Atomic Physics 3 rd year B1 P. Ewart Oxford Physics: 3rd Year, - - PowerPoint PPT Presentation

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Atomic Physics 3 rd year B1 P. Ewart Oxford Physics: 3rd Year, - - PowerPoint PPT Presentation

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Atomic Physics 3 rd 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,

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Oxford Physics: 3rd Year, Atomic Physics

Atomic Physics

3rd year B1

  • P. Ewart
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SLIDE 2

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

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Oxford Physics: 3rd Year, Atomic Physics

Atomic Physics:

  • Astrophysics
  • Plasma Physics
  • Condensed Matter
  • Atmospheric Physics
  • Chemistry
  • Biology

Technology

  • Street lamps
  • Lasers
  • Magnetic Resonance Imaging
  • Atomic Clocks
  • Satellite navigation: GPS
  • etc
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Astrophysics

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Condensed Matter

Zircon mineral crystal C60 Fullerene

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Snow crystal

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Lasers

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Biology

DNA strand

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Oxford Physics: 3rd Year, Atomic Physics

  • How we study atoms:

– emission and absorption of light – spectral lines

  • Atomic orders of magnitude
  • Basic structure of atoms

– approximate electric field inside atoms

Lecture 1

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Oxford Physics: 3rd Year, Atomic Physics

ψ1 ψ2

ψ( ) = + t

ψ ψ

1 2

IΨ( ) t I

2

Ψ( ) t Ψ( τ) t+

Oscillating charge cloud: Electric dipole

I I Ψ( + τ) t

2

Atomic radiation

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Oxford Physics: 3rd Year, Atomic Physics

Spectral Line Broadening

Homogeneous e.g. Lifetime (Natural) Collisional (Pressure) Inhomogeneous e.g. Doppler (Atomic motion) Crystal Fields

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Oxford Physics: 3rd Year, Atomic Physics

Lifetime (natural) broadening

N( ) t I( ) ω Time, t frequency

, ω

Intensity spectrum Number of excited atoms

Exponential decay Lorentzian lineshape

Electric field amplitude Fourier Transform E(t)

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Oxford Physics: 3rd Year, Atomic Physics

Lifetime (natural) broadening

N( ) t I( ) ω Time, t frequency

, ω

Intensity spectrum Number of excited atoms

Exponential decay Lorentzian lineshape

Electric field amplitude E(t)

`τ ~ 10-8s `Δν ~ 108 Hz

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Oxford Physics: 3rd Year, Atomic Physics

Collision (pressure) broadening

N( ) t I( ) ω Time, t frequency

, ω

Intensity spectrum Number of uncollided atoms

Exponential decay Lorentzian lineshape

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SLIDE 15

Oxford Physics: 3rd Year, Atomic Physics

Collision (pressure) broadening

N( ) t I( ) ω Time, t frequency

, ω

Intensity spectrum Number of uncollided atoms

Exponential decay Lorentzian lineshape

`τc ~ 10-10s `Δν ~ 1010 Hz

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SLIDE 16

Oxford Physics: 3rd Year, Atomic Physics

N(v) I( ) ω atomic speed, v frequency

, ω

Doppler broadening Distribution of atomic speed

Maxwell-Boltzmann distribution Gaussian lineshape

Doppler (atomic motion) broadening

` Typical Δν ~ 109 Hz

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Oxford Physics: 3rd Year, Atomic Physics

Atomic orders of magnitude Atomic energy: 10-19 J → ~2 eV Thermal energy:

1/40 eV

Ionization energy, H: 13.6 eV 109,737 cm-1 Atomic size, Bohr radius: 5.3 x 10-11m Fine structure constant, α = v/c: 1/137 Bohr magneton, μB: 9.27 x 10-24 JT-1 = Rydberg Constant

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Oxford Physics: 3rd Year, Atomic Physics

r U(r) 1/r ~Z/r “Actual” Potential

The Central Field

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Oxford Physics: 3rd Year, Atomic Physics

~Z Zeff 1

Radial position, r

Important region

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Lecture 2

  • The Central Field Approximation:

– physics of wave functions (Hydrogen)

