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

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

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 2 2 2 2 2 2

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 0 50 100 150 200 250 300 350 Photon angle (deg) 0 50 100 150 200 250 300 350 Photon angle (deg) DW/PWBA ≈ 2 DW/PWBA ≈ 1.3

· · · · · 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 0 50 100 150 200 250 300 350 Photon angle (deg) DW/PWBA ≈ 2 − 5 · · · · · DW (point nucleus) ——– DW (extended nucleus)

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 5 10 15 Collision energy (MeV) 20

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)

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

Experiment(Krugmann, v. Neumann-Cosel 2014,2016) 43 + 73. 8 MeV Experiment(Krugmann, v.Neumann-Cosel 2014,2016) 43 + 73.8 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 60 70 80 90 100 110 120 130 140 150 Scattering angle (deg) 0 0.5 1 1.5 2 2.5 Excitation energy (MeV)

Excitation of states with any multipolarity Application Excitation of states with any multipolarity (monopole E 0 : 0 → 0 , E = 0.676 MeV) + + 1 2 x Comparison with theory (nuclear structure information via nuclear models) Transition strengths in deformed nuclei (=⇒ phase transitions: vibrator/rotor model)

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)

Old experiment 2+ excitation in 12C(e, etγ) Ex = 4.439 MeV, ϑf = 80◦ and decay to the ground state (ω = Ex ) Result: Distinguishphasebetween charge and magnetic scattering

Planned experimentat the S-DALINAC (Pietralla) 2+ excitation in 92Zr(e, etγ) Ex = 0.9345/1.847 MeV Predictions: (Ponomarev, Jakubaßa 2016) Ee = 75 MeV, ϑf = 179◦, ϕ = 0, ω = Ex = 1.847 MeV Mn subshell contributionsBremsstrahlungcontribution

Collision energy (MeV) Importance of bremsstrahlung depends strongly ondetector resolution 0.001 w = 0.9345 MeV w = 1.847 MeV Cross section (b/MeVsr^2) 0.0001 1e-05 LaBr-detector: ∆ω/ω = 3% 1e-06 1e-07 20 40 60 80 100 120 140 160 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)

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

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