X-rays The electric field E(r,t) is given as a cosine function.

X-rays X-rays

)cos(),( tkrtrE

The electric field E(r,t) is given as a cosine function.

X-rays X-rays

In formal derivations the vector potential A is used.

The electric field E(r,t) is directly related to the vector potential A(r,t).

),(),( trAtrE t

Interaction of x-rays with matter 1Interaction of x-rays with matter 1

The photon moves towards the atom


The photon meets an electron and is annihilated


The electron gains the energy of the photon and is turned into a blue electron.


The blue electron (feeling lonely) leaves the atomand scatters of neighbors (cf. EXAFS) or escapes from the sample (cf. XPS)


The probability of photon annihilation determines the intensity of the transmitted photon beam

I0I

Ek


The photon meets an electron and is scattered


The photon leaves the atom under a different angle.(Interference between scattering events yields XRD)

I(,k,q)

I’(’,k’,q’)

I”(Ek,k”,)

Energy Spectroscopy

Direction Structure

Polarization Magnetism

Interaction of x-rays with matterInteraction of x-rays with matter

HINT(1) describes the interaction of the vector field A on

the momentum operator p of an electron, or in other words the electric field E acting on the electron moments.

The momentum operator p is given as the electron charge q times the displacement operator r.


ApHT mce

INT )1(1


The photon meets the electron and is annihilated

A

p=q•r

HINT(1) describes the interaction of the vector field A on

the momentum operator p of an electron, or in other words the electric field E acting on the electron moments.

The momentum operator p is given as the electron charge q times the displacement operator r.


ApHT mce

INT )1(1

HINT(2) describes the second order interaction of the

vector field A.

This gives rise to the elastic scattering of the x-rays by the electrons.

This is the basis for x-ray diffraction (XRD) and small angle x-ray scattering (SAXS)


2

2)2( 2

2AH

mce

INT


• XAFS studies photoelectric absorption

• Elastic scattering (Thompson)

• Inelastic scattering

• (Compton)100 1k 10k 100k 1M

1

10

100

Photonuclear

Electron-

positron

Photoelectric

Thompson

Compton

Inte

nsi

ty (

log

)

Energy (eV)

Mn

if EEiffXAS TI

2

1~

Excitation of core electrons to empty states.

Spectrum given by the Fermi Golden RuleFermi Golden Rule

X-ray absorption and X-ray photoemissionX-ray absorption and X-ray photoemission

I(FIXED)


X-ray emission: core hole decayX-ray emission: core hole decay

Basis for X-ray Fluorescence (XRF) and Energy Dispersive X-ray analysis (EDX)


ApH mce

INT )1(

2

2)2( 2

2AH

mce

INT

Photoelectric effect:(annihilation of photon)XAS, XPSXES, XRF, EDX

X-ray scattering:(photon-in photon-out)XRD, SAXS


X-ray scattering:- with Hint(2)

- with Hint(1) via a (virtual) intermediate state

= Resonant X-ray scattering

)1(2/1

)1()2(2 INTiHEINTINT HHHTi


The photon meets an electron and is annihilated


The electron gains the energy of the photon and is turned into a virtual blue electron.


The virtual blue electron loses a photon with exactly the same energy as gained


The photon leaves the atom

Resonant X-ray scatteringResonant X-ray scattering

Combination of XAS and XES [only Hint(1)]- RXES- Resonant Inelastic X-ray Scattering (RIXS) (also called Resonant X-ray Raman Spectroscopy)

Combination of Hint(1) and Hint(2)

- Resonant XRD (also called: anomalous)- Multi-wavelength anomalous Diffraction (MAD)- Resonant SAXS (ASAXS)- TEDDI

X-rays The electric field E(r,t) is given as a cosine function.

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