Gamma Decay

wizzstuffingΠολεοδομικά Έργα

16 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

98 εμφανίσεις

7
-
1

Gamma Decay


Readings


Modern Nuclear Chemistry,
Chap. 9;


Nuclear and Radiochemistry,
Chapter 3


Energetics


Decay Types


Transition Probabilities


Internal Conversion


Angular
Correlations


Moessbauer spectroscopy



Emission of photon during
deexcitation of the nucleus


Wide range of energies


Isomers


two configurations


different total angular
momenta


Energy differences


long
-
lived nuclear states are called
isomeric states


gamma ray decay is called
isomeric transition (IT
)


Few
keV to many MeV

7
-
2



Transitions


De
-
excitation of excited states are


瑲慮獩瑩湳




-

and

J
摥捡礠灲潣p獳敳敡癥⁰牯摵捴
湵捬c畳u楮i敩瑨敲⁧潵搠獴慴攠潲Ⱐ浯牥晴敮
an excited state


Emission of electromagnetic radiation (


牡摩慴楯温Ⱐ楮瑥牮慬
J
捯湶敲獩潮s敬e捴牯湳Ⱐ潲
湥n汹l捲敡瑥搠e汥l瑲潮慮a灯獩瑲潮


Internal
conversion
from interaction
between
nucleus and extranuclear electrons leading to
emission of electron


kinetic
energy equal to difference between
energy of nuclear transition involved and
binding energy of the
electron


7
-
3



Transitions


Pair production


Exceeds 1.02 MeV


Emitted with kinetic energies that total
excitation energy minus 1.02 MeV


Uncommon mode


Characterized by a change in energy without
change in Z and A


E =
hv


Majority of


瑲慮獩楯湳⁨i癥癥特獨潲琠s楦i瑩浥猬

J
ㄲ獥捯湤s




transitions important for determining decay
schemes

7
-
4

Energetics


Recoil from gamma decay


Energy of excited state must equal


Photon energy, and recoil

*
M*c
2
=Mc
2
+E


r


Momentum same for recoil and photon


If E


㴠㈠䵥嘬⁡湤⁁㴵=


recoil energy is about 40 eV


Use 931.5
MeV
/AMU


Calculate recoil energy from 15.1
MeV

photon from
12
C

M
2
E
M
2
T
2
2
r
r









MeV
E
M
T
r
2
02
.
1
))
5
.
931
(
12
(
2
1
.
15
2
2
2






7
-
5

Multipole Radiation & Selection Rules


Since


牡摩慴潮慲楳敳e晲潭⁥汥捴牯f慧湥瑩挠
敦晥捴猬s楴捡渠扥⁴桯畧桴c潦⁡猠捨慮来⁩渠瑨攠
捨慲来⁡湤⁣畲牥湴c摩d瑲扵瑩b湳n楮畣汥i


Charge distributions resulting electric
moments


Current distributions yield magnetic
moments


Gamma decay can be classified
as magnetic (M)
or electric (E)


E and M multipole radiations differ in parity
properties


Transition probabilities decrease rapidly with
increasing angular
-
momentum changes


as in

J
摥捡d

7
-
6

Multipole Radiation & Selection Rules


Carries of angular momentum


l=1,2,3,4


2
l

pole (dipole,
quadrupole, octupole…)


Shorthand notation for electric (or magnetic)
2
l

pole

radiation


El or Ml


E2 is electric quadrupole


I
i
+
I
f







I
i
-
I
f

, where I
i

is the initial spin state and I
f
is the final
spin state


If initial and final state have the same parity electric
multipoles of even l and magnetic multipoles of odd l are
allowed


If different parity, the opposite is true


Example:


Transition is between a 4+ and a 2+ state


l between 6 and 2


E even, M odd


E2, M3, E4, M5, E6 transitions are allowed


Generally lowest multipole observed

7
-
7



0


〠瑲慮獩a楯湳i捡湮潴c瑡攠灬慣攠p礠灨潴潮y敭楳i楯i


P
hoton
has spin and therefore must remove at least
one unit of angular momentum


If no change in parity in 0


〠瑲慮獩a楯測i摥
J
數捩瑡楯渠浡礠
潣捵爠批b敭楳i楯渠潦⁡渠湴敲湡n
J
捯湶敲獩潮c敬e捴c潮潲⁢礠
獩s畬u慮敯畳a敭楳i楯渠潦⁡渠敬散e牯
J
灯獩p牯渠灡楲p(




ㄮ〲1
MeV)


72
Ge,
214
Po,
18
O,
42
Ca


Transitions
between two I=0 states of opposite parity cannot
take place by any first
-
order process


would require simultaneous emission of two


煵q湴愠
or two conversion electrons


7
-
8

7
-
9

Isomeric Transitions


An IT is a


摥捡d晲f洠慮楳潭敲i挠獴s瑥


Transition probability or partial decay constant for


敭e獳楯s







E
2l
A
2l/3

(l not 1)


