Atomic Effects on Nuclear Transitions

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Atomic Effects on Nuclear Transitions
Ante Ljubicic, Rudjer Bokovic Institute, Zagreb,
Croatia
Introduction
The following processes will be discussed
Nuclear excitation in positron-electron
annihilation
Nuclear excitation in electron transition
NEPEA
NEET
Th U. Tenesee 1952. Exp Kyoto U. 1972.
Th Osaka U. 1973 Exp Osaka U. 1978
Why these three processes?

• large discrepancies between the theory and
  experiment,
• interaction pictures for these processes have
  similar structure, they show
• interaction between two oscillators in the
  same atom, and
• our simple theoretical model could remove these
  discrepancies

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NEET process
Typical experimental set-up for the NEET
investigations
We can consider the NEET process as the two-step
process , i.e. first the X-ray is emitted by the
electron, and then subsequently absorbed by the
nucleus.
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Transition probability is defined as
Therefore it could be expressed as
However using this expression we obtain results
which are too small compared to experiments. In
order to overcome this problem we introduced a
simple model of Indistiguishable Quantum
Oscillators ( IQO ). Using this model we were
able to obtain reasonable agreement with
experiments.
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• Let us first assume that the two oscillators,
  with equal multipolarities and transition
  energies, are far away from each other, so that D
  gtgt ? . In that case they exchange real photons.
  It means that if electron oscillator with
  radiative width Gel gtgt GN emits photons, then
  number of photons absorbed by the nuclear
  oscillator will be proportional to

Nabs Gel ( GN / Gel ) GN

• However if these two oscillators are so close
  that D lt ?, then the two oscillators exchange
  virtual photons, and we can not distinguish
  between them.

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In this case we would expect that they behave as
one oscillator with the line-width equal to the
sum of individual line-widths, i. e.
GTot Gel GN
and number of counts absorbed by the second
oscillator will be
Nabs GTot Gel GN Gel

• And this is exactly the basis of our model of
  two Indistinguishable Quantum Oscillators,
  the IQO model.

- Quite generally, the IQO model says that if we
can not distinguish between the two oscillators
then the two oscillators with the two individual
line-widths behave as one oscillator with one
line-width equal to the sum of the two
individual line-widths.
- Two oscillators are indistinguishable if they
have equal transition energy ?, equal
multipolarity, and if the separation D between
the two oscillators is less than the wavelength ?
of the exchanged resonant photon.
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Now we can apply our IQO model to the NEET
processes.
In our previous expression for PNEET
we only have to replace
GN ? Ge GN Ge
and we obtain
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Using this expression we have calculated several
PNEET and compared them with the experimental
results
As we can see the agreement between the
experiment and our calculations based on the IQO
model is reasonable.
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NEPEA
The best case is 115In, because its nuclear level
scheme is well known. First experiment by Kyoto
group in 1972. Indium sample was irradiated by
positrons from 22Na. Positrons slow down in the
sample
and at resonant positron kinetic energy
E E1078 2mc2 BK 83 keV
Transition from the 336-keV metastable state was
observed in the experiment.
annihilate with K-shell electrons, the 1078-keV
gamma-ray is emitted and nuclear level of the
same energy is excited.
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• In their analysis they assumed that number of
  effective 115In atoms in the sample is G1078
  . Therefore from

Ngamma sexp F NIn G1078
they obtained sexp 10-24 , but theory predicts
sth 10-26 .
We could estimate this process using the IQO
model.
The NEPEA process could also be treated as a
system of two oscillators, and if the two
oscillators are close enough we can replace
G1078 ? GK gtgt G1078
Then for larger G we expect smaller cross section
and better agreement with theory.
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- We must check how close the two oscillators
are, i.e. if we can apply the IQO model.
- To a first approximation we can define the
indistinguishability factor ßK for K-shell
electron as the probability of finding it within
the distance from the nucleus D lt ? . In that
case
- However it cannot be assumed that there is a
sharp break between distinguishability and
indistinguishability at D ?, and it is
necessary to introduce a simple model to allow
for this. - It is assumed that each particle can
be represented by a Gaussian
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where ??/2. In that case we obtain
for 115In
- We can also calculate similar factor ß for
positrons and then re-analyze experimental result
previously reported by Kyoto group.

• Several other experiments were performed and all
  of them obtained cross sections which are several
  orders of magnitude larger than theoretical
  predictions.

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We re-analyzed 3 experiments using our IQO model
and obtained good agreement with the most recent
theoretical predictions of Kaliman et al.
Other experiments

• Theories
• Grechukhin Soldatov
• Pisk et al.
• Horvat et al.
• Kolomietz

103Rh sexp 1.3x10-24 cm2
107,109Ag sexp 4.0x10-23 cm2
113In sexp 1.9x10-24 cm2
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Conclusion We have analyzed six experiments in
which atomic effects could play important role in
exciting nuclear levels. We have employed the
model of IQO and quite generally obtained good
agreement between the theory and experiment.
Therefore I believe that the IQO model is a
realistic one and we will use it in order to
explain other processes in which nuclei interact
with atomic electrons.