Gamma Decay. Radioactive Decay Alpha Decay Radioactive Decay Alpha Decay Beta Decay.
When an nucleus releases the transition energy Q (say 14.4 keV) in a -decay, the does not carry...
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Transcript of When an nucleus releases the transition energy Q (say 14.4 keV) in a -decay, the does not carry...
![Page 1: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/1.jpg)
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
Nm
pQE N
2
2
2
2
2 cm
EQ
N
![Page 2: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/2.jpg)
If this change is large enough, the will not be absorbed by an identical nucleus. 2
2
2 cm
pQE
N
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 cm
EQE
N
absorbed
2
2
2
2
22
cm
E
cm
E
NN
![Page 3: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/3.jpg)
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 the initial energy state was.
For atomic transitions, the typical lifetime is ~108 sec
The energy uncertainty eV10 7 E
![Page 4: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/4.jpg)
Notice the uncertainty E >> 2TN
Q
2TN
with an enormous amount of overlap allowing resonance fluorescence
![Page 5: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/5.jpg)
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 nuclear transitions, the typical lifetime is ~1010 sec
The energy uncertainty eV10 5 E
![Page 6: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/6.jpg)
This time the uncertainty E << 2TN
Q
2TN
which provides no overlap allowing resonance fluorescence
![Page 7: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/7.jpg)
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
keV
cm
EE
N
recoil
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.
![Page 8: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/8.jpg)
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.
![Page 9: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/9.jpg)
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
GeVN
keVeVErecoil
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.
![Page 10: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/10.jpg)
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
c
csourceobserved /1
/1
v
v
v is positive
for an approaching
source
)1(
)/1(
)/1)(/1(
)/1)(/1(22 c
cv
cc
ccvv s
so v
v
vv
vv
)/1( cvvso
vIf v/c <<1 this simplifies to
This can be written as
![Page 11: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/11.jpg)
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 v
vv
ckeV
chvvvheV
ss4.14)(002.0
0
![Page 12: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/12.jpg)
Cool an embedded sample to produce recoilless emissionand drive the source or absorber to scan the resonance.
vibrator
servo-motorcontrols
dataacquisition
radioactivesource
absorbingsample detector
![Page 13: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/13.jpg)
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
![Page 14: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/14.jpg)
![Page 15: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/15.jpg)
![Page 16: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/16.jpg)
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.
Source
Absorber
Detector
191Irv
191Ir
![Page 17: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/17.jpg)
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!
![Page 18: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/18.jpg)
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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
![Page 20: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/20.jpg)
http://www.fastcomtec.com/fwww/moss.htm
http://www.cryoindustries.com/moss.htm
http://www.dwiarda.com/scientific/Moessbauer.html
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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
).(
)(2
1
42
422
O
O
mghmc
mvmcEbottom
Let the particle rebound elastically at the bottom and return.
![Page 22: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/22.jpg)
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? Or is the mass now greater than it began?
What must be true, even for the photon is
.)(
42
2
Omghmc
mc
E
E
bottom
top
![Page 23: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/23.jpg)
)(
42
2
Omghmc
mc
E
E
bottom
top
242 /)(/1
1
mccghE
E
bottom
top
O
.1 2c
gh
E
E
bottom
top
![Page 24: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/24.jpg)
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
cghv
cghv
cghvvv
bottom
bottom
bottombottomtopbottom
![Page 25: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/25.jpg)
The redshift is:
2/ cghv
v
bottom
topbottom
![Page 26: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/26.jpg)
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 should provide 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.
2
0/1 cgh
![Page 27: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062714/56649d045503460f949d83ed/html5/thumbnails/27.jpg)
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
mgc
keVgh
c
EmghE 6.22
4.1422
eVE 11105.3
1511
109.44.14
)105.3(2
keV
eV
E
E
E
E
updown
1510)5.01.5(
updown E
E
E
EThe measured difference was