# Gamma Decay

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16 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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7
-
1

Gamma Decay

Modern Nuclear Chemistry,
Chap. 9;

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

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-
2

Transitions

De
-
excitation of excited states are

-

and

J

an excited state

J

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

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-
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

J
ㄲ獥捯湤s

transitions important for determining decay
schemes

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-
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

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-
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Since

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

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-
6

Carries of angular momentum

l=1,2,3,4

2
l

pole (dipole,

Shorthand notation for electric (or magnetic)
2
l

pole

El or Ml

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

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-
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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

J

J

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

or two conversion electrons

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-
8

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-
9

Isomeric Transitions

An IT is a

Transition probability or partial decay constant for

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

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

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-
10

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11

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

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-
12

Internal Conversion Coefficients

Internal conversion is an alternative to

J

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

internal conversion process to rate of

ranges from zero to infinity

coefficients for any shell generally increase with
decreasing energy, increasing

䤬慮搠楮捲敡獩湧⁚

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-
13

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-
14

IC and Nuclear Spectroscopy

Internal conversion electrons show a line spectrum
corresponding
to the

J

… 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

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-
15

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-
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Angular Correlations

Assumes

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

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-
17

Angular Correlations

Schematic diagram of
angular correlations

(a) shows angular
distribution of

1

(b) shows magnetic
substrates
populated in

1

䨽ㄠ瑯䨽

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-
18

Angular correlation

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

J

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

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)

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-
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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)

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-
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

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-
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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

photon

E

v
c
E
cos
J
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-
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

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-
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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

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-
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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

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-
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
]
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-
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

inhomogeneous magnetic field

E
T

around 1cm/2

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-
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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

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Decay Scheme

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29

Mössbauer Devise

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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

Moessbauer spectroscopy

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-
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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

60m
Co.

Describe Moessbauer spectroscopy

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

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-
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?