1. Atomic Effects on Nuclear Transitions The following processes will be discussed: Ante Ljubi č i ć, Rudjer Bo š kovi ć Institute, Zagreb, Croatia 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 Introduction Nuclear excitation in positron-electron annihilation Nuclear excitation in electron transition NEPEA NEET Th: Osaka U. 1973 Exp: Osaka U. 1978 Th: U. Tenesee 1952. Exp: Kyoto U. 1972.

2. 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. Typical experimental set-up for the NEET investigations: NEET process

3. Therefore it could be expressed as Transition probability is defined 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.

4. - 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 Γ el >> Γ N emits photons, then number of photons absorbed by the nuclear oscillator will be proportional to N abs ~ Γ el ( Γ N / Γ el ) ~ Γ N - 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. e N*N* Ne N*N* N e e

5. - 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. 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. Γ Tot ≈ Γ el + Γ N and number of counts absorbed by the second oscillator will be N abs ~ Γ Tot ~ Γ el + Γ N ~ Γ el

6. Γ N → Γ e + Γ N ≈ Γ e we only have to replace Now we can apply our IQO model to the NEET processes. In our previous expression for P NEET and we obtain

7. Nucleus Experiment ReferencesIQO model 237 Np (2.1±0.6) × 10 -4 Saito et al. [1980] 1.3 × 10 -4 197 Au (5.0±0.6) × 10 -8 Kishimoto et al. [2006] 9.4 × 10 -9 189 Os ≤ 3 × 10 -10 Ahmad et al. [2002] 3.6 × 10 -10 Using this expression we have calculated several P NEET 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.

8. NucleusExperimentReferencesTheoryReferences 237 Np2.1 x 10 -4 Saito et al.1.5 x 10 -7 Pisk et al,1989 19808.5 x 10 -9 Ho et al.,1991 3.1 x 10 -12 Tkalya, 1992 1.3 x 10 -4 Ljubicic et al.,1998 197 Au5 x 10 -8 Kishimoto et al3.5 x 10 -5 Pisk et al.,1989 20064.2 x 10 -7 Ho et al.,1991 1.4 x 10 -7 Tkalya,1992 9.2 x1 0 -9 Ljubicic et al.,1998 189 Os5.7 x 10 -9 Shinohara et al.2.5 x 10 -7 Pisk et al.,1989 19871.2 x 10 -9 Ho et al.,1991 < 3 x 10 -10 Ahmad et al.1.1 x 10 -10 Tkalya, 1992 20021.3 x 10 -10 Ahmad et al,2000 3.6 x 10 -10 Ljubicic et al.,1998

9. NEPEA E + = E 1078 – 2mc 2 + |B K | ≈ 83 keV annihilate with K-shell electrons, the 1078- keV gamma-ray is emitted and nuclear level of the same energy is excited. The best case is 115 In, because its nuclear level scheme is well known. First experiment by Kyoto group in 1972. Indium sample was irradiated by positrons from 22 Na. Positrons slow down in the sample Γ e+e+ e+e+ and at resonant positron kinetic energy Transition from the 336-keV metastable state was observed in the experiment.

10. Γ e+e+ e+e+ - In their analysis they assumed that number of effective 115 In atoms in the sample is ~ Γ 1078. Therefore from N gamma ~ σ exp Φ + N In Γ 1078 they obtained σ exp ≈ 10 -24, but theory predicts σ th ≈ 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 Γ 1078 → Γ K >> Γ 1078 Then for larger Γ we expect smaller cross section and better agreement with theory.

11. - 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 β K 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

12. - Several other experiments were performed and all of them obtained cross sections which are several orders of magnitude larger than theoretical predictions. - We can also calculate similar factor β + for positrons and then re- analyze experimental result previously reported by Kyoto group. where Δ= λ/2. In that case we obtain for 115 In

13. Nucleus Old approach, before 1982 New approach, after 1991 Experiment Theory (Present & Chen) Experiment (using IQO model) Theory (Kaliman et al.) 115 In10 -24 10 -26 1.2×10 -26 2.0×10 -26 111 Cd8.6×10 -25 2.4×10 -26 2.4×10 -25 3.9×10 -25 176 Lu9×10 -22 1.2×10 -24 2.7×10 -26 2.2×10 -26 103 Rh σ exp ≈ 1.3x10 -24 cm 2 107,109 Ag σ exp ≈ 4.0x10 -23 cm 2 113 In σ exp ≈ 1.9x10 -24 cm 2 We re-analyzed 3 experiments using our IQO model and obtained good agreement with the most recent theoretical predictions of Kaliman et al. Theories: -Grechukhin & Soldatov -Pisk et al. -Horvat et al. -Kolomietz Other experiments:

14. 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.