarisation Transfer

ComptonAsymmetriesCross SectionPolarisation Transfer

3 Simulations

4 Next steps


Total Cross Section

σComptonpol = σCompton

0

[1 + zcz−ACompton

]~Sγ = (xl , yl , zc) ~Sele = (x−, y−, z−)

σAnnihpol = σAnnih

0

[1 + z+z−AAnnih

L + (x+x− + y+y−) AAnnihT

]~Spos = (x+, y+, z+) ~Sele = (x−, y−, z−)


Total Cross Section Asymmerties (Compton)

2 4 6 8 10En0me

-0.05

0.05

0.1

0.15

0.2

0.25

ACompton Compton total XS asymmetry

2000 4000 6000 8000 10000En0me

0.4

0.5

0.6

0.7

ACompton Compton total XS asymmetry

limEn0→0

ACompton = 0

limEn0→∞

ACompton = 1


Total Cross Section Asymmerties (Annihilation)

2 4 6 8 10

En0me

-0.2

0.2

0.4

0.6

0.8

1

AAnnih Annihilation total XS asymmetry

2000 4000 6000 8000 10000

En0me

-0.3

-0.2

-0.1

0.1

AAnnih Annihilation total XS asymmetry

longitudinal transverselim

En0→me

AAnnihT = 1

limEn0→∞

AAnnihT = −1

2

limEn0→me

AAnnihL = 1

limEn0→∞

AAnnihL = 0


Differential Cross Section (Annihilation)

dσAnnih(ξin1 , ξin

2 , ξout1 , ξout

2 )

dΩ=

dσAnnih0

dΩ

[1 + ξin

1 Aξin2

T]×[ (

C3

(ξin1 (1) + ξin

2 (1))

+ C2ξin2 (3) + C1ξ

in1 (3)

)ξout1 (3)

−(C3

(ξin1 (1) + ξin

2 (1))

+ C1ξin2 (3) + C2ξ

in1 (3)

)ξout2 (3)

+(ξout1 (1) + ξout

2 (1))L0

+ξout1 (1)

(ξin1 Lγ1

1 ξin2

T)

+ ξout1 (2)

(ξin1 Lγ1

2 ξin2

T)

+ξout2 (1)

(ξin1 Lγ2

1 ξin2

T)

+ ξout2 (2)

(ξin1 Lγ2

2 ξin2

T)

+ξout1 Correlation(ξin

1 , ξin2 )ξout

2T

]


Annihilation Differential Cross Section Asymmetries

A =

Axx 0 Axz

0 Ayy 0Axz 0 Azz


Annihilation Differential Cross Section Asymmetries

0.3 0.4 0.5 0.6 0.7Ε

-1

-0.8

-0.6

-0.4

-0.2

A Ein = 1 MeV

0.2 0.4 0.6 0.8Ε

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

A Ein = 10 MeV

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1A Ein = 100 MeV

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1A Ein = 1000 MeV

Azz Axx Axz AyyPavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 8 / 18

Annihilation Differential Cross Section

0.2 0.4 0.6 0.8Ε

1

2

3

4

5

d2 ΣdΕdΦ Ein = 10 MeV

100% Longitudinal - 100%Longitudinal Unpolarised


Polarisation Transfer in Annihilation

0.2 0.4 0.6 0.8Ε

-1

-0.5

0.5

1Circ POS: Long=+1, ELE: Long+1

0.2 0.4 0.6 0.8Ε

-1

-0.5

0.5

1Circ POS: Long=-1, ELE: Long-1

0.2 0.4 0.6 0.8Ε

-1

-0.75

-0.5

-0.25

0.25

0.5

Pol POS: Long=-1, ELE: Long=+1

0.2 0.4 0.6 0.8Ε

0.2

0.4

0.6

0.8

1Pol POS: Long=+1, ELE: Long=-1

photon #1 photon #2 linear polarisation Initial energy 10 MeVPavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 10 / 18

