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Resonance fluorescence absorption (& re-emission) of s emitted by nuclei of the same type. g. Radiation from a sample of excited atoms illuminates a collection of identical (ground state) atoms which can absorb them to become excited themselves. - PowerPoint PPT Presentation
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When an nucleus releases the transition energy Q (say 14.4 keV) in a -decay, the does not carry the full 14.4 keV.
Conservation of momentum requires the nucleus recoil.
Resonance fluorescence absorption (& re-emission) of s emitted by nuclei of the same type
Radiation from a sample of excited atoms illuminates a collection of identical (ground state) atomswhich can absorb them to become excited themselves.
NTQE
ppN fi EEQ
Nmp
QE N
2
2
2
2
2 cm
EQ
N
If this change is large enough, the will not be absorbed by an identical nucleus. 2
2
2 cmp
QEN
emitted
In fact, for absorption, actually need to exceed the step between energylevels by enough to provide the nucleus with the needed recoil:
p=E/cTN =
pN2
2mN
= p2
2mN
The photon energy is mismatched by
2
2
2 cmE
QEN
absorbed
2
2
2
2
22
cmE
cmE
NN
For atomic resonance experiments, note Q ~ few eV (for visible transitions) and mN ~ Au ~ A1000 MeV
MeV
eVTN 1000)10010()101( 2
1012 – 1010eV
But how precisely fixed is the emitted energy anyway?
Recall:
there is a “natural width” to the energy, related to how stable was the initial energy state.
For atomic transitions, the typical lifetime is ~108 sec
The energy uncertainty eV10 7 E
Notice the uncertainty E >> 2TN
Q
2TN
with an enormous amount of overlap allowing resonance fluorescence
For NUCLEAR resonance experiments Q ~ few MeV (for -ray emissions)
with mN ~ Au ~ A1000 MeV
MeV
MeVkeVTN 1000)10010()10100( 2
0.1 – 104eV
For atomic transitions, the typical lifetime is ~1010 sec
The energy uncertainty eV10 5 E
This time the uncertainty E << 2TN
Q
2TN
which provides no overlap allowing resonance fluorescence
57Co7/2
5/2
EC
=270d
57Fe1/23/2 14.4keV
136keV
=10-7s
As an example consider the distinctive 14.4 keV from 57Fe.
The recoil energy of the iron-57 nucleus is
this is 5 orders of magnitude greater than the natural linewidth of the iron transition which produced the photon!
eVGeV
keVcm
EE
Nrecoil
002.0)022.53(2
)4.14(
22
2
2
With = 107 s, =108 eV
~90% of the 57Fe* decays are through this intermediate level produce 14.4 keV s.
1958 Rudolf MössbauerWorking with 129-keV ray of 191Ir
Discovered by imbedding theradioactive samples in crystals, and cooling them, their tightly held crystal positionsprevented them from recoiling.
The energy of recoil had been absorbed by the lattice as a whole.
To keep the within its natural linewidth how many iron nuclei would have to recoil together in our example of 57Fe?
)022.53(2)4.14(10
28
GeVNkeVeVErecoil
000,200N
Very small compared to Avogadro's number! (In fact a speck too small to be seen in a microscope).
Any tiny crystal within a 57Cobalt-containing piece of iron would meet the conditions for resonance absorption if cooled sufficiently.
You can also destroy that resonance by moving the source relative to the absorber and Doppler shifting the photons off resonance.
The Doppler shift of a photon is a relativistic shift given by
cvcvvv sourceobserved /1
/1
v is positive
for an approaching
source
)1()/1(
)/1)(/1()/1)(/1(
22 cvcvv
cvcvcvcvvv s
so
)/1( cvvv so If v/c <<1 this simplifies to
This can be written as
shift recoiling emissions to resonance by moving the source relative to the absorber and Doppler shifting the photons to the necessary energy for absorption.
Continuing our 57Fe example: The source velocity necessary to shift the photon to resonance absorption energy is
This was in fact demonstrated with the source in a centrifuge
m/sec 42
4.14)(002.0 0
cvkeV
cvhvvvheV ss
Cool an embedded sample to produce recoilless emissionand drive the source or absorber to scan the resonance.
vibrator
servo-motorcontrols
dataacquisition
radioactivesource
absorbingsample detector
Continuing with our example of 57Fe :
Using the uncertainty in energy given by as a measure of how far you need to
Doppler shift frequencies to be off resonance:
cvkeVeV /4.1410 8
gives:0.0002 meter/sec = 2 mm/sec
Setting
Mossbauer Absorption of 191Ir129-keV gamma rays from iridium-191 were measured as a function of source velocity. A velocity of only about 1.5 cm/s was enough to drop the absorption to half its peak value. Sample and absorber were cooled to 88K.