F
or
given spin change, half lives decrease rapidly with increasing A and
more rapidly with increasing E


Use of extreme single
-
particle
model as basis of charge and current
distribution


Single particle model assumes nuclear properties dictated by unpaired
nucleon


Assumes


瑲湳楴楯渠捡渠扥c摥獣物扥搠慳瑲湳楴楯渠潦愠獩湧汥湵捬敯渠
from one angular
-
momentum state to another


Remainder of
the nucleus being represented as a potential
well


Model
predicts, for given nucleus, low
-
lying states of widely differing
spins in certain regions of neutron and proton numbers


numbers preceding the shell closures at N or Z values of 50, 82, 126


coincide with “islands of isomerism



Predictions strong for M4 isomers, E2 isomers 100 faster than predicted


Variations in nuclear shape from model


7
-
10

7
-
11

Weisskopf single particle estimates of the transition rates for
electric multipoles (left) and magnetic multipoles (right)

7
-
12

Internal Conversion Coefficients


Internal conversion is an alternative to

J
牡敭楳獩潮


Interaction
between nucleus and extranuclear
electrons leading to emission of electron with kinetic
energy equal to difference between energy of nuclear
transition involved and binding energy of the electron


Internal conversion coefficient


楳牡瑩漠潦⁲慴攠潦
internal conversion process to rate of


敭e獳楯i


ranges from zero to infinity


coefficients for any shell generally increase with
decreasing energy, increasing

䤬慮搠楮捲敡獩湧⁚

7
-
13

7
-
14

IC and Nuclear Spectroscopy


Internal conversion electrons show a line spectrum
corresponding
to the

J
瑲湳楴楯渠敮敲杹e浩湵猠扩湤楮朠敮敲杩敳e潦⁴桥h䬬K䰬L䴬M
… shells in which the conversion occurs


difference in energy between successive lines are used to
determine Z



K
/

L

ratios can be used to characterize multipole order and thus

䤠慮搠



this
ratio doesn’t
vary as widely as the individual
coefficients


If Z of x
-
ray
-
emitting species known, it can be determined
whether it decays by EC or IT


For EC, x
-
rays
will be of
Z
-
1


For IT, x
-
rays from
Z

7
-
15

7
-
16

Angular Correlations


Assumes


牡祳
桡癥漠瑲慣h潦
瑨攠畬u楰潬攠楮i敲慣e楯渠瑨慴
条癥⁢楲瑨瑯⁴桥h


Usually true
but different multipole fields give rise to
different angular distributions of emitted radiation
with respect to nuclear
-
spin direction of the emitting
nucleus


ordinarily deal with samples of radioactive
material that contains randomly oriented
nuclei



Observed
angular distribution of


rays is
isotropic

7
-
17

Angular Correlations


Schematic diagram of
angular correlations


(a) shows angular
distribution of
dipole radiation for

洠㴰m慮搠

洠㴠


1



(b) shows magnetic
substrates
populated in

1


捡獣慤攠晲潭⁊㴰⁴漠
䨽ㄠ瑯䨽

7
-
18

Angular correlation


If nuclear spins can be aligned in one direction,
angular distribution of emitted

J
牡楮瑥湳楴i睯畬搠
摥灥湤⁰牥摩捴d扬b潮瑨攠楮i瑩氠湵捬敡爠獰渠慮搠
浵汴楰m汥l捨慲c捴敲c潦⁴桥⁲摩d瑩n


Can
use strong external electric or magnetic field
at low temperatures or observe a


牡⁩渠
捯c湣楤敮捥n睩瑨⁡⁰牥捥摩湧牡摩慴a潮


I
n
coincidence experiment, where angle


between the two sample
-
detector axes is
varied, the coincidence rate will vary as a
function of






4
4
2
2
cos
cos
1
)
(
a
a
W



)
90
(
)
90
(
)
180
(
o
o
o
W
W
W
A


Correlation
function:

where
A=a
2
+a
4

(fits)

7
-
19

Mössbauer Spectroscopy


Principles


Conditions


Spectra

Principles


Nuclear transitions


emission and absorption of gamma rays

sometimes called nuclear gamma resonance spectroscopy


Only suitable source are isotopes


Emission from isotope is essentially monochromatic


Energy tuning done by Doppler effect

Vibration of source and absorber

spectra recorded in mm/s (1E
-
12 of emission)

7
-
20

Recoil


Gaseous atom or molecule emits radiation (energy E)


momentum of E/c


Recoil (P) =
-
E/c =Mv

M = mass of emitter, v is recoil velocity


Associated recoil energy of emitter


E
R

=Mv
2
/2= E
2
/2Mc
2


E
R
(in eV)= 537 E
2
/M (E in MeV)


