1. On the role of bremsstrahlung in electron-nucleus collisions
Doris Jakubaßa-Amundsen University of Munich (LMU)
November, 2016

2. On the role of bremsstrahlung in electron-nucleus collisions
Doris Jakubaßa-Amundsen University of Munich (LMU)
November, 2016
Contents:
The bremsstrahlung process (e, etγ)
Electron-photon polarization correlations
Comparison between theory and experiment in the MeV region
Background in nuclear excitation N (e, et)N∗
Theoretical description
Comparison with experimental spectra for 150Nd(e, er)
Coincident nuclear excitation and decay N (e, etγ)N

3. The bremsstrahlung process
spin-0 nuclei (Z = 40 − 80)
Elementary process (e, etγ): .2
d 3σ
4π2ωkf Ei Ef . . .
(ζi, sλ) =
.(ψ (ζ )|αs e |ψ (ζ )).
∗ −ikr .
dωd Ωkd Ωf
kic 5 .
f f λ i i ζf . . .
d 3σ =
1 + . Cµν ζµsν
dωd Ωkd Ωf
µ,ν
Cµν = polarization correlations betweenelectronandphoton Sum rule (Pratt, Jakubaßa 2016):
C 2
32 + C12 + C20 + C03 + C31 + C11 − C23 = 1

4. ψ = ei kr Numerical calculations(Tseng,Pratt 1971, Yerokhin 2010)
Partial-wave expansion of electronic scattering states ψ = . ψjlm
jlm
Solve radial Dirac equation in nuclear potential (for each j , l )
PWBA for Ee ” 20 MeV: Plane-wave
ψ = ei kr
d 3σ = d 3σ (point nucleus) · |F (q)|2
q = ki − kf − k momentum transfer
Coulomb distortion( Ee = 10 MeV, ω = 2 MeV, ϑf = 40◦/70◦): 1
0.1
Nd (Z=60) DW
PWBA
Cross section (b/MeVsr^2)
Cross section (b/MeVsr^2)
0.1
Zr (Z=40)
0.01
0.01
0.001
0.001
0.0001 DW
0.0001
PWBA
Photon angle (deg)
Photon angle (deg)
DW/PWBA ≈ 2
DW/PWBA ≈ 1.3

5. · · · · · DW (point nucleus) ——– DW (extended nucleus)
Ee = 15 MeV, ω = 3/4Ee ,
ϑf = 150◦
0.01
Pb (Z=82) DW
PWBA
Cross section (b/MeVsr^2)
0.001
0.0001
1e-05
1e-06
1e-07
Photon angle (deg)
DW/PWBA ≈ 2 − 5
· · · · · DW (point nucleus)
——– DW (extended nucleus)

6. Experiment
Polarized electrons: ζi = ez cos αs + ex sin αs ∈ (ki, k)-plane Measured:linearly polarized photonsvia Compton scattering Extract: Tilt angle χ(αs ) of polarization plane wrt reaction plane
sin 2χ(0 ) = − ◦ √ C 31
C 2 2
03 +C31
sin 2χ(90◦) = √ C11
C 2 2
03 +C11
Measured:circularly polarized photonsvia magnetic absorber 1
0.8
0.6
0.4
0.2
-0.2
-0.4
-0.6
Nillius, Aulenbacher (2015)
3.5 MeV e+ Au, θk = 21◦
0.95
C32
Spin asymmetry
0.75
Au (Z=79)
αs = 0 :
αs = 90◦ :
C32
C12
0.75
C12
0.95
(flip of ζ ) i
Collision energy (MeV) 20

7. Application
Relativistic electron dynamics in strong fields (Test of theory)
Diagnostics of spin-polarized beams
Spin transport in thick conversion targets
(for polarized positron source)