  • Many-electron atoms

– atomic structures and the Periodic Table

  • Energy levels

– deviations from hydrogen-like energy levels – finding the energy levels; the quantum defect

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Oxford Physics: 3rd Year, Atomic Physics

Schrödinger Equation (1-electron atom) Hamiltionian for many-electron atom:

Individual electron potential in field of nucleus Electron-electron interaction

This prevents separation into Individual electron equations

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Oxford Physics: 3rd Year, Atomic Physics

Central potential in Hydrogen: V(r)~1/r, separation of ψ into radial and angular functions:

ψ = R(r)Ym

l(θ,φ)χ(ms)

Therefore we seek a potential for multi-electron atom that allows separation into individual electron wave-functions of this form

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Oxford Physics: 3rd Year, Atomic Physics

Electron – Electron interaction term:

Treat this as composed of two contributions: (a)a centrally directed part (b)a non-central Residual Electrostatic part

+ e- e-

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Oxford Physics: 3rd Year, Atomic Physics

Hamiltonian for Central Field Approximation

H1 = residual electrostatic interaction

Perturbation Theory Approximation: H1 << Ho

^ ^ ^ Central Field Potential

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Oxford Physics: 3rd Year, Atomic Physics

Zero order Schrödinger Equation: H0 ψ = Ε0 ψ

H0 is spherically symmetric so equation is separable - solution for individual electrons:

^ ^

Radial Angular Spin

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Oxford Physics: 3rd Year, Atomic Physics

Central Field Approximation:

What form does U(ri) take?

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SLIDE 28

+

  • Hydrogen atom

Z +

  • Many-electron atom

Z +

  • Z

+

  • Z

+

  • Z protons+ (Z – 1) electrons

U(r) ~ 1/r

Z protons

U(r) ~ Z/r

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Oxford Physics: 3rd Year, Atomic Physics

r U(r) 1/r ~Z/r “Actual” Potential

The Central Field

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Oxford Physics: 3rd Year, Atomic Physics

~Z Zeff 1

Radial position, r

Important region

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Oxford Physics: 3rd Year, Atomic Physics

Finding the Central Field

  • “Guess” form of U(r)
  • Solve Schrödinger eqn. → Approx ψ.
  • Use approx ψ to find charge distribution
  • Calculate Uc(r) from this charge distribution
  • Compare Uc(r) with U(r)
  • Iterate until Uc(r) = U(r)
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Oxford Physics: 3rd Year, Atomic Physics

Energy eigenvalues for Hydrogen:

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Oxford Physics: 3rd Year, Atomic Physics

1 2 3 4 n Energy

  • 13.6 eV

l = 0 1 2 s p d

H Energy level diagram

Note degeneracy in l

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Oxford Physics: 3rd Year, Atomic Physics

Revision of Hydrogen solutions: Product wavefunction: Spatial x Angular function Normalization : Eigenfunctions of angular momentum operators Eigenvalues

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Oxford Physics: 3rd Year, Atomic Physics

|Y1

+(

)| θ,φ

2

|Y1

0(

)| θ,φ

2

Angular momentum orbitals

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Oxford Physics: 3rd Year, Atomic Physics

|Y1

+(

)| θ,φ

2

|Y1

0(

)| θ,φ

2

Angular momentum orbitals Spherically symmetric charge cloud with filled shell

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Oxford Physics: 3rd Year, Atomic Physics 2 4 6 2 4 6 8 10 2 4 6 8 10 20 Zr a /

  • Zr a

/

  • Zr a

/

  • Ground state, n = 1, = 0

l

1st excited state, n = 2, l = 0 2nd excited state, n = 3, l = 2 n = 3, l = N = 2, l = 1 n = 3, l = 1 2 1.0 1 0.5 0.4

Radial wavefunctions

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Oxford Physics: 3rd Year, Atomic Physics

Radial 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

  • Peak probability (size) ~ n2
  • l = 0 wavefunction has (n-1) nodes
  • l = 1 has (n-2) nodes etc.
  • Maximum l=(n-1) has no nodes

Electrons arranged in “shells” for each n

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Oxford Physics: 3rd Year, Atomic Physics

The Periodic Table Shells specified by n and l quantum numbers Electron configuration

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Oxford Physics: 3rd Year, Atomic Physics

The Periodic Table

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Oxford Physics: 3rd Year, Atomic Physics

The Periodic Table Rare gases

He: 1s2 Ne: 1s22s22p6 Ar: 1s22s22p63s23p6 Kr: (…)4s24p6 Xe: (…..)5s25p6 Rn: (……)6s26p6

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Oxford Physics: 3rd Year, Atomic Physics

The Periodic Table Alkali metals

Li: 1s22s Na: 1s22s22p63s Ca: 1s22s22p63s23p64s Rb: (…)4s24p65s Cs: (…..)5s25p66s etc.