For radiation near UV or below with normal atoms
or molecules v is very small


With gamma decay E is large enough to have a
measurable effect


E
T
=E+ E
R

for emission

7
-
21

Recoil


If E is to excite a nucleus


E= E
T

+ E
R


Molecules in gas or liquid cannot reabsorbed photon


In practice lattice vibrational modes may be excited during
absorption


Emitting nuclei in chemical system


Thermal equilibrium, moving source


Doppler shift of emitted photon



J

楳⁡i杬攠扥瑷敥渠摩牥d瑩潮潦潴潮潦⁴桥h湵捬敵猠慮搠敭楴瑥搠
photon


E

v
c
E
cos
J
7
-
22

Recoil Free Fraction

J

can vary from
-
1 to 1,so distribution is E
T

-
E
R

distribution around 0.1 eV at room temp

Some chemical energy goes into photon, and some recoil
energy goes into lattice phonon


Heisenberg uncertainly implies distribution of energy
from finite half
-
life



G
⡩渠敖⤠㴴⸵㕅
J
ㄶ⽴
1/2

(sec)


What Mössbauer did


Total recoil in two parts, kinetic and vibrational


If emitter and absorber are part of lattice,
vibrations are quantized


Recoil energy transfer only in correct quanta


7
-
23

Recoil Free Fraction


If recoil energy is smaller than quantized
vibration of lattice the whole lattice vibrates


Mass is now mass of lattice, v is small, and so is
kinetic part of recoil energy


E

E
T

and recoil energy goes into lattice phonon
system


lattice system is quantized, so it is possible to find
a state of the system unchanged after
emission


0.9
for metallic, 0.2 for
metal
-
organic


related
to stiffness of crystal

7
-
24

Recoil free fraction


E > 150 keV nearly all events vibrate lattice


E = E
T

for a small amount of decays


Where E = E
T
gives rise to Mössbauer spectra


Portion of radiation which is recoil free is “recoil
-
free fraction”


Vibration of lattice reduced with reduced T


Recoil
-
free fraction increases with decreasing T


T range from 100 to 1000 K


Half
-
lives greater than 1E
-
11 seconds, natural width
around 1E
-
5 eV


For gamma decay of 100 keV, Doppler shift of

1E
-
5 eV is at a velocity of 3 cm/s

7
-
25

Isomeric or Chemical Shift


Volume of nucleus in excited state is different from
ground state


Probability of electron orbitals found in the nucleus is
different


Difference appears as a difference in the total electron
binding state and contributes to transition energy


E
T

= ²E(nucl) + ²E(elect) [binding energies]


Consider an emitting nucleus (excited) and absorber
(ground) in different chemical states


Difference in ²E(elect) and therefore E
T



Change is chemical shift


E
(
elect
)

2
5

Ze
2
(
r
ex
2

r
gr
2
)
[

ex
(
0
)
2


gr
(
0
)
2
]
7
-
26

Magnetic Dipole Splitting


magnetic moment will add to transition energy


E
T

= ²E(nucl) + ²E(elect)+ ²E(mag)


Change in magnetic moment will effect shift


Split also occurs (2I+1) values


around 1cm/s

Electric Quadrapole Splitting


inhomogeneous magnetic field


E
T

= ²E(nucl) + ²E(elect)+ ²E(mag)+²E(quad)


around 1cm/2

7
-
27

Technique


Intensity of photon from emitter is detected


Velocity of emitter and absorber recorded


important to know these values


May be cooled and place in magnetic field


Used in


amorphous materials


catalysts


soil


coal


sediments


electron exchange

7
-
28

Decay Scheme

7
-
29

Mössbauer Devise

7
-
30

Topic Review


Trends in gamma decay


How does it come about, how is it different
from alpha and beta


Energetics of gamma decay


Decay Types


Photon emission, IC, pair production


E and M transitions


Probabilities, modes, and how to define


Angular Correlations


How are they measured and what do they
inform about the nucleus


Moessbauer spectroscopy

7
-
31

Questions


195
Pt has a ground state spin and parity of ½
-
, with
excited states at 0.029 MeV (3/2
-
) and 0.130 MeV (5/2
-
).
Does the 5/2 level decay primarily to the 3/2
-

level or to
the ½
-

level? Why? What is the transition multipolarity?


What is the spin of a photon?


What type of gamma decay is expected from a 0+ to 0+
transition?


Classify the most likely multipolarity for the

J
牡礠摥捡礠
潦
60m
Co.


Describe Moessbauer spectroscopy


Why do angular correlations arise in the nucleus? How
are they measured

7
-
32

Pop Quiz


51
V has a ground state spin and parity of 7/2
-

with excited states at 0.3198 MeV (5/2
-
) and at
0.930 MeV (3/2
-
).


Sketch the decay scheme


What is the energy and multipolarity of the
gamma ray that deexcites each excited
state?