gammaray decay

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Lecture 13
gamma-ray decay
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?-ray decays

• These occur within a given nucleus
• cf ? or ? decay

• The nucleus, formed in an excited state, drops to
  a lower-energy state by emitting energy as a
  photon (?-ray).
• e.g. Part 3 11B p ? 12C

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?-ray decays

• What can we learn?
• the energies of the excited states in the
  nucleus,
• cf. H atom spectroscopy
• the relative intensities of the ?-rays in
  possible cascades, with angular correlation data
  may allow I? assignments.
• Better data allows improvements of model the
  nucleus

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?-ray decays

• What determines the probability of decay between
  states?
• The energy
• The AM difference between states
• The transition matrix

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Dipole Radiation
Electric
Magnetic
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Dipole Radiation
Electric
Magnetic
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Multipole radiation
Each multipole radiation has an increasingly
complex angular dependence
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Charge Distribution
A charge spatial distribution can be expressed as
If ? 1 get dipole distribution If ? 2 get
quadrupole distribution
Classically the time variation of these charge
distributions gives EM emission.
In real-life world we usually only set up dipole
radiation. In the nucleus, oscillations of
deformed (quadrupole or higher) charge
distribution ? more complicated radiation
patterns.
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Power radiated by classical radiator of
multipolarity ?
(2?1)!! 1 x 3 x 5 x 7 .
For a nucleus, lets approximate Q?m. For Dipole
oscillations Q1 Zed where d is the amp of
vibration
For Quadrupole oscillations Q2 Ze(3z2-r2)
? 6.5ZeR2(?R/R) lt ZeR2
In general to zero approximation Q?m lt ZeR?
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Radiated Power
For medium size nucleus R10-15 m, and emission
of a 1-MeV ?-ray R/? 5 x 10-3 E2/E1 power
2 x 10-5  for atom ? 4000 A, R 0.5
A. R/? 10-4 E2/E1 power 10-8
Only E1 radiation relevant
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Quantisation
? ? l,
and
Now the transitions are between quantum states,
and the photon carries off AM l. NOTE. A photon
always has AM. So transitions from 0 ? 0 are not
allowed.
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Allowed transitions and relative emission
probabilities
That is, the vector difference between the AM of
the initial state Ii and the final state If must
have the appropriate z-component change ?m.
The consequence of this is that the allowed
values of l are given by ? Ii - If ? ? l ? Ii
If
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Allowed transitions and relative emission
probabilities
Depending on the AM carried off by the photon
there are requirements regarding the parity of
the states involved. For electric multipole
transitions ?i?f (-1)l. For magnetic multipole
transitions ?i?f (-1)l1.
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Relative emission probabilities
0 ? 2, 2 ? 0 ?l 2, ? no, E2
4 ? 2 6 gt ?l gt 2 ?l 2, ? no, E2 ?l 3, ?
no, M3 ?l 4, ? no, E4 ?l 5, ? no, M5 ?l
6, ? no, E6
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Relative emission probabilities
An order-of-magnitude estimate is made on the
assumption that the initial wave function is a
single-particle proton state with AM l and the
final state is an s-state (l0). ? Weisskopf units
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Relative emission probabilities
For given l transition rates vary dramatically
with ?-ray energy.
e.g. 20 orders of magnitude for l5 transitions
between 100 kev and 10 MeV,
for E1 it is about 6 orders.
The magnetic transitions show the same trends,
but the rates are lower by about 2 orders of
magnitude.
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How realistic are these estimates?
In general the measured transition rates (?) are
significantly smaller than the calculated ones.
(T1/2 larger)
Not surprising--- Assumed pure simple
single-particle wavefunctions. This is seldom
likely to be the case. Assumed that only protons
are involved. In half the cases it is the
neutron that changes orbit.
Real states live longer!
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How realistic are these estimates?
E2 transitions for deformed nuclei decay more
rapidly.
Going against the trend, E2 transitions for
deformed nuclei have larger transition rates than
estimated (shorter lifetimes).
Why is this???
Weisskopf value
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How realistic are these estimates?
E2 transitions for deformed nuclei decay more
rapidly.
Why is this???
All are E2 decays l 2
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Internal Conversion
There is an interesting effect on these
transition-rate graphs at low ?- energies. Note
that the transition rate increases markedly below
about 100 keV, particularly for high multipoles
(E5, E4,..), and large A
This is the result of internal conversion.
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Internal Conversion
What is it? The ?-ray transition energy is
transferred to an atomic orbital electron (most
likely a K-shell), and this electron is emitted
with a kinetic energy of E -BE.
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Internal Conversion
 How does this come about? The EM field conveys
the energy to an atomic electron Increased
probability if 1. orbital electrons are close
to the nucleus ? heavy atoms (recall ratom is
prop 1/Z). 2. when a ?-ray transition involves a
large AM transfer (? l). That is, the state has
a long lifetime.
In some instances (e.g. a 0 ? 0 transition) when
?-decay is forbidden electron conversion is the
only decay mechanism.