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Oxford Physics: 3rd Year, Atomic Physics

White light source Atomic Vapour Spectrograph Absorption spectrum

Absorption spectroscopy

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Oxford Physics: 3rd Year, Atomic Physics

Finding the Energy Levels

Hydrogen Binding Energy, Term Value

Tn = R n2

Many electron atom,

Tn = R . (n – δ(l))2 δ(l) is the Quantum Defect

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Oxford Physics: 3rd Year, Atomic Physics

Finding the Quantum Defect

  • 1. Measure wavelength
  • f absorption lines
  • 2. Calculate: = 1/
  • 3. "Guess" ionization potential, T(n ) i.e. Series Limit
  • 4. Calculate T(n ):

= T(n ) - T(n )

  • 5. Calculate: n* or

T(n ) = R /(n - )

λ ν

  • i

i

  • i

i

ν δ(l)

2

λ

δ(l) Δ(l)

T(n )

i

Quantum defect plot

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Oxford Physics: 3rd Year, Atomic Physics

Lecture 3

  • Corrections to the Central Field
  • Spin-Orbit interaction
  • The physics of magnetic interactions
  • Finding the S-O energy – Perturbation Theory
  • The problem of degeneracy
  • The Vector Model (DPT made easy)
  • Calculating the Spin-Orbit energy
  • Spin-Orbit splitting in Sodium as example
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Oxford Physics: 3rd Year, Atomic Physics

r U(r) 1/r ~Z/r “Actual” Potential

The Central Field

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Oxford Physics: 3rd Year, Atomic Physics

Corrections to the Central Field

  • Residual electrostatic interaction:
  • Magnetic spin-orbit interaction:

H2 = -μ.Borbit

^

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Oxford Physics: 3rd Year, Atomic Physics

Magnetic spin-orbit interaction

^

  • Electron moves in Electric field of nucleus,

so sees a Magnetic field Borbit

  • Electron spin precesses in Borbit with energy:
  • 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

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Oxford Physics: 3rd Year, Atomic Physics

Larmor 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

  • rbiting/spinning charge

ΔE = - μ.B

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Oxford Physics: 3rd Year, Atomic Physics

B parallel to l μ parallel to s Spin-Orbit interaction: Summary

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Oxford Physics: 3rd Year, Atomic Physics

?

Perturbation energy Radial integral Angular momentum operator How to find < s . l > using perturbation theory?

^ ^

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Oxford Physics: 3rd Year, Atomic Physics

Perturbation theory with degenerate states

Perturbation Energy: Change in wavefunction: So won’t work if Ei = Ej i.e. degenerate states. We need a diagonal perturbation matrix, i.e. off-diagonal elements are zero New wavefunctions: New eignvalues:

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Oxford Physics: 3rd Year, Atomic Physics

The Vector Model

Angular momenta represented by vectors: l2, s2 and j2, 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). Projections of vectors: l, s and j on z-axis are ml, ms and mj Constants of the Motion Good quantum numbers

lh mlh

z

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Oxford Physics: 3rd Year, Atomic Physics

Summary of Lecture 3: Spin-Orbit coupling

  • Spin-Orbit energy
  • Radial integral sets size
  • f the effect.
  • Angular integral < s . l > needs Degenerate Perturbation Theory
  • New basis eigenfunctions:
  • j and jz are constants of the motion
  • 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

j l s

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Oxford Physics: 3rd Year, Atomic Physics

lz l l

j j s s sz s

l

j j ( a ) i i ( d ) I i ( b ) i i ( c ) i i Z Z Z Z

(a) No spin-orbit coupling (b) Spin–orbit coupling gives precession around j (c) Projection of l on z is not constant (d) Projection of s on z is not constant ml and ms are not good quantum numbers Replace by j and mj Fixed in space

