photons in the universewolle/telekolleg/kern/lecture/...lorentz factor: πΎπΎ= 1...
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Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Spectral lines of hydrogen
absorption
hydr
ogen
gas
absorption spectrum
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Element production on the sun
5
Hydrogen emission spectrum
wave length nm
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Spectral analysis
6
H
Spectral analysis Kirchhoff und Bunsen: Every element has a characteristic emission band
Max Planck
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Nuclear Resonance Fluorescence
Nuclear Resonance Fluorescence (NRF) is analogous to atomic resonance fluorescence but depends upon the number of protons AND the number of neutrons in the nucleus
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Photon-nuclear reactions with MeV Ξ³-rays
pure electromagnetic interaction spin selectivity (mainly E1, M1, E2 transitions)
Ξ³-ray
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Photon-nuclear reactions with MeV Ξ³-rays Ξ³-ray pure electromagnetic interaction
spin selectivity (mainly E1, M1, E2 transitions)
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Low energy photon scattering at S-DALINAC
βwhiteβ photon spectrum wide energy region examined
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Principle of measurement and self absorption
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
First Ξ³Ξ³-coincidences in a Ξ³-beam
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
First Ξ³Ξ³-coincidences in a Ξ³-beam
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
First Ξ³Ξ³-coincidences in a Ξ³-beam
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Total power received by Earth from the Sun
174 Peta (1015) Watt
@ extreme light infrastructure, Europe
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Compton scattering and inverse Compton scattering
Compton scattering:
Elastic scattering of a high-energy Ξ³-ray on a free electron. A fraction of the Ξ³-ray energy is transferred to the electron. The wave length of the scattered Ξ³-ray is increased: Ξ»β > Ξ».
βππ β₯ ππππππ2
πΈπΈπΎπΎβ² =πΈπΈπΎπΎ
1 +πΈπΈπΎπΎππππππ2
β 1 β ππππππππ
Inverse Compton scattering:
Scattering of low energy photons on ultra-relativistic electrons. Kinetic energy is transferred from the electron to the photon. The wave length of the scattered Ξ³-ray is decreased: Ξ»β < Ξ».
ππβ² β ππ β1 β π½π½ β πππππππππΎπΎ1 + π½π½ β πππππππππΏπΏ
ππβ² β ππ =βππππππ
β 1 β πππππππππΎπΎ
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Inverse Compton scattering
Electron is moving at relativistic velocity Transformation from laboratory frame to reference frame of e- (rest frame):
in order to repeat the derivation for Compton scattering
πΈπΈπΎπΎ = πΎπΎ β πΈπΈπΎπΎ 1 βπ£π£ππππππππππππβπΎπΎ
Doppler shift
Lorentz factor: πΎπΎ = 1 β π½π½2 β1/2 = 1 + ππππππππππ
931.5β0.00055
πΈπΈπΎπΎβ² =πΈπΈπΎπΎ
1 +πΈπΈπΎπΎππππππ2
β 1 β ππππππππ Compton scattering in rest frame
πΈπΈπΎπΎβ² = πΎπΎ β πΈπΈπΎπΎβ² 1 +π£π£ππππππππππππβπΎπΎβ²
Limit πΈπΈπΎπΎ βͺ ππππππ2
πΈπΈπΎπΎβ² β πΎπΎ2 β πΈπΈπΎπΎ 1 βπ£π£ππππππππππππβπΎπΎ 1 +
π£π£ππππππππππππβπΎπΎβ²
transformation into the laboratory frame
πΈπΈπΎπΎβ² β 4πΎπΎ2 β πΈπΈπΎπΎ
electron and Ξ³ interaction ππππβπΎπΎ~1800 Ξ³β emission relative to electron ππππβπΎπΎβ²~00
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Laser Compton backscattering
Energy β momentum conservation yields ~4πΎπΎ2 Doppler upshift Thomsons scattering cross section is very small (6Β·10-25 cm2)
High photon and electron density are required
