Resonant photon absorption The Mossbauer effect Photon attenuation Radiation attenuation by: --...
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Transcript of Resonant photon absorption The Mossbauer effect Photon attenuation Radiation attenuation by: --...
Resonant photon absorption
The Mossbauer effect
Photon attenuation
Radiation attenuation by:-- photoelectric effect-- compton scattering (E << 1.02 MeV)
€
I Δx( ) = I 0( ) e− μ pe+μ cs( )Δx
Atomic interactions
Source Detector
Absorber
x€
Eγ
Photon attenuation
Consider nuclear resonant absorption
Source Detector
Absorber
x€
Eγ
0.0
E*
0.0
E*
Assume source and absorber are identical
€
Eγ = E*
€
E* = Eγ
Kinematics
Assume source and absorber are identical
Source Detector
Absorber
x€
Eγ
0.0
E*
0.0
E*
€
Eγ = E*
€
E* = Eγ
€
TR =pγ
2
2MR
€
Eγ = E* − TR
€
TR =pγ
2
2MR
€
rp γ
€
rp R
emission
€
rp γ
€
rp R
absorption
€
Eγ + 2TR = E*
for resonant absorption
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
Source Absorber
Ignore energy scale
Estimates
€
TR =pγ
2
2MR≈
2MeV 2
2 57 ×103 MeV( )≈1.75 ×10−5 MeV
Consider an 57Fe source 57Co 57Co Fe
€
Eγ = E* − TR ≈14.413 KeV −1.75 ×10−2KeV
Eγ =14.396 KeV
0.0
E*
0.0
E*
€
Γ ≈hτ=
00.659 ×10−18KeV s
98 ×10−9 s
Γ ≈ 0.66 ×10−11KeV
Natural width of the state
Enter -- Mr. Mossbauer
Place 57Fe source bound in a metal matrix
€
TR =pγ
2
2MR≈
pγ2
2 ∞≈ 0
€
Eγ = E* − TR
Eγ = E*
Place 57Fe absorber bound in a metal matrix
€
TR =pγ
2
2MR≈
pγ2
2 ∞≈ 0
€
Eγ = E* − TR
Eγ = E*
Resonant Absorption!
Kinematics
Assume source and absorber are identical
-v+v
Source Detector
Absorber
x€
Eγ
0.0
E*
0.0
E*
€
Eγ = E*
€
E* = Eγ
move source
move source
€
Eγ' = Eγ + ED
ED ≈ Eγv
c
Doppler shift frequency:h’- h = ED
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
Source Absorber
-v
no resonant
absorption
Source Absorber
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
no resonant
absorption
Source Absorber
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
small resonant
absorption
Source Absorber
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
more resonant
absorption
Source Absorber
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
v = 0.0
maximum resonant
absorption
Source Absorber
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
less resonant
absorption
Source Absorber
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
small resonant
absorption
Source Absorber
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
no resonant
absorption
Source Absorber
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
no resonant
absorption
Transmission curve
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
5 10 15 20 25 30 35
Energy (keV)
P(E)
Resulting transmission curve
Kinematics
Assume source and absorber are NOT
identical
Source Detector
Absorber
x€
Eγ
0.0
Ea*
0.0
Es*
Doppler kinematics
Assume source and absorber are NOT
identical
Resonant absorption
€
Eγ' = Ea
*
ED = Es* − Ea
*
when -
-v+v
Source Detector
Absorber
x€
Eγ
0.0
Ea*
0.0
Es*
€
Eγ' = Eγ + ED
ED ≈ Eγv
c
move absorber!
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
Source Absorber transition energy shifted
-v
no resonant
absorption
Source
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
small resonant
absorption
Absorber transition energy shifted
Source
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
more resonant
absorption
Absorber transition energy shifted
Source
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
more resonant
absorption
Absorber transition energy shifted
Source
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
v = 0.0
less resonant
absorption
Absorber transition energy shifted
Source
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
smallresonant
absorption
Absorber transition energy shifted
Source
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
no resonant
absorption
Absorber transition energy shifted
Source
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
no resonant
absorption
Absorber transition energy shifted
Source
Quantum state for source and absorber
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35
Energy (keV)
P(E)
-v
no resonant
absorption
Absorber transition energy shifted
Transmission curve
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
5 10 15 20 25 30 35
Energy (keV)
P(E)
Doppler energy shifted
€
ED = Eγv
c
“Isotope shift”
€
v = 0
Isotope shift
Resonant absorption
€
Eγ' = Ea
*
ED = Es* − Ea
*
when -
-v+v
Source Detector
Absorber
x€
Eγ
move absorber!