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Oxford Physics: 3rd Year, Atomic Physics

Vector model defines:

j l s

Vector triangle Magnitudes

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Oxford Physics: 3rd Year, Atomic Physics

Using basis states: | n, l, s, j, mj› to find expectation value: The spin-orbit energy is:

ΔE = βn,l x (1/2){j(j+1) – l(l+1) – s(s+1)}

∼ βn,l x ‹ ½ { j2 – l2 – s2 } ›

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Oxford Physics: 3rd Year, Atomic Physics

ΔE = βn,l x (1/2){j(j+1) – l(l+1) – s(s+1)}

Sodium 3s: n = 3, l = 0, no effect 3p: n = 3, l = 1, s = ½, -½, j = ½ or 3/2 ΔE(1/2) = β3p x ( - 1); ΔE(3/2) = β3p x (1/2) j = 3/2 j = 1/2

3p (no spin-orbit)

2j + 1 = 4 2j + 1 = 2 1/2

  • 1
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Oxford Physics: 3rd Year, Atomic Physics

  • Two-electron atoms:

the residual electrostatic interaction

  • Adding angular momenta: LS-coupling
  • Symmetry and indistinguishability
  • Orbital effects on electrostatic interaction
  • Spin-orbit effects

Lecture 4

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Oxford Physics: 3rd Year, Atomic Physics

Coupling of li and s to form L and S: Electrostatic interaction dominates

l1 is1 l2

s2

L S L = +

l l

1 2

S = +

s s

1 2

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Oxford Physics: 3rd Year, Atomic Physics

L = 1 S = 1 S = 1 S = 1 L = 1 L = 1 J = 2 J = 1 J = 0

Coupling of L and S to form J

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Na Configuration: 1s22s22p63s

Oxford Physics: 3rd Year, Atomic Physics

Magnesium: “typical” 2-electron atom Mg Configuration: 1s22s22p63s2 “Spectator” electron in Mg Mg energy level structure is like Na but levels are more strongly bound

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Oxford Physics: 3rd Year, Atomic Physics

Residual electrostatic interaction

3s4s state in Mg: Zero-order wave functions Perturbation energy:

?

Degenerate states

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Oxford Physics: 3rd Year, Atomic Physics

Linear combination of zero-order wave-functions Off-diagonal matrix elements:

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Oxford Physics: 3rd Year, Atomic Physics

Off-diagonal matrix elements: Therefore as required!

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Oxford Physics: 3rd Year, Atomic Physics

Energy level with no electrostatic interaction

J +K

  • K

Singlet Triplet

Effect of Direct and Exchange integrals

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Oxford Physics: 3rd Year, Atomic Physics

l2 l1

Orbital orientation effect on electrostatic interaction

Overlap of electron wavefunctions depends on orientation

  • f orbital angular momentum:

so electrostatic interaction depends on L

l1 l2 L L = + l l

1 2

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Oxford Physics: 3rd Year, Atomic Physics

Residual Electrostatic and Spin-Orbit effects in LS-coupling

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Oxford Physics: 3rd Year, Atomic Physics

1 1 1 3 3 3

S P D S P D

  • 2

1 3s S

2 1

3s3p P

1

1

3s3p P

3

2,1,0

3s3d D

1

2

4s 5s ns 3p

2

3pn

intercombination line (weak) resonance line (strong)

Term diagram of Magnesium

Singlet terms Triplet terms

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SLIDE 71

Oxford Physics: 3rd Year, Atomic Physics

HO H1 H2 H3: Nuclear Effects on atomic energy H3 << H2 << H1 << HO The story so far: Hierarchy of interactions

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Lecture 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 Rules
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Nuclear effects in atoms

Nucleus:

  • stationary
  • infinite mass
  • point

Corrections Nuclear spin → magnetic dipole interacts with electrons

  • rbits centre of mass with

electrons charge spread over nuclear volume

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SLIDE 74

Nuclear Spin interaction

Magnetic dipole ~ angular momentum μ = - γλħ μl = - gl μBl μs = - gsμΒs μΙ = - gIμΝI gI ~ 1 μΝ = μΒ x me/mP ~ μΒ / 2000

