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Atomic Physics

Atomic Physics
Atomic Physics rd 3 year B1 P. Ewart Oxford Physics: 3rd Year, Atomic Physics• Lecture notes • Lecture slides • Problem sets All available on Physics web site: http:www.physics.ox.ac.uk/users/ewart/index.htm Oxford Physics: 3rd Year, Atomic PhysicsAtomic Physics: • Astrophysics • Plasma Physics • Condensed Matter • Atmospheric Physics • Chemistry •Biology Technology • Street lamps • Lasers • Magnetic Resonance Imaging • Atomic Clocks • Satellite navigation: GPS •etc Oxford Physics: 3rd Year, Atomic PhysicsAstrophysicsCondensed Matter Zircon mineral crystal C Fullerene 60Snow crystalLasersBiology DNA strandLecture 1 • How we study atoms: – emission and absorption of light – spectral lines • Atomic orders of magnitude • Basic structure of atoms – approximate electric field inside atoms Oxford Physics: 3rd Year, Atomic Physicsψ ψ 1 2 Atomic radiation ψ(t) = ψψ + 12 Ψ(τ t+ ) Ψ(t) 2 2 IΨ(t)I I Ψ(t + τ)I Oscillating charge cloud: Electric dipole Oxford Physics: 3rd Year, Atomic PhysicsSpectral Line Broadening Homogeneous e.g. Lifetime (Natural) Collisional (Pressure) Inhomogeneous e.g. Doppler (Atomic motion) Crystal Fields Oxford Physics: 3rd Year, Atomic PhysicsLifetime (natural) broadening Intensity spectrum Number of excited atoms Electric field amplitude N(t) I(ω) E(t) Fourier Transform frequency, ω Time, t Exponential decay Lorentzian lineshape Oxford Physics: 3rd Year, Atomic PhysicsLifetime (natural) broadening Intensity spectrum Number of excited atoms Electric field amplitude N(t) I(ω) E(t) 8 8 `τ 10 s `Δν 10 Hz frequency, ω Time, t Exponential decay Lorentzian lineshape Oxford Physics: 3rd Year, Atomic PhysicsCollision (pressure) broadening Intensity spectrum Number of uncollided atoms N(t) I(ω) frequency, ω Time, t Exponential decay Lorentzian lineshape Oxford Physics: 3rd Year, Atomic PhysicsCollision (pressure) broadening Intensity spectrum Number of uncollided atoms N(t) I(ω) 10 10 `τ 10 s `Δν 10 Hz c frequency, ω Time, t Exponential decay Lorentzian lineshape Oxford Physics: 3rd Year, Atomic PhysicsDoppler (atomic motion) broadening Distribution of atomic speed Doppler broadening N(v) I(ω) frequency, ω atomic speed, v MaxwellBoltzmann Gaussian lineshape distribution 9 ` Typical Δν 10 Hz Oxford Physics: 3rd Year, Atomic PhysicsAtomic orders of magnitude 19 Atomic energy: 10 J → 2 eV 1 Thermal energy: / eV 40 Ionization energy, H: 13.6 eV 1 = Rydberg Constant 109,737 cm 11 Atomic size, Bohr radius: 5.3 x 10 m Fine structure constant, α = v/c: 1/137 24 1 Bohr magneton, μ : 9.27 x 10 JT B Oxford Physics: 3rd Year, Atomic PhysicsThe r Central Field 1/r Z/r U(r) “Actual” Potential Oxford Physics: 3rd Year, Atomic PhysicsZ eff Important Z region 1 Radial position, r Oxford Physics: 3rd Year, Atomic PhysicsLecture 2 • The Central Field Approximation: – physics of wave functions (Hydrogen) • Manyelectron atoms – atomic structures and the Periodic Table • Energy levels – deviations from hydrogenlike energy levels – finding the energy levels; the quantum defectSchrödinger Equation (1electron atom) Hamiltionian for manyelectron atom: Individual electron potential Electronelectron interaction in field of nucleus This prevents separation into Individual electron equations Oxford Physics: 3rd Year, Atomic PhysicsCentral