8. 1 ω xE− 2 e−( ) d 3σbrems Ex f f i i Nuclear excitation by electrons
(spin-0 nuclei)
Electron intensity: N(e, et)N∗ + . (e, et,γ )
. 3 . γ
d 2σ 1 2
. . .
= .N0 Ex
. (φ (M )|J (x )|φ ) (ψ (ζ )|j (r)|ψ (ζ )) ν
dωd Ωf
f f ν N i
f f i i
Mf ,ζf ,ζi .ν=0 . . 2 e
i (E /c )|r−x |
x N .
1 ω xE− 2 ×
· √
e−( ) .
|r − xN| . πΓ Γ
+ d Ωk .
d 3σbrems .
dωd Ω d Ω
k f

9. Experiment(Krugmann, v. Neumann-Cosel 2014,2016) 43 + 73. 8 MeV
Experiment(Krugmann, v.Neumann-Cosel 2014,2016) MeV 150Nd(e, et), ϑf = 69◦ − 141◦
Bremsstrahlungbackground:
d 2σbrems d 2σPWBA DW
= ×
dωd Ωf dωd Ωf
PWBA
Absolute excitation spectra
Elastic scattering
100 1
Nd (Z=60)
43 MeV
73.8 MeV
10-1
10-2
10-3
10-4
10-5
Cross section (b/MeVsr)
Cross section (b/sr)
0.1
43 MeV
0.01
0.001
(a)
73.8 MeV
0.0001
10-6
Scattering angle (deg)
Excitation energy (MeV)

10. Excitation of states with any multipolarity
Application
Excitation of states with any multipolarity
(monopole E 0 : 0 → 0 , E = MeV)
+ +
1 2 x
Comparison with theory
(nuclear structure information via nuclear models)
Transition strengths in deformed nuclei
(=⇒ phase transitions: vibrator/rotor model)

11. 1 . . .MExDec + Mbrems. MExDec Adec exc Adec fn (Mn) Ani (Mn) Mn
Coincident nuclear excitation and decay to ground state
Electron intensityin coincidence with photonsat ω = Ex
Coherent N(e, etγ)N + (e, et,γ )
1 . . .2
d 3σ
.MExDec + Mbrems.
= N0 . .
dωd Ωkd Ωf 2
fi fi
ζf ,ζi λ . Mn
MExDec 1
Adec exc
fn (Mn) Ani (Mn)
(Mn) = ω − E fi
+ i Γ/2 x
Adec
fn (Mn) = d xN (φf |J(xN ) sλ |φn(Mn)) e ∗
−i kxN
Symmetry of transition current density JLLr (n → f ) = JLLr (i → n)

12. Old experiment
2+ excitation in 12C(e, etγ) Ex = MeV, ϑf = 80◦ and decay to the ground state (ω = Ex )
Result:
Distinguishphasebetween charge and magnetic scattering

13. Planned experimentat the S-DALINAC (Pietralla)
2+ excitation in 92Zr(e, etγ) Ex = /1.847 MeV Predictions: (Ponomarev, Jakubaßa 2016)
Ee = 75 MeV, ϑf = 179◦, ϕ = 0, ω = Ex = MeV
Mn subshell contributionsBremsstrahlungcontribution

14. Collision energy (MeV)
Importance of bremsstrahlung depends strongly
ondetector resolution
0.001
w = MeV
w = MeV
Cross section (b/MeVsr^2)
0.0001
1e-05
LaBr-detector: ∆ω/ω = 3%
1e-06
1e-07
Collision energy (MeV)
Application
ϑf = 40◦, θk = −90◦ = 270◦
ϕ = 0, ω = Ex
Bound-state transitions
Nuclear structure investigations (influence of magnetic scattering)
(valence shell – cross shell excitation)

15. Summary
Importance of bremsstrahlung (e, etγ) Spin asymmetries: Test of theory
Vector polarimeter
Control of polarized beams
Backgroundin nuclear excitation ( e, et) Backgroundin coincident excitation and decay
( e, etγ)
Suppression
for large scattering angles for light nuclei
for high detector resolution for high beam energy

16. Thank you! Doris Jakubaßa-Amundsen University of Munich (LMU)
On the role of bremsstrahlung in electron-nucleus collisions