Perturbation energy:

Η3 = − μΙ . Bel ^

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Magnetic field of electrons: Orbital and Spin

Closed shells: zero contribution s orbitals: largest contribution – short range ~1/r3 l > 0, smaller contribution - neglect

Bel

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SLIDE 76

Bel = (scalar quantity) x J

Usually dominated by spin contribution in s-states: Fermi “contact interaction”. Calculable only for Hydrogen in ground state, 1s

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Coupling of I and J

Depends on I Depends on J Nuclear spin interaction energy: empirical Expectation value

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SLIDE 78

Vector model of nuclear interaction

F F F I I I J J J

I and J precess around F

F = I + J

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SLIDE 79

Hyperfine structure

Hfs interaction energy: Vector model result: Hfs energy shift: Hfs interval rule:

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SLIDE 80

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 → I

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SLIDE 81

Isotope effects

reduced mass Orbiting about centre of mass Orbiting about Fixed nucleus, infinite mass +

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SLIDE 82

Isotope effects

reduced mass Orbiting about centre of mass Orbiting about Fixed nucleus, infinite mass +

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SLIDE 83

Lecture 6

  • Selection Rules
  • Atoms in magnetic fields

– basic physics; atoms with no spin – atoms with spin: anomalous Zeeman Effect – polarization of the radiation

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SLIDE 84

Parity selection rule

Parity (-1)l must change Δl = + 1 N.B. Error in notes eqn (161)

  • r

r

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SLIDE 85

Configuration

Only one electron “jumps”

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SLIDE 86

Selection Rules:

Conservation of angular momentum

h h J1 J1 J2 = J1 J2 = J1

ΔL = 0, + 1 ΔS = 0 ΔMJ = 0, + 1

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Oxford Physics: 3rd Year, Atomic Physics

Atoms in magnetic fields

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Oxford Physics: 3rd Year, Atomic Physics

Effect of B-field

  • n an atom

with no spin

Interaction energy - Precession energy:

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SLIDE 89

Oxford Physics: 3rd Year, Atomic Physics

Normal Zeeman Effect Level is split into equally Spaced sub-levels (states) Selection rules on ML give a spectrum of the normal Lorentz Triplet Spectrum

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SLIDE 90

Oxford Physics: 3rd Year, Atomic Physics

Effect of B-field

  • n an atom

with spin-orbit coupling

Precession of L and S around the resultant J leads to variation of projections of L and S

  • n the field direction
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Oxford Physics: 3rd Year, Atomic Physics

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SLIDE 92

Oxford Physics: 3rd Year, Atomic Physics

Total magnetic moment does not lie along axis

  • f J.

Effective magnetic moment does lie along axis of J, hence has constant projection on Bext axis

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SLIDE 93

Oxford Physics: 3rd Year, Atomic Physics

Interaction energy Effective magnetic moment Perturbation Theory: expectation value of energy Energy shift of MJ level

Perturbation Calculation of Bext effect on spin-orbit level

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Oxford Physics: 3rd Year, Atomic Physics

Projections of L and S

  • n J are given by

Vector Model Calculation of Bext effect on spin-orbit level

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SLIDE 95

Oxford Physics: 3rd Year, Atomic Physics

Vector Model Calculation of Bext effect on spin-orbit level

Perturbation Theory result

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SLIDE 96

Oxford Physics: 3rd Year, Atomic Physics

Anomalous Zeeman Effect: 3s2S1/2 – 3p2P1/2 in Na

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SLIDE 97

Oxford Physics: 3rd Year, Atomic Physics

Polarization of Anomalous Zeeman components associated with Δm selection rules

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SLIDE 98

Oxford Physics: 3rd Year, Atomic Physics

Lecture 7

  • Magnetic effects on fine structure
  • Weak field
  • Strong field
  • Magnetic field effects on hyperfine structure:
  • Weak field
  • Strong field
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SLIDE 99

Oxford Physics: 3rd Year, Atomic Physics

Summary of magnetic field effects on atom with spin-orbit interaction

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SLIDE 100

Oxford Physics: 3rd Year, Atomic Physics

Total magnetic moment does not lie along axis

  • f J.