potential in Hydrogen: V(r)1/r, separation of ψ into radial and angular functions: m ψ = R(r)Y (θ,φ)χ(m ) l s Therefore we seek a potential for multielectron atom that allows separation into individual electron wavefunctions of this form Oxford Physics: 3rd Year, Atomic PhysicsElectron – Electron interaction term: Treat this as composed of two contributions: (a)a centrally directed part (b)a noncentral Residual Electrostatic part e e + Oxford Physics: 3rd Year, Atomic PhysicsHamiltonian for Central Field Approximation Central Field Potential H = residual electrostatic interaction 1 Perturbation Theory Approximation: H H 1 o Oxford Physics: 3rd Year, Atomic PhysicsZero order Schrödinger Equation: H ψ = Ε ψ 0 0 H is spherically symmetric so equation is separable 0 solution for individual electrons: Radial Angular Spin Oxford Physics: 3rd Year, Atomic PhysicsCentral Field Approximation: What form does U(r ) take i Oxford Physics: 3rd Year, Atomic Physics + Z+ Hydrogen atom Manyelectron atom Z+ Z+ Z+ Z protons+ (Z – 1) electrons Z protons U(r) 1/r U(r) Z/rThe r Central Field 1/r Z/r U(r) “Actual” Potential Oxford Physics: 3rd Year, Atomic PhysicsZ eff Important Z region 1 Radial position, r Oxford Physics: 3rd Year, Atomic PhysicsFinding the Central Field • “Guess” form of U(r) • Solve Schrödinger eqn. → Approx ψ. • Use approx ψ to find charge distribution • Calculate U (r) from this charge distribution c • Compare U (r) with U(r) c • Iterate until U (r) = U(r) c Oxford Physics: 3rd Year, Atomic PhysicsEnergy eigenvalues for Hydrogen: Oxford Physics: 3rd Year, Atomic Physicsl = 0 1 2 n s p d 0 H Energy level 4 diagram 3 2 Energy Note degeneracy in l 13.6 eV 1 Oxford Physics: 3rd Year, Atomic PhysicsRevision of Hydrogen solutions: Product wavefunction: Spatial x Angular function Normalization : Eigenfunctions of angular momentum operators Eigenvalues Oxford Physics: 3rd Year, Atomic PhysicsAngular momentum orbitals + 2 Y() θ,φ 1 0 2 Y() θ,φ 1 Oxford Physics: 3rd Year, Atomic PhysicsAngular momentum orbitals Spherically symmetric charge cloud with filled shell + 2 Y() θ,φ 1 0 2 Y() θ,φ 1 Oxford Physics: 3rd Year, Atomic PhysicsRadial wavefunctions 21.0 10.5 2 4 6 Zr/a 2 4 6 8 10 o Zr/a o Ground state, n = 1, l = 0 1st excited state, n = 2, l = 0 N = 2, l = 1 0.4 2 4 6 8 10 20 Zr/a o 2nd excited state, n = 3, l = 0 n = 3, l = 1 n = 3, l =2 Oxford Physics: 3rd Year, Atomic PhysicsRadial wavefunctions • l = 0 states do not vanish at r = 0 • l ≠ 0 states vanish at r = 0, and peak at larger r as l increases 2 • Peak probability (size) n • l = 0 wavefunction has (n1) nodes • l = 1 has (n2) nodes etc. • Maximum l=(n1) has no nodes Electrons arranged in “shells” for each n Oxford Physics: 3rd Year, Atomic PhysicsThe Periodic Table Shells specified by n and l quantum numbers Electron configuration Oxford Physics: 3rd Year, Atomic PhysicsThe Periodic Table Oxford Physics: 3rd Year, Atomic PhysicsThe Periodic Table Rare gases 2 He: 1s 2 2 6 Ne: 1s 2s 2p 2 2 6 2 6 Ar: 1s 2s 2p 3s 3p 2 6 Kr: (…) 4s 4p 2 6 Xe: (…..)5s 5p 2 6 Rn: (……)6s 6p Oxford Physics: 3rd Year, Atomic PhysicsThe Periodic Table Alkali metals 2 Li: 1s 2s 2 2 6 Na: 1s 2s 2p 3s 2 2 6 2 6 Ca: 1s 2s 2p 3s 3p 4s 2 6 Rb: (…) 4s 4p 5s 2 6 Cs: (…..)5s 5p 6s etc. Oxford Physics: 3rd Year, Atomic PhysicsAbsorption spectroscopy Atomic Spectrograph Vapour White