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Atomic Effects on Nuclear Transitions
Ante Ljubičić, Rudjer Bošković Institute, Zagreb, Croatia
Introduction
The following processes will be discussed:
Nuclear excitation in electron
transition
NEET
Th: Osaka U. 1973
Exp: Osaka U. 1978
Nuclear excitation in
positron-electron annihilation
NEPEA
Th: U. Tenesee 1952.
Exp: Kyoto U. 1972.
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
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.
Transition probability is defined as
PNEET
number of excited nuclear states

number of created electron vacancies
Therefore it could be expressed as
PNEET



eR g N 
NR NT




2
eT 2 
2
 NT  







N
 e
2  

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.
N*
e
N
e
- Let us first assume that the two oscillators, with equal multipolarities
and transition energies, are far away from each other, so that D >> λ . In
that case they exchange real photons. It means that if electron oscillator
with radiative width Γel >> ΓN emits photons, then number of photons
absorbed by the nuclear oscillator will be proportional to
Nabs ~ Γel ( ΓN / Γel ) ~ ΓN
N*
e
N
e
- However if these two oscillators are so
close that D < λ, then the two oscillators
exchange virtual photons, and we can not
distinguish between them.
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.
ΓTot ≈ Γel + ΓN
and number of counts absorbed by the second oscillator will be
Nabs ~ ΓTot ~ Γel + ΓN ~ Γel
- 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 ω, equal multipolarity, and if the separation D between the
two oscillators is less than the wavelength λ of the exchanged
resonant photon.
Now we can apply our IQO model to the NEET processes.
In our previous expression for PNEET
PNEET



eR g N 
NR NT




2
eT 2 
2
 NT  







N
 e
2  

we only have to replace
ΓN → Γe + ΓN ≈ Γe
and we obtain
PNEET



eR eR
gN 

  f (e )

2
2 
2
 eT  






 2 
N
 e

 
Using this expression we have calculated several PNEET and compared
them with the experimental results:
Nucleus
Experiment
References
IQO model
237Np
(2.1±0.6)×10-4
Saito et al. [1980]
1.3×10-4
197Au
(5.0±0.6)×10-8
Kishimoto et al. [2006]
9.4×10-9
189Os
≤ 3×10-10
Ahmad et al. [2002]
3.6×10-10
As we can see the agreement between the experiment and our calculations
based on the IQO model is reasonable.
Nucleus
Experiment References
Theory
References
237Np
2.1 x 10-4
Saito et al.
1.5 x 10-7
Pisk et al ,1989
1980
8.5 x 10-9
Ho et al.,1991
3.1 x 10-12
Tkalya, 1992
1.3 x 10-4
Ljubicic et al.,1998
Kishimoto et al
3.5 x 10-5
Pisk et al.,1989
2006
4.2 x 10-7
Ho et al.,1991
1.4 x 10-7
Tkalya,1992
9.2 x1 0-9
Ljubicic et al.,1998
Shinohara et al.
2.5 x 10-7
Pisk et al.,1989
1987
1.2 x 10-9
Ho et al.,1991
Ahmad et al.
1.1 x 10-10
Tkalya, 1992
2002
1.3 x 10-10
Ahmad et al,2000
3.6 x 10-10
Ljubicic et al.,1998
197Au
189Os
5 x 10-8
5.7 x 10-9
< 3 x 10-10
NEPEA
13/2+
1290.6
11/2+
5/2+
1132.6
3/2-
597.1
0.42 ps
0.07 ps
1078.2 0.99 ps
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
e
. 0.25 ns
+
1/2-
336.2
4.5 h
e
+
Γ
9/2+
115In
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 1078keV gamma-ray is emitted and nuclear level
of the same energy is excited.
e+
e+
- In their analysis they assumed
that number of effective 115In
atoms in the sample is ~ Γ1078 .
Therefore from
Ngamma ~ σexp Φ+ NIn Γ1078
Γ
they obtained σexp ≈ 10-24 , but
theory predicts σth ≈ 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
Γ1078 → ΓK >> Γ1078
Then for larger Γ we expect smaller cross
section and better agreement with theory.
- 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 βK for K-shell electron as the probability of finding it
within the distance from the nucleus D < λ . In that case

2

r
 K dr
2
K 
0

2

r
 K dr
2
0
- However it cannot be assumed that there is a sharp break between
distinguishability and indistinguishability at D = λ, 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
G  exp( r 2 / 22 )
where Δ=λ/2. In that case we obtain

K 
GK
0

2
r 2 dr
 0.18
for 115In
2
  K r dr
2
0
- We can also calculate similar factor β+ for positrons and then reanalyze 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.
We re-analyzed 3 experiments using our IQO model and
obtained good agreement with the most recent theoretical
predictions of Kaliman et al.
Old approach, before 1982
Nucleus
New approach, after 1991
Theory
Experiment
Theory
(Present & Chen)
(using IQO model)
(Kaliman et al.)
Experiment
115In
10-24
10-26
1.2×10-26
2.0×10-26
111Cd
8.6×10-25
2.4×10-26
2.4×10-25
3.9×10-25
176Lu
9×10-22
1.2×10-24
2.7×10-26
2.2×10-26
Other experiments:
103Rh
σexp ≈ 1.3x10-24 cm2
107,109Ag
σexp≈ 4.0x10-23 cm2
113In
σexp ≈ 1.9x10-24 cm2
Theories:
Grechukhin &
Soldatov
Pisk et al.
Horvat et al.
Kolomietz
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.