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Fundamental physics in strong Coulomb fields
Lecture 1: Introduction
Ruprecht-Karls-Universität Heidelberg, October 22, 2014
Fundamental physics in strong Coulomb fields
Series of lectures in the winter term 2014/2015Dates: Wednesdays, 16:00-17:30 (OK?), once per week,Oct 22, 2014 – Feb 04, 2015 (no lecture on: Dec. 24, 31)Location: KIP (INF 227), Hörsaal 2Lecture No. 130000201421214; Grading by an oral exam
Experiment:Dr. Stanislav Tashenov, Atomic Polarization SpectroscopyGroup, Physikalisches Institut, Heidelberg UniversityEmail: [email protected]; Phone:06221-54-19493Theory:PD Dr. Zoltán Harman, MPI for Nuclear Physics, DivisionTheoretical Quantum Dynamics and Quantum ElectrodynamicsEmail: [email protected]; Phone: 06221-516-170
Homepage (with lecture slides):www.physi.uni-heidelberg.de/Forschung/apix/APS/lectures
Basic physical properties
Size: r = a0Z , with a0 being the Bohr radius (a0 = 5.26× 10−11 m,
radius of the electron orbit in the ground state of the H atom)→ smaller radii due to the Coulomb attraction of the nucleus!
Energy scale: En = − me4
8ε20h2
Z2
n2 ≈ −13.6 eV Z2
n2
Transition energy between n = 2→ 1, in Fe (Z = 26):hνKα = ∆E = E2 − E1 ≈ 13.6 eV 262
(11 −
14
)≈ 6895 eV;
hνLα = E3 − E2 ≈ 1277 eV:→ energies of the emitted/absorbedphotons is typically in the x-ray regime!(notation Kα: transition to n = 1, i.e. K shell; α: ∆n = 1)
Classical electron velocity:vc = Zα = 0.19 (Fe, Z=26); =0.67 (U, Z=92)(here, α = e2
4πε0~c : fine-structure constant)v ≈ c: fast, relativistic electrons!Dirac equation instead of Schrödingerequation
Schrödinger equation with Schrödinger Hamiltonian:
i~∂
∂tψ(r, t) = Hψ(r, t) ,
HS =~2
2m∆ + V(r)
here: ψ: scalar wave function
Dirac Hamiltonian:
HD = −i~cα∇ + V(r) + mc2α0
here: ψ: 4-component (bispinor) wave function;α0, αi (i = 1, 2, 3): 4×4-matricesV(r): Coulomb Potential of the nucleus
Expansion parameters of the theory:
Zα ≈ v/c: interaction of an electronwith the Coulomb field of the nucleusα/r
Zα/r = 1/Z: relative strength of theelectron-electron interaction
α = e2
(4πε0)~c ≈ 1/137: fine-structureconstant
Theory: expansion of atomic properties inthese parameters – or all-order methods
QED corrections: self-energy and vacuum polarization
QED corrections: sizeable contributions in highly charged ions;i.e. ≈10-30 eV in Kr (Z=36)
SE
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VP
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Fundamental radiative processes involving HCI
Photo-absorption(radiative excitation):
Photoemission(radiative decay):
Fundamental processes determining the optical properties of amediumPhotoabsorption followed by photoemission:~ω + Aq+ → Aq+∗ → ~ω + Aq+: resonant photon scattering orresonance fluorescence, fundamental process of (x-ray) laserspectroscopy
Cross section for resonant, elastic photon scattering (resonancefluorescence):
σi→e→f (~ω) = S~Ae/(2π)
(~ω + Ei − Ee)2 + (~Ae)2
4
.
with Ae: Einstein A coefficient of the excited state (e); probability ofradiative decay per unit timeresonance strength (energy-integrated area under a peak):
S =π2c2~3
(~ω)2ge
gi
Ae→f
AeAe→i ∝
Ae→f
(~ω)2 ∝ gf
|~ω = Ee − Ei
S��
��
Γe = ~Ae: line width-�
Photoionisation: ”photon comes in, electron goes out”
Direct photoionisation (DPI, orphotoelectric effect):~ω + Aq+ → A(q+1)+
electron removed from thebinding potential of thenucleus by absorption of aphoton
Resonant (Auger) photoionisation(RPI):~ω + Aq+ → Aq+∗∗ → A(q+1)∗ + e−
resonant excitation of an electronby photoabsorption
Auger effect or autoionization
Photorecombination: ”e− comes in, photon goes out”
Radiative recombination (RR):Aq+ → A(q−1)+ + ~ωRR
Capture of a free electronby irradiation of a photon(inverse of thephotoelectric effect)
Dielectronic recombination (DR):Aq+ + e− → A(q−1)+∗∗ →~ωDR + A(q−1)+
Radiationless resonant capture ofa free electron (inverse of theAuger effect)
Radiative decay of anautoionizing state
Theoretical topics to be covered
Basics of ionic structure: hydrogenlike ions, Schrödingerequation, Dirac equation, single-particle solutions, spectroscopicnotation; many-electron systems, electron configurations,jj-coupling, Hartree-Fock method, fine structure of atomic levels
Nuclear effects in highly charged ions: finite nuclear radius,nuclear charge distribution
Interaction of atoms and atomic ions with the radiation field:photon emission and -absorption, induced and spontaneousdecay, Einstein coefficients. Electric dipole transitions, selectionrules. Resonant scattering of photons, lifetime of excited states,natural line width, Lorentz profile
Photoionisation: direct photoelectric effect, transitionprobability, cross section. Resonances, Auger decay, quantuminterference, Fano line shape
Photorecombination: radiative recombination, detailed balance;dielectronic recombination, Auger notation, quantuminterference
Basics of quantum electrodynamics: QED corrections in highlycharged ions: Lamb shift, self-energy, vacuum polarization,Uehling potential
Recommended reading
Beyer, Shevelko: Introduction to the physics ofhighly charged ions
Greiner: Relativistische Quantenmechanik - Wellengleichungen
Greiner: Quantentheorie - Spezielle Kapitel
Greiner: Quantenelektrodynamik
Eichler, Meyerhof: Relativistic atomic collisions
Friedrich: Theoretische Atomphysik
Foot: Atomic physics
Budker: Atomic physics
Pradhan, Nahar: Atomic astrophysics and spectroscopy
See you next week!