light source Absorption spectrum Oxford Physics: 3rd Year, Atomic PhysicsFinding the Energy Levels Hydrogen Binding Energy, Term Value T = R n 2 n Many electron atom, T = R . n 2 (n – δ(l)) δ(l) is the Quantum Defect Oxford Physics: 3rd Year, Atomic PhysicsFinding the Quantum Defect 1. Measure wavelength λ of absorption lines 2. Calculate: ν = 1/ λ 3. "Guess" ionization potential, T(n ) i.e. Series Limit o 4. Calculate T(n ): i ν = T(n ) T(n ) io i 5. Calculate: n or δ(l) 2 T(n ) = R /(n δ(l)) i Quantum defect plot Δ(l) T(n ) i Oxford Physics: 3rd Year, Atomic PhysicsLecture 3 • Corrections to the Central Field • SpinOrbit interaction • The physics of magnetic interactions • Finding the SO energy – Perturbation Theory • The problem of degeneracy • The Vector Model (DPT made easy) • Calculating the SpinOrbit energy • SpinOrbit splitting in Sodium as example Oxford Physics: 3rd Year, Atomic PhysicsThe r Central Field 1/r Z/r U(r) “Actual” Potential Oxford Physics: 3rd Year, Atomic PhysicsCorrections to the Central Field • Residual electrostatic interaction: • Magnetic spinorbit interaction: H = μ.B 2 orbit Oxford Physics: 3rd Year, Atomic PhysicsMagnetic spinorbit interaction • Electron moves in Electric field of nucleus, so sees a Magnetic field B orbit • Electron spin precesses in B with energy: orbit μ.B which is proportional to s.l • Different orientations of s and l give different total angular momentum j = l + s. • Different values of j give different s.l so have different energy: The energy level is split for l + 1/2 Oxford Physics: 3rd Year, Atomic PhysicsLarmor Precession Magnetic field B exerts a torque on magnetic moment μ causing precession of μ and the associated angular momentum vector λ The additional angular velocity ω’ changes the angular velocity and hence energy of the orbiting/spinning charge ΔE = μ.B Oxford Physics: 3rd Year, Atomic PhysicsSpinOrbit interaction: Summary B parallel to l μ parallel to s Oxford Physics: 3rd Year, Atomic PhysicsPerturbation energy Radial integral Angular momentum operator How to find s . l using perturbation theory Oxford Physics: 3rd Year, Atomic PhysicsPerturbation theory with degenerate states Perturbation Energy: Change in wavefunction: So won’t work if E = E i j i.e. degenerate states. We need a diagonal perturbation matrix, i.e. offdiagonal elements are zero New wavefunctions: New eignvalues: Oxford Physics: 3rd Year, Atomic PhysicsThe Vector Model Angular momenta represented by vectors: 2 2 2, l , s and j and l, s j and with magnitudes: l(l+1), s(s+1) and j(j+1). and l(l+1), s(s+1) and j(j+1). z Projections of vectors: m h l lh l, s and j on zaxis are m , m and m l s j Constants of the Motion Good quantum numbers Oxford Physics: 3rd Year, Atomic PhysicsSummary of Lecture 3: SpinOrbit coupling • SpinOrbit energy • Radial integral sets size of the effect. • Angular integral s . l needs Degenerate Perturbation Theory • New basis eigenfunctions: s • j and j are constants of the motion z j l • Vector Model represents angular momenta as vectors • These vectors can help identify constants of the motion • These constants of the motion represented by good quantum numbers Oxford Physics: 3rd Year, Atomic PhysicsZ Z Fixed in (a) No spinorbit j j space coupling s (b) Spin–orbit coupling l gives precession l s around j (c) Projection of l on z (a) ii (b) ii is not constant (d) Projection of s on z Z Z is not constant j j l z m and m are not good l s l quantum numbers s z Replace by j and m j s Oxford Physics: 3rd Year, Atomic Physics (c) ii (dIi)Vector model defines: s Vector triangle j l Magnitudes Oxford Physics: 3rd Year, Atomic Physics2 2 2 ∼ β x ‹ ½ j –l –s › n,l Using basis states: n, l, s, j, m › to find expectation value: j The spinorbit energy is: ΔE = β x (1/2)j(j+1) – l(l+1) – s(s+1) n,l Oxford Physics: 3rd Year, Atomic Physics1 ΔE = β x ( /2)j(j+1) – l(l+1) – s(s+1) n,l Sodium 3s: n = 3, l = 0, no effect 3 3p: n = 3, l = 1, s = ½, ½, j = ½ or /2 1 3 1 ΔE( /2) = β x ( 1); ΔE( /2) = β x ( /2) 3p 3p j = 3/2 2j + 1 = 4 1/2 3p (no spinorbit) j = 1/2 2j + 1 = 2 1 Oxford Physics: 3rd Year, Atomic PhysicsLecture 4 • Twoelectron atoms: the residual electrostatic interaction • Adding angular momenta: LScoupling • Symmetry and indistinguishability • Orbital effects on electrostatic interaction • Spinorbit effects Oxford Physics: 3rd Year, Atomic PhysicsCoupling of l and s to form L and S: i Electrostatic interaction dominates l s 2 2 L S is l 1 1 S = ss + ll L = + 1 2 1 2 Oxford Physics: 3rd Year, Atomic PhysicsCoupling of L and S to form J S = 1 S = 1 L = 1 L = 1 S = 1 L = 1 J = 2 J = 1 J = 0 Oxford Physics: 3rd Year, Atomic PhysicsMagnesium: “typical” 2electron atom Mg Configuration: 2 2 6 2 1s 2s 2p 3s Na Configuration: 2 2 6 1s 2s 2p 3s “Spectator” electron in Mg Mg energy level structure is like Na but levels are more strongly bound Oxford Physics: 3rd Year, Atomic PhysicsResidual electrostatic interaction 3s4s state in Mg: Zeroorder wave functions Perturbation energy: Degenerate states Oxford Physics: 3rd Year, Atomic PhysicsLinear combination of zeroorder wavefunctions Offdiagonal matrix elements: Oxford Physics: 3rd Year, Atomic PhysicsOffdiagonal matrix elements: Therefore as required Oxford Physics: 3rd Year, Atomic PhysicsEffect of Direct and Exchange integrals Singlet +K K Triplet J Energy level with no electrostatic interaction Oxford Physics: 3rd Year, Atomic PhysicsOrbital orientation effect on electrostatic interaction l 2 l 1 L l l 2 1 L = ll + 1 2 Overlap of electron wavefunctions depends on orientation of orbital angular momentum: so electrostatic interaction depends on L Oxford Physics: 3rd Year, Atomic PhysicsResidual Electrostatic and SpinOrbit effects in LScoupling Oxford Physics: 3rd Year, Atomic PhysicsTerm diagram of Magnesium Singlet terms Triplet terms 3pn 11 1 333 SP D SPD o2 1 2 3p ns 5s 1 3s3d D 2 4s 1 3s3p P 1 3 3s3p P resonance line 2,1,0 (strong) intercombination line (weak) 21 3s S 0 Oxford Physics: 3rd Year, Atomic PhysicsThe story so far: Hierarchy of interactions H O H 1 H 2 H : Nuclear Effects on atomic energy 3 H H H H 3 2 1 O Oxford Physics: 3rd Year, Atomic PhysicsLecture 5 • Nuclear effects on energy levels – Nuclear spin – addition of nuclear and electron angular momenta • How to find the nuclear spin •Isotope effects: – effects of finite nuclear mass – effects of nuclear charge distribution • Selection RulesNuclear effects in atoms Corrections Nucleus: Nuclear spin→ magnetic dipole • stationary interacts with electrons orbits centre of mass with • infinite mass electrons • point charge spread over nuclear volumeNuclear Spin interaction Magnetic dipole angular momentum μ = γλħ μ = g μ l μ = g μ s l l