0.0
Ea*
0.0
Es*
Isotope shift:Level shifts due to atomic electronic
charge distribution in the
nucleus.
Constant velocity data
57FeWhat is the J for the ground state and the 14.4 Kev state?
ENSDF/NNDS
What is the multipolarity of the transition?
What is the degeneracy for the -- ground state and the -- 14.4 Kev state?
If there is a B field, then we can have a
nuclear Zeeman effect that will
remove the degeneracies
If there is a B field, then we can have a
nuclear Zeeman effect that will
remove the degeneracies
57Fe+v-v
move source with constant acceleration
Source Detector
Absorber
x€
Eγ
€
E1/2
€
E3/2
0.0
Es*
€
3
2
−
€
1
2
−
€
+3
2
€
−3
2€
+1
2
€
−1
2
m-sublevels
€
−1
2
€
+1
2
Dipole transition selection rules
€
I =1
€
m = ±1,0
Mossbauer resonant absorption with constant acceleration
-v +v0
maximum +v
maximum -vtim
e v = 0
v = 0
v = 0
Source velocity curve
Source displacement curve
data
v
t
Use MCS/MCAUse MCS/MCA
€
t
€
v= dwell time= one channel
Possible absorption transitions
Source Detector
Absorber
x€
Eγ
€
E1/2
€
E3/2
0.0
Es*
€
3
2
−
€
1
2
−
€
+3
2
€
−3
2€
+1
2
€
−1
2
m-sublevels
€
−1
2
€
+1
2
Possible absorption transitions
€
E1/2
€
E3/2
€
3
2
−
€
1
2
−
€
+3
2
€
−3
2€
+1
2
€
−1
2
m-sublevels
€
−1
2
€
+1
2
6 54 32 1
€
E1/2 > ΔE3/2
€
1,3 = ΔE3/2
€
3,5 = ΔE3/2
€
E3,6 = ΔE1/2
€
E1,4 = ΔE1/2
Possible absorption transitions
€
E1/2 > ΔE3/2
€
1,3 = ΔE3/2
€
3,5 = ΔE3/2
€
E3,6 = ΔE1/2
€
E1,4 = ΔE1/2
€
2,4 = ΔE3/2
€
4,6 = ΔE3/2
Compare these predictions with the measurements…Compare these predictions with the measurements…
…follow guidelines in Problem. 10.C. and eventually determine
€
E3/2
€
E1/2
The Pound-Rebecca Experiment
Be prepared to explain what the experiment discovered and how the Mossbauer resonant
photon absorption was essential to the measurement.
Be prepared to explain what the experiment discovered and how the Mossbauer resonant
photon absorption was essential to the measurement.
Possible absorption transitions
€
E1/2
€
E3/2
€
3
2
−
€
1
2
−
€
+3
2
€
−3
2€
+1
2
€
−1
2
m-sublevels
€
−1
2
€
+1
2
6 54 32 1
€
E1/2 > ΔE3/2
€
1,3 = ΔE3/2
€
3,5 = ΔE3/2
€
E3,6 = ΔE1/2
€
E1,4 = ΔE1/2
Case 1
Possible absorption transitions
€
E1/2
€
E3/2
€
3
2
−
€
1
2
−
€
+3
2
€
−3
2€
+1
2
€
−1
2
m-sublevels
€
−1
2
€
+1
2
5 63 41 2
€
E1/2 < ΔE3/2
€
1,3 = ΔE3/2
€
3,5 = ΔE3/2
€
E4,5 = ΔE1/2
€
E2,3 = ΔE1/2
Case 2
Possible absorption transitionsm-sublevels
€
E1/2 < ΔE3/2
€
1,2 = ΔE3/2
€
2,4 = ΔE3/2
€
E2,3 = ΔE1/2
€
E4,5 = ΔE1/2
€
E1/2
€
E3/2
€
3
2
−
€
1
2
−
€
+3
2
€
−3
2€
+1
2
€
−1
2
€
+1
2
€
−1
2
6 5 23 14
Case 3
Possible absorption transitionsm-sublevels
€
E1/2 > ΔE3/2
€
1,2 = ΔE3/2
€
E2,3 = ΔE3/2
€
E2,4 = ΔE1/2
€
E3,5 = ΔE1/2
€
E1/2
€
E3/2
€
3
2
−
€
1
2
−
€
+3
2
€
−3
2€
+1
2
€
−1
2
€
+1
2
€
−1
2
6 5 24 13
Case 4