Polarisation Transfer in Annihilation

0.2 0.4 0.6 0.8Ε

-0.4

-0.2

0.2

0.4

0.6

0.8

1Pol POS: Long=+1, ELE: Long=0

0.2 0.4 0.6 0.8Ε

-1

-0.8

-0.6

-0.4

-0.2

0.2

0.4

Pol POS: Long=-1, ELE: Long=0

photon #1 photon #2 linear polarisation Initial energy 10 MeV


Differential Cross Section (Compton)

dσCompton(ξin1 , ξin

2 , ξout1 , ξout

2 )

dΩ=

dσCompton0

dΩ

[1 + ξin

1 (1)A0 + ξin1 Aξin

2T

]×[

ξout1 (1)

(Lγ

0 + ξin1 (1)Lγ

1 + ξin1 (3)Lγ

2ξin2 (1)

)ξout1 (2)

(ξin1 (2)Mγ

1 + ξin1 (3)Mγ

2 ξin2 (2)

)ξout1 (3)

(ξin1 (3)Nγ

1 + ξin2 (1)Nγ

2 + ξin2 (3)Nγ

3 + ξin1 Nγ

4 ξin2

T)

ξout2 (1)

(ξin1 (3)Le

1 + ξin2 (1)Le

2 + ξin2 (3)Le

3 + ξin1 Le

4ξin2

T)

ξout2 (2)

(ξin2 (2)Me

1 + ξin1 Me

2ξin2

T)

ξout2 (3)

(ξin1 (3)Ne

1 + ξin2 (1)Ne

2 + ξin2 (3)Ne

3 + ξin1 Ne

4ξin2

T)

+ξout1 Correlation(ξin

1 , ξin2 )ξout

2T

]Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 12 / 18

Compton Differential Cross Section Asymmetries

0.2 0.4 0.6 0.8Ε

-0.8

-0.6

-0.4

-0.2

0.2

0.4

AsymmetryEin = 1 MeV

0.2 0.4 0.6 0.8 1Ε

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

Asymmetry Ein = 10 MeV

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

Asymmetry Ein = 100 MeV

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1Asymmetry Ein = 1000 MeV

Circular - Longitudinal Linear Circular - In-planePavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 13 / 18

Compton Differential Cross Section

0.2 0.4 0.6 0.8 1Ε

5

10

15

20

d2 ΣdΕdΦ Ein = 10 MeV

100% Circular - 100%Longitudinal Unpolarised


Polarisation Transfer in Compton Scattering

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1Γ: Circ=+1, e-: Long=+1

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1Γ: Circ=-1, e-: Long=+1

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1Γ: Circ=-1, e-: Long=-1

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1Γ: Circ=1, e-: Long=-1

photon electron Initial energy 10 MeVPavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 15 / 18

Polarisation Transfer in Compton Scattering

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1Γ: Circ=1, e-: POL=0

0.2 0.4 0.6 0.8 1Ε

-1

-0.5

0.5

1Γ: Circ=-1, e-: POL=0

photon electron Initial energy 10 MeV


Simulations. E166 Analyzing Power (Karim)

3 6 9 120

2

4

6

8

10

12

14

16

18

20

Peter/Vahagn layout 5a Positron. E166_G4_SIM./Annihilation (Vahagn's aproach) Positron. E166_G4_SIM./Annihilation (Calculated x-section and pol-transfer Pavel/Andreas) Positron. E166_G4_SIM. Updated release. 02.08.2006

Ana

lyzi

ng p

ower

[%]

Positron Energy [MeV]


Next steps

Check everything

GEANT4 version 4.8.1

Think on Polarimeter design

Prepare publications


Documents

Polarised Compton Scattering and Annihilation in Flight · Total Cross Section Asymmerties (Annihilation) 2 4 6 8 10 En 0 m e-0.2 0.2 0.4 0.6 0.8 1 A Annih Annihilation total XSasymmetry