B s s Β μ = g μ I Ι I Ν g 1 μ = μ x m /m μ / 2000 I Ν Β e P Β Perturbation energy: Η = − μ . B 3 Ι elMagnetic field of electrons: Orbital and Spin Closed shells: zero contribution 3 s orbitals: largest contribution – short range 1/r l 0, smaller contribution neglect B elB = (scalar quantity) x J el Usually dominated by spin contribution in sstates: Fermi “contact interaction”. Calculable only for Hydrogen in ground state, 1sCoupling of I and J Depends on I Depends on J Nuclear spin interaction energy: empirical Expectation valueVector model of nuclear interaction I and J precess around F F = I + J I F I I F J J J FHyperfine structure Hfs interaction energy: Vector model result: Hfs energy shift: Hfs interval rule:Finding the nuclear spin, I • Interval rule – finds F, then for known J → I • Number of spectral lines (2I + 1) for J I, (2J + 1) for I J •Intensity Depends on statistical weight (2F + 1) finds F, then for known J → IIsotope effects reduced mass Orbiting about Fixed nucleus, infinite mass + Orbiting about centre of massIsotope effects reduced mass Orbiting about Fixed nucleus, infinite mass + Orbiting about centre of massLecture 6 • Selection Rules • Atoms in magnetic fields – basic physics; atoms with no spin – atoms with spin: anomalous Zeeman Effect – polarization of the radiationr Parity selection rule r N.B. Error in notes eqn (161) l Parity (1) must change Δl = + 1Configuration Only one electron “jumps”Selection Rules: Conservation of angular momentum J = J h 2 1 J = J 2 1 h J J 1 1 ΔL = 0, + 1 ΔS = 0 ΔM = 0, + 1 JAtoms in magnetic fields Oxford Physics: 3rd Year, Atomic PhysicsEffect of Bfield on an atom with no spin Interaction energy Precession energy: Oxford Physics: 3rd Year, Atomic PhysicsNormal Zeeman Effect Level is split into equally Spaced sublevels (states) Selection rules on M L give a spectrum of the normal Lorentz Triplet Spectrum Oxford Physics: 3rd Year, Atomic PhysicsEffect of Bfield on an atom with spinorbit coupling Precession of L and S around the resultant J leads to variation of projections of L and S on the field direction Oxford Physics: 3rd Year, Atomic PhysicsOxford Physics: 3rd Year, Atomic PhysicsTotal magnetic moment does not lie along axis of J. Effective magnetic moment does lie along axis of J, hence has constant projection on B axis ext Oxford Physics: 3rd Year, Atomic PhysicsPerturbation Calculation of B effect on spinorbit level ext Interaction energy Effective magnetic moment Perturbation Theory: expectation value of energy Energy shift of M level J Oxford Physics: 3rd Year, Atomic PhysicsVector Model Calculation of B effect on spinorbit level ext Projections of L and S on J are given by Oxford Physics: 3rd Year, Atomic PhysicsVector Model Calculation of B effect on spinorbit level ext Perturbation Theory result Oxford Physics: 3rd Year, Atomic PhysicsAnomalous Zeeman Effect: 2 2 3s S –3p P in Na 1/2 1/2 Oxford Physics: 3rd Year, Atomic PhysicsPolarization of Anomalous Zeeman components associated with Δm selection rules Oxford Physics: 3rd Year, Atomic PhysicsLecture 7 • Magnetic effects on fine structure Weak field Strong field • Magnetic field effects on hyperfine structure: Weak field Strong field Oxford Physics: 3rd Year, Atomic PhysicsSummary of magnetic field effects on atom with spinorbit interaction Oxford Physics: 3rd Year, Atomic PhysicsTotal