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: tashenov@physi.uni-heidelberg.de; Phone:06221-54-19493Theory:PD Dr. Zoltán Harman, MPI for Nuclear Physics, DivisionTheoretical Quantum Dynamics and Quantum ElectrodynamicsEmail: harman@mpi-hd.mpg.de; 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!