Atomic Effects on Nuclear Transitions

Atomic Effects on NuclearTransitions Ante Ljubičić, Rudjer Bošković Institute, Zagreb, Croatia Introduction The following processes will be discussed: Nuclear excitation in electron transition Nuclear excitation in positron-electron annihilation NEET NEPEA 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

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 Therefore it could be expressed as However using this expression we obtain results which are too small compared toexperiments. 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 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 • 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 Dbetween the two oscillators is less than the wavelength λof the exchanged resonant photon.

Now we can apply our IQO model to the NEET processes. In our previous expression for PNEET we only have to replace ΓN →Γe + ΓN ≈ Γe and we obtain

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.

e+ e+ Γ 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.

e+ e+ Γ • In their analysis they assumed that number of effective 115In atoms in the sample is ~Γ1078 . Therefore from Ngamma ~σexpΦ+ NInΓ1078 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 checkhowclose 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 - 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

where Δ=λ/2. In that case we obtain for 115In - We can also calculate similar factor β+ 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.

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 σexp ≈ 1.3x10-24 cm2 107,109Ag σexp≈ 4.0x10-23 cm2 113In σexp ≈ 1.9x10-24 cm2

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.

Atomic Effects on Nuclear Transitions