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Gamma rays resulting after inverse Compton scattering
A. H. Compton Nobel Prize 1927
photon scattering on relativistic electrons (Ξ³ >> 1)
βππ = 2.3 eV β‘ 515 ππππ
ππππππππππ = 720 ππππππ β πΎπΎππ = 1 +ππππππππππ ππππππ
931.5 β π΄π΄ππ π’π’= 1410
πΈπΈπΎπΎ = 2πΎπΎππ21 + πππππππππΏπΏ
1 + πΎπΎπππππΎπΎ2 + ππ02 + 4πΎπΎπππΈπΈπΏπΏ
ππππ2β πΈπΈπΏπΏ
4πΎπΎπππΈπΈπΏπΏππππ2
= recoil parameter
πππΏπΏ = πππΈπΈπππππΏπΏππ
= normalized potential vector of the laser field
E = laser electric field strength πΈπΈπΏπΏ = βπππΏπΏ
πΎπΎππ = πΈπΈππππππ2
= 11βπ½π½2
= Lorentz factor
maximum frequency amplification: head-on collision (ΞΈL = 00) & backscattering (ΞΈΞ³ = 00)
πΈπΈπΎπΎ~4πΎπΎππ2 β πΈπΈπΏπΏ β 18.3 ππππππ
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Scattered photons in collision
Luminosity: πΏπΏ = πππΏπΏβππππ4ππβπππ π
2
πππΏπΏ = 0.5 π½π½ βπππΏπΏ = 2.4 ππππ = 3.86 β 10β19 π½π½ β‘ 515 ππππ
β πππΏπΏ= 1.3 β 1018
πππ π = 15 ππππ
ππ = 1 ππππ
β ππππ= 6.25 β 109
β ππ
Ξ³-ray rate: πππΎπΎ = πΏπΏ β πππππππππππππππ ππππ = 0.67 β 10β24 ππππ2
β 2.9 β 1032 β ππ ππππβ2ππβ1
β 2 β 108 β ππ ππβ1 (full spectrum)
Yb: Yag J-class laser
10 Peta (1015) Watt
repetition rate: ππ = 3.2 ππππππ
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Thomson Scattering
J. J. Thomson Nobel prize 1906
Thomson scattering = elastic scattering of electromagnetic radiation by an electron at rest β the electric and magnetic components of the incident wave act on the electron β the electron acceleration is mainly due to the electric field β the electron will move in the direction of the oscillating electric field β the moving electron will radiate electromagnetic dipole radiation β the radiation is emitted mostly in a direction perpendicular to the motion of the electron β the radiation will be polarized in a direction along the electron motion
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Thomson Scattering
J. J. Thomson Nobel prize 1906
ππππππ ππππΞ©
=12ππ02 β 1 + ππππππ2ππ
ππ0 =ππ2
4ππππ0ππππππ2= 2.818 β 10β15 ππ
ππππ = οΏ½ππππππ ππππΞ©
ππΞ© =2ππππ02
2οΏ½ 1 + ππππππ2ππ ππππππ
0
=8ππ3ππ02 = 6.65 β 10β29 ππ2 = 0.665 ππ
differential cross section
classical electron radius
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Scattered photons in collision
ΞΈ = 0 ΞΈ = Ο
πΈπΈπΎπΎ = 2πΎπΎππ21 + πππππππππΏπΏ
1 + πΎπΎπππππΎπΎ2 + ππ02 + 4πΎπΎπππΈπΈπΏπΏ
ππππ2β πΈπΈπΏπΏ
πππ π ππππ = 1/πΎπΎ
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Inverse Compton scattering of laser light
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Extreme Light Infrastructure β Nuclear Physics
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Nuclear Resonance Fluorescence
Widths of particle-bound states: Ξ β€ 10ππππ
Breit-Wigner absorption resonance curve for isolated resonance:
ππππ πΈπΈ = πποΏ½Μ οΏ½π22π½π½ + 1
2Ξ0Ξ
πΈπΈ β πΈπΈππ 2 + Ξ 2β 2 ~ Ξ0 Ξβ
Resonance cross section can be very large: ππ0 β 200 ππ (for Ξ0 = Ξ, 5 MeV)
Example: 10 mg, A~200 β Ntarget = 3Β·1019, NΞ³ = 100, event rate = 0.6 [s-1]
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Nuclear Resonance Fluorescence
Count rate estimate 104 Ξ³/(s eV) in 100 macro pulses 100 Ξ³/(s eV) per macro pulse example: 10 mg, A ~ 200 target resonance width Ξ = 1 eV 2 excitations per macro pulse 0.6 photons per macro pulse in detector pp-count rate 6 Hz 1000 counts per 3 min
8 HPGe detectors 2 rings at 900 and 1270
Ξ΅rel(HPGe) = 100% solid angle ~ 1% photopeak Ξ΅pp ~ 3%
narrow band width 0.5%
Hans-JΓΌrgen Wollersheim - 2017 Indian Institute of Technology Ropar
Nuclear Resonance Fluorescence
narrow bandwidth allows selective excitation and detection of decay channels