Effective magnetic moment does lie along axis of J, hence has constant projection on Bext axis

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SLIDE 101

Oxford Physics: 3rd Year, Atomic Physics

Interaction energy Effective magnetic moment Perturbation Theory: expectation value of energy Energy shift of MJ level

Perturbation Calculation of Bext effect on spin-orbit level

What is gJ ?

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SLIDE 102

Oxford Physics: 3rd Year, Atomic Physics

Projections of L and S

  • n J are given by

Vector Model Calculation of Bext effect on spin-orbit level

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SLIDE 103

Oxford Physics: 3rd Year, Atomic Physics

Vector Model Calculation of Bext effect on spin-orbit level

Perturbation Theory result

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SLIDE 104

Oxford Physics: 3rd Year, Atomic Physics

Anomalous Zeeman Effect: 3s2S1/2 – 3p2P1/2 in Na gJ(2P1/2) = 2/3 gJ(2S1/2) = 2 Landé g-factor

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SLIDE 105

Oxford Physics: 3rd Year, Atomic Physics

Strong field effects on atoms with spin-orbit coupling

Spin and Orbit magnetic moments couple more strongly to Bext than to each other.

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SLIDE 106

Oxford Physics: 3rd Year, Atomic Physics

Strong field effect on L and S.

L and S precess independently around Bext

Spin-orbit coupling is relatively insignificant mL and mS are good quantum numbers

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SLIDE 107

Oxford Physics: 3rd Year, Atomic Physics

Splitting of level in strong field: Paschen-Back Effect N.B. Splitting like Normal Zeeman Effect Spin splitting = 2 x Orbital gS = 2 x gL

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SLIDE 108

Oxford Physics: 3rd Year, Atomic Physics

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SLIDE 109

Oxford Physics: 3rd Year, Atomic Physics

Magnetic field effects on hyperfine structure

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SLIDE 110

Oxford Physics: 3rd Year, Atomic Physics

Hyperfine structure in Magnetic Fields

Hyperfine interaction Electron/Field interaction Nuclear spin/Field interaction

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SLIDE 111

Oxford Physics: 3rd Year, Atomic Physics

Weak field effect on hyperfine structure

I and J precess rapidly around F. F precesses slowly around Bext I, J, F and MF are good quantum numbers μF

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SLIDE 112

Oxford Physics: 3rd Year, Atomic Physics

Only contribution to μF is component of μJ along F

μF = -gJμB J.F x F F F

magnitude direction

gF = gJ x J.F F2

Find this using Vector Model

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SLIDE 113

Oxford Physics: 3rd Year, Atomic Physics

gF = gJ x J.F F2 F I J F = I + J I2 = F2 + J2 – 2J.F J.F = ½{F(F+1) + J(J+1) – I(I+1)}

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SLIDE 114

Oxford Physics: 3rd Year, Atomic Physics

N.B. notes error eqn 207 ΔE =

Each hyperfine level is split by gF term

Ground level of Na: J = 1/2 ; I = 3/2 ; F = 1 or 2 F = 2: gF = ½ ; F = 1: gF = -½

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SLIDE 115

Oxford Physics: 3rd Year, Atomic Physics

Sign inversion of gF for F = 1 and F = 2 I = 3/2 J = 1/2 F = 2 I = 3/2 J = -1/2 F = 1

J.F positive J.F negative

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SLIDE 116

Oxford Physics: 3rd Year, Atomic Physics

Strong field effect on hfs. J precesses rapidly around Bext (z-axis) I tries to precess around J but can follow only the time averaged component along z-axis i.e. Jz So AJ I.J term → AJ MIMJ ΔE =

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SLIDE 117

Oxford Physics: 3rd Year, Atomic Physics

Strong field effect on hfs.

Na ground state

Energy Dominant term

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SLIDE 118

Oxford Physics: 3rd Year, Atomic Physics

ΔE =

Strong field effect on hfs.