magnetic moment does not lie along axis of J. Effective magnetic moment does lie along axis of J, hence has constant projection on B axis ext Oxford Physics: 3rd Year, Atomic PhysicsPerturbation Calculation of B effect on spinorbit level ext Interaction energy Effective magnetic moment Perturbation Theory: expectation value of energy Energy shift of M level J What is g J Oxford Physics: 3rd Year, Atomic PhysicsVector Model Calculation of B effect on spinorbit level ext Projections of L and S on J are given by Oxford Physics: 3rd Year, Atomic PhysicsVector Model Calculation of B effect on spinorbit level ext Perturbation Theory result Oxford Physics: 3rd Year, Atomic PhysicsLandé gfactor Anomalous Zeeman Effect: 2 2 3s S –3p P in Na 1/2 1/2 2 g ( P ) = 2/3 J 1/2 2 g ( S ) = 2 J 1/2 Oxford Physics: 3rd Year, Atomic PhysicsStrong field effects on atoms with spinorbit coupling Spin and Orbit magnetic moments couple more strongly to B than to each other. ext Oxford Physics: 3rd Year, Atomic PhysicsStrong field effect on L and S. m and m are L S good quantum numbers L and S precess independently around B ext Spinorbit coupling is relatively insignificant Oxford Physics: 3rd Year, Atomic PhysicsSplitting of level in strong field: PaschenBack Effect N.B. Splitting like Spin splitting = 2 x Orbital Normal Zeeman Effect g = 2 x g S L Oxford Physics: 3rd Year, Atomic PhysicsOxford Physics: 3rd Year, Atomic PhysicsMagnetic field effects on hyperfine structure Oxford Physics: 3rd Year, Atomic PhysicsHyperfine structure in Magnetic Fields Hyperfine Electron/Field Nuclear spin/Field interaction interaction interaction Oxford Physics: 3rd Year, Atomic PhysicsWeak field effect on hyperfine structure I and J precess rapidly around F. F precesses slowly around B ext I, J, F and M F are good quantum numbers μ F Oxford Physics: 3rd Year, Atomic PhysicsOnly contribution to μ is F component of μ along F J μ = g μ J.F x F F J B FF magnitude direction Find this using g = g x J.F F J Vector Model 2 F Oxford Physics: 3rd Year, Atomic Physicsg = g x J.F F J I F 2 F J F = I + J 2 2 2 I = F + J –2J.F J.F = ½F(F+1) + J(J+1) – I(I+1) Oxford Physics: 3rd Year, Atomic PhysicsΔE = N.B. notes error eqn 207 Each hyperfine level is split by g term F Ground level of Na: J = 1/2 ; I = 3/2 ; F = 1 or 2 F = 2: g = ½ ; F F = 1: g = ½ F Oxford Physics: 3rd Year, Atomic PhysicsSign inversion of g for F = 1 and F = 2 F J = 1/2 F = 2 J = 1/2 I = 3/2 I = 3/2 F = 1 J.F positive J.F negative Oxford Physics: 3rd Year, Atomic PhysicsStrong field effect on hfs. ΔE = J precesses rapidly around B (zaxis) ext I tries to precess around J but can follow only the time averaged component along zaxis i.e. J z So A I.J term → A M M J J I J Oxford Physics: 3rd Year, Atomic PhysicsDominant term Strong field effect on hfs. Energy Na ground state Oxford Physics: 3rd Year, Atomic PhysicsStrong field effect on hfs. Energy: ΔE = J precesses around field B ext I tries to precess around J I precesses around what it can “see” of J: The zcomponent of J: J Z Oxford Physics: 3rd Year, Atomic PhysicsMagnetic field effects on hfs Weak field: F, M are good quantum nos. F Resolve μ along F to get effective magnetic moment and g J F ΔE(F,M ) = g μ M B F F B F ext → “Zeeman” splitting of hfs levels Strong field: M and M are good quantum nos. I J J precesses rapidly around