Resonant photon absorption
The Mossbauer effect
Photon attenuation
E
Source
Detector
x

Absorber
Radiation attenuation by:
-- photoelectric effect
-- compton scattering
(E << 1.02 MeV)



  pe   cs x
Ix   I0 e
Atomic interactions
Photon attenuation
E
Source
x

Detector
Absorber
E *  E
E*
E*
0.0
0.0
E  E *
Consider nuclear
resonant absorption
Assume source and
absorber are identical
TR 
Kinematics
p2
2M R
p
pR
p
pR
emission


TR 
p2
2M R
absorption
E


Source
x


Detector
Absorber
E*
E*
 for resonant
absorption
0.0
E  2TR  E *
E  E *  TR
0.0
E *  E
E  E *

Assume source and
absorber are identical
Quantum state for source and absorber
0.6
0.5
P(E)
0.4
0.3
0.2
0.1
Ignore
energy
scale
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
Estimates
Consider an 57Fe source
TR 
p2
2M R


2MeV 2
2 57 10 3 MeV

57Co
57Co
Fe
 1.75 105 MeV
E   E *  TR  14.413 KeV 1.75 102 KeV
E   14.396 KeV
E*
E*

0.0
0.0
  0.66 1011 KeV


00.659 1018 KeV s
98 109 s
Natural width of the state

Enter -- Mr. Mossbauer
Place 57Fe source bound in a metal matrix
TR 
p2
2M R

p2
2
0
E  E *  TR
E  E *
Place 57Fe absorber bound in a metal matrix
TR 
p2
2M R

p2
2
0
E  E *  TR
E  E *
Resonant
Absorption!
Kinematics
move source
+v
-v
E
Source

Doppler shift
 frequency:
h’- h = ED
E *  E
x
Absorber
Detector
move source
E*
E*
E'  E  E D
0.0
0.0
v
E D  E
c
E  E *
Assume source and
absorber are identical
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
no
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
no
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
small
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
more
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
v = 0.0
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
maximum
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
less
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
small
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
no
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
no
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
Energy ( keV)
Source
Absorber
35
Transmission curve
0.45
0.4
0.35
P(E)
0.3
0.25
0.2
0.15
0.1
0.05
0
5
10
15
20
25
30
Energy ( keV)
Resulting transmission curve
35
Kinematics
E
Source
x

Detector
Absorber
Es*
0.0
Ea*
0.0
Assume source and
absorber are NOT
identical
Doppler kinematics
+v
move absorber!
-v
E
Source
x

Absorber
Es*
when -
0.0
Ea*
0.0
E'  E a*
E D  E s*  E a*
Resonant absorption

Detector
E'  E  E D
v
E D  E
c
Assume source and
absorber are NOT
identical
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
no
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
small
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
more
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
more
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
v = 0.0
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
less
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
small
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
no
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
no
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
-v
Quantum state for source and absorber
0.6
0.5
0.4
P(E)
no
resonant
absorption
0.3
0.2
0.1
0
5
10
15
20
25
30
35
Energy ( keV)
Source
Absorber transition energy
shifted
Transmission curve
0.45
0.4
0.35
v0
P(E)
0.3
0.25
0.2
0.15
0.1
E D  E

0.05
0
5
10
15
20
25
v
c
30
35
Energy (keV)

“Isotope shift”
Doppler energy shifted
Isotope shift
+v
-v
move absorber!
E
Source
x

Absorber
Es*
when -
0.0
Ea*
0.0
E'  E a*
E D  E s*  E a*
Resonant absorption
Detector
Isotope shift:
Level shifts due to
atomic electronic
charge
distribution in the
nucleus.
Constant velocity
data
57Fe
What 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
move source with
constant acceleration
-v
57Fe
+v
E
Source
Detector
x

Absorber
Es*
3
2
m-sublevels
E 3/ 2


0.0

1
2

 1

2
 1

2


E1/ 2


3
2 1

2
1

3 2
2
Dipole transition selection rules
I  1


m  1,0
Mossbauer resonant absorption
with constant acceleration
time
t
-v
v
Use MCS/MCA
0
+v
 t = dwell time
v = one channel
Source velocity curve

v =0
maximum +v
v=0
maximum -v
v=0
data
Source displacement curve
Possible absorption transitions
E
Source
Detector
x

Absorber
Es*
3
2
m-sublevels
E 3/ 2


0.0

1
2

 1

2
 1

2


E1/ 2


3
2 1

2
1

3 2
2
Possible absorption transitions
E1/2  E3/2
m-sublevels
E 3/ 2
3
2

1
2

1,3  E 3/ 2

6 4 2 5 3 1

 3,5  E 3 / 2
 1

2
 1

2

E1/ 2
E 3,6  E1/ 2

3

2 1

2
1

3 2

2
E1,4  E1/ 2
Possible absorption transitions
E1/2  E3/2
1,3  E 3/ 2
 3,5  E 3 / 2
 2,4  E 3/ 2
 4,6  E 3/ 2
E 3,6  E1/ 2
E1,4  E1/ 2



Compare these predictions with the measurements…

…follow guidelines in Problem. 10.C. and eventually
determine E1/ 2 E 3/ 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.
Possible absorption transitions
E1/2  E3/2
m-sublevels
Case 1
E 3/ 2
3
2

1
2

1,3  E 3/ 2

6 4 2 5 3 1

 3,5  E 3 / 2
 1

2
 1

2

E1/ 2
E 3,6  E1/ 2

3

2 1

2
1

3 2

2
E1,4  E1/ 2
Possible absorption transitions
E1/2  E3/2
m-sublevels
Case 2
E 3/ 2
3
2

1
2

1,3  E 3/ 2

5 3 1 6 4 2

 3,5  E 3 / 2
 1

2
 1

2

E1/ 2
E 4,5  E1/ 2

3

2 1

2
1

3 2

2
E 2,3  E1/ 2
Possible absorption transitions
E1/2  E3/2
m-sublevels
Case 3
E 3/ 2
3
2

1
2

1,2  E 3 / 2
6 5 3

4 2 1

 2,4  E 3/ 2
 1

2
 1

2

E1/ 2
E 2,3  E1/ 2

3

2 1

2
1

3 2

2
E 4,5  E1/ 2
Possible absorption transitions
E1/2  E3/2
m-sublevels
Case 4
E 3/ 2
3
2

1
2

1,2  E 3 / 2
6 5 4

3 2 1

E 2,3  E 3/ 2
 1

2
 1

2

E1/ 2
E 2,4  E1/ 2

3

2 1

2
1

3 2

2
E 3,5  E1/ 2