A half-width of only about 0.65 x 10-5 electron volts makes this absorption an extremely sensitive test of any influence which would shift the frequency. It is sensitive enough to measure the Zeeman splittings from the magnetic field of the nucleus.
SourceAbsorber
Detector
191Irv
191Ir
The incredibly high resolution of the Mössbauer effect in 57Fe makes possible the measurement of the nuclear Zeeman effect .
O. C. Kistmer and A. W. Sunyar, Physical Review Letters, 4, 412(1960). The splittings are 11 orders of magnitude smaller than the nuclear transition energy!
Nuclear Hyperfine Interactions Observable with Mossbauer SpectroscopyObserved Effect Illustration Observed Spectrum
Isomer ShiftInteraction of the nuclear charge distribution with the electron cloud surrounding the nuclei in both the absorber and source
Zeeman Effect(Dipole Interaction)Interaction of the nuclear magnetic dipole moment with the external applied magnetic field on the nucleus.
Quadrupole SplittingInteraction of the nuclear electric quadrupole moment with the EFG and the nucleus
http://www.fastcomtec.com/fwww/moss.htm
http://www.cryoindustries.com/moss.htm
http://www.dwiarda.com/scientific/Moessbauer.html
Gravitational redshift A ``gedänken'' experiment first suggested by Einstein:
A particle of rest mass m is dropped to fall freely with an acceleration g from a tower of height h.
It reaches the ground with a velocity , so its total energy E, as measured by an observer at the foot of the tower is
ghv 2
).(
)(21
42
422
OO
mghmc
mvmcEbottom
Let the particle rebound elastically at the bottom and return.
Suppose the rebounding particle could be converted to a photon of energy Ebottom & upon its arrival at the top changed back into a
particle of rest mass m = E/c2.
).(
42
2
OmghmcE
mcE
bottom
top
Should mtop=mbottom? That would mean the mass is now greater than it began.
What must be true, even for the photon is
.)(
42
2
Omghmc
mcEE
bottom
top
)(
42
2
Omghmc
mcEE
bottom
top
242 /)(/11
mccghEE
bottom
top
O
.1 2c
ghEE
bottom
top
Since for photons we have Etop = htop
2/1 cghvbottomtop This implies a photon climbing in the earths gravitational field
will lose energy and consequently be redshifted.
2
2
2
/ ]/11[
/1
cghvcghv
cghvvv
bottom
bottom
bottombottomtopbottom
The redshift is:
2/ cghv
v
bottom
topbottom
In just 22.6 meters, the fractional redshift
is only 4.92 10-15 but using the Mössbauer effect on the 14.4 keV gamma ray from 57Fe has a high enough resolution to detect that difference!
In the early 60's physicists Pound, Rebka,and Snyder at the Jefferson Physical Laboratory at Harvard measured the shift to within 1% of this predicted shift.
Pound, R. V. and Rebka, G. A. Jr. "Gravitational Red-Shift in Nuclear Resonance." Phys. Rev. Lett. 3, 439-441, 1959.
20 /1 cgh
The gain in energy for a photon which falls distance h = 22.6 m is
Comparing the energy shifts on the upward and downward paths gives a predicted difference
mgckeVgh
cE
mghE 6.224.1422
eVE 11105.3
1511
109.44.14
)105.3(2
keVeV
EE
EE
updown
1510)5.01.5(
updown EE
EE
The measured difference was
The gain in energy for a photon which falls distance h = 22.6 m is
Comparing the energy shifts on the upward and downward paths gives a predicted difference The measured difference was
The success of this experiment owed much to the care of Pound and Rebka in preparing the source. They electroplated cobalt-57 onto the surface of a thin sheet of iron and then heated the combination at 1220 K for an hour. The heat treatment caused the cobalt to diffuse into the iron to a depth of about 300 nm or 1000 atomic spacings. The source was then mounted on the cone of a loudspeaker driven at 10Hz to sweep the source velocity in a sinusoidal variation. The detector was a thin sheet of iron about 14 micrometers thick which was also annealed. The heat treatments were found to be crucial in obtaining high resolution.
Gravity and the Photon The relativistic energy expression attributes a mass to any energetic particle, and for the photon
The gravitational potential energy is then
When the photon escapes the gravity field, it will have a different frequency
Since it is reduced in frequency, this is called the gravitational red shift or the Einstein red shift.
Gravitational Red Shift According to the principle of equivalence from general relativity, any frequency shift which can be shown to arise from acceleration of a radiating source could also be produced by the appropriate gravitational field. Thus the expected shift in radiation frequency in a gravitational field can be related to the relativistic doppler shift experienced from an accelerating light source.