B ; ext I precesses around zcomponent of J i.e. what it can “see” of J ΔE(M ,M ) = g μ M B + A M M B ext J I J J J I J → hfs of “Zeeman” split levels Oxford Physics: 3rd Year, Atomic PhysicsLecture 8 • Xrays: excitation of “innershell” electrons • High resolution laser spectroscopy The Doppler effect Laser spectroscopy “Dopplerfree” spectroscopy Oxford Physics: 3rd Year, Atomic PhysicsX – Ray Spectra Oxford Physics: 3rd Year, Atomic PhysicsCharacteristic Xrays • Wavelengths fit a simple series formula • All lines of a series appear together – when excitation exceeds threshold value • Threshold energy just exceeds energy of shortest wavelength Xrays • Above a certain energy no new series appear. Oxford Physics: 3rd Year, Atomic PhysicsEjected electron Generation of characteristic Xrays Xray Incident high voltage electron e e Oxford Physics: 3rd Year, Atomic PhysicsXray series Oxford Physics: 3rd Year, Atomic PhysicsXray spectra for increasing electron impact energy Kthreshold Lthreshold Wavelength E E E 3 2 1 Max voltage Oxford Physics: 3rd Year, Atomic Physics Xray Intensity2 Binding energy for electron in hydrogen = R/n 2 2 Binding energy for “hydrogenlike” system = RZ /n Screening by other electrons in inner shells: Z → (Z –σ) Binding energy of innershell electron: 2 2 E = R(Z –σ) / n n Transitions between innershells: 2 2 2 2 E E = ν = R(Z –σ ) / n (Z –σ ) / n n m i i j j Oxford Physics: 3rd Year, Atomic PhysicsFine structure of Xrays Oxford Physics: 3rd Year, Atomic PhysicsXray absorption spectra Oxford Physics: 3rd Year, Atomic PhysicsAuger effect Oxford Physics: 3rd Year, Atomic PhysicsHigh resolution laser spectroscopy Oxford Physics: 3rd Year, Atomic PhysicsDoppler broadening Doppler Shift: MaxwellBoltzmann distribution of Atomic speeds Distribution of Intensity Doppler width Oxford Physics: 3rd Year, Atomic Physics Notes errorCrossed beam Spectroscopy Oxford Physics: 3rd Year, Atomic PhysicsSaturation effect on absorption Absorption profile for weak probe Absorption profile for weak probe – with strong pump at ω o Strong pump at ω reduces population of ground state for L atoms Doppler shifted by (ω –ω ). L o Hence reduced absorption for this group of atoms. Oxford Physics: 3rd Year, Atomic PhysicsSaturation effect on absorption Absorption of Absorption of weak probe strong pump ωω L L Probe and pump laser at same frequency ω L But propagating in opposite directions Probe Doppler shifted down = Pump Doppler shifted up. Hence probe and pump “see” different atoms. Oxford Physics: 3rd Year, Atomic PhysicsSaturation of “zero velocity” group at ω O Counterpropagating pump and probe “see” same atoms at ω = ω L O i.e. atoms moving with zero velocity relative to light Oxford Physics: 3rd Year, Atomic PhysicsSaturation spectroscopy Oxford Physics: 3rd Year, Atomic PhysicsPrinciple of Dopplerfree twophoton absorption Photon Doppler shifted up + Photon Doppler shifted down Oxford Physics: 3rd Year, Atomic PhysicsTwophoton absorption spectroscopy Oxford Physics: 3rd Year, Atomic PhysicsDopplerfree spectroscopy of molecules in high temperature flames Oxyacetylene Torch 3000K Oxford Physics: 3rd Year, Atomic PhysicsDopplerfree spectrum of OH molecule in a flame Oxford Physics: 3rd Year, Atomic PhysicsThe End Oxford Physics: 3rd Year, Atomic Physics
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