Energy:

J precesses around field Bext I tries to precess around J I precesses around what it can “see” of J: The z-component of J: JZ

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SLIDE 119

Oxford Physics: 3rd Year, Atomic Physics

Magnetic field effects on hfs

Weak field: F, MF are good quantum nos. Resolve μJ along F to get effective magnetic moment and gF ΔE(F,MF) = gFμBMFBext → “Zeeman” splitting of hfs levels Strong field: MI and MJ are good quantum nos. J precesses rapidly around Bext; I precesses around z-component of J i.e. what it can “see” of J ΔE(MJ,MI) = gJμBMJBext + AJMIMJ → hfs of “Zeeman” split levels

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SLIDE 120

Oxford Physics: 3rd Year, Atomic Physics

Lecture 8

  • X-rays: excitation of “inner-shell” electrons
  • High resolution laser spectroscopy
  • The Doppler effect
  • Laser spectroscopy
  • “Doppler-free” spectroscopy
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SLIDE 121

Oxford Physics: 3rd Year, Atomic Physics

X – Ray Spectra

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Oxford Physics: 3rd Year, Atomic Physics

  • 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 X-rays

  • Above a certain energy no new series appear.

Characteristic X-rays

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Oxford Physics: 3rd Year, Atomic Physics

Generation of characteristic X-rays

Ejected electron X-ray e- e-

Incident high voltage electron

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Oxford Physics: 3rd Year, Atomic Physics

X-ray series

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Oxford Physics: 3rd Year, Atomic Physics

Wavelength X-ray Intensity X-ray spectra for increasing electron impact energy L-threshold K-threshold

Max voltage

E1 E2> E3>

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Oxford Physics: 3rd Year, Atomic Physics

Binding energy for electron in hydrogen = R/n2 Binding energy for “hydrogen-like” system = RZ2/n2 Screening by other electrons in inner shells: Z → (Z – σ) Binding energy of inner-shell electron: En = R(Z – σ)2 / n2 Transitions between inner-shells: En - Em= ν = R{(Z – σi)2 / ni

2 - (Z – σj)2 / nj 2}

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Oxford Physics: 3rd Year, Atomic Physics

Fine structure

  • f X-rays
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Oxford Physics: 3rd Year, Atomic Physics

X-ray absorption spectra

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Oxford Physics: 3rd Year, Atomic Physics

Auger effect

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Oxford Physics: 3rd Year, Atomic Physics

High resolution laser spectroscopy

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Oxford Physics: 3rd Year, Atomic Physics

Doppler broadening

Doppler Shift: Maxwell-Boltzmann distribution of Atomic speeds Distribution of Intensity Doppler width Notes error

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Oxford Physics: 3rd Year, Atomic Physics

Crossed beam Spectroscopy

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Oxford Physics: 3rd Year, Atomic Physics

Absorption profile for weak probe Absorption profile for weak probe – with strong pump at ωo Strong pump at ωL reduces population of ground state for atoms Doppler shifted by (ωL – ωo). Hence reduced absorption for this group of atoms.

Saturation effect on absorption

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Oxford Physics: 3rd Year, Atomic Physics

Absorption of weak probe

ωL

Probe and pump laser at same frequency ωL But propagating in opposite directions Probe Doppler shifted down = Pump Doppler shifted up. Hence probe and pump “see” different atoms.

Saturation effect on absorption

Absorption of strong pump

ωL

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Oxford Physics: 3rd Year, Atomic Physics

Saturation of “zero velocity” group at ωO

Counter-propagating pump and probe “see” same atoms at ωL = ωO i.e. atoms moving with zero velocity relative to light

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Oxford Physics: 3rd Year, Atomic Physics

Saturation spectroscopy

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Oxford Physics: 3rd Year, Atomic Physics

Photon Doppler shifted up + Photon Doppler shifted down

Principle of Doppler-free two-photon absorption

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Oxford Physics: 3rd Year, Atomic Physics

Two-photon absorption spectroscopy

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Oxford Physics: 3rd Year, Atomic Physics

Doppler-free spectroscopy of molecules in high temperature flames

Oxy-acetylene Torch ~ 3000K

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Oxford Physics: 3rd Year, Atomic Physics

Doppler-free spectrum of OH molecule in a flame

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Oxford Physics: 3rd Year, Atomic Physics

The End