A new mechanism for nuclear excitations via two-photon electron transitions is proposed and studied theoretically. Detailed calculations were performed for the E1E1 1s2s 1S0 → 1s2 1S0 two-photon decay of heliumlike 225Ac87+ ions and, especially, for the resonant excitation of the 3/2+ isomeric state at the energy 40.09(5) keV. The probability for such a two-photon decay via the nuclear excitation is found to be
PNETP = 3.5 × 10-9. The possibility for an experimental proof of the proposed mechanism is discussed.
For many decades already, atomic physics has been found a key position in understanding and improving our knowledge about the nuclear chart. In particular, much information about nuclear spins, nuclear magnetic moments and mean-square charge radii originate from atomic spectroscopy . In addition to the properties of the nuclear ground or isomeric states, moreover, atomic spectroscopy were found useful also to reveal the internal nuclear dynamics, e.g., the single nuclear resonances that can be accessed via electron transitions (fig. 1).
One of the intriguing applications of atomic spectroscopy in nuclear physics concerns the low-lying isomeric nuclear excitation of the thorium isotope 229mTh  with an excitation energy of just a few eV. This nuclear transition has been widely discussed in the literature for establishing a nuclear clock technology of unprecedented accuracy. Other potential applications refer, for instance, to the development of new isotope separation techniques or simply to the storage of energy and its later controlled release.
Recently, a new mechanism for nuclear excitations has been presented and discussed , to which we refer as nuclear excitation by two-photon electron transitions (NETP). This mechanism is based on the simultaneous emission of two photons that just share the atomic transition energy. In contrast to the usual single-photon transitions, however, where the photon frequency is given by the transition energy, the energy distribution of the spontaneously emitted photon pair forms a continuous spectrum.
This implies also, that some of the photons exactly match in their frequency with the nuclear transition energy, as long as the nuclear excitation energy is smaller than the total electron transition energy. Therefore, instead of just a two-photon transition of the electron(s), the nucleus may resonantly absorb one of the photon and becomes excited.
The newly-suggested mechanism can also be seen as a two-photon transition of an electron in the presence of an intermediate (nuclear) cascade state. In order to describe the NETP process, the electrons and nucleus must therefore be treated as combined system, in which the intermediate cascade state is just given by the excited nucleus and the electrons in their ground level. For a given electronic two-photon decay, the presence of a such cascade state increases the photon emission intensity in the region of the resonant energy. Figure 2 displays such a two-step NETP process in a more picturesque form. While the electrons are in the excited state (i), the nucleus initially still remains in its ground state (GS). If the electrons then decay under the emission of (two) photons into their ground state (f) via the intermediate cascade state, a photon γ1 is emitted with the energy ω1, while the second photon with energy ω2 is re-absorbed by the nucleus. In the second step, the nucleus later decays radiatively from its excited state (ES) into the GS under the emission of the nuclear fluorescence photon γ2 with just the energy ω2, but with some further delay owing to the finite lifetime of the isomeric nuclear state. According to energy conservation, of course, the total energy of the two photons is still the same and equal to the total energy ΔE of the electron transition i → f, i.e., ΔE = ω1 + ω2. Another advantage of the NETP process is that such resonant nuclear excitations may occur for all nuclear levels with an excitation energy smaller than the total transition energy ΔE.
Proof of the NETP Process
For the E1E1 two-photon transition 1s2s 1S0 → 1s2 1S0 of heliumlike 225Ac87+ ions with a (known) nuclear excited 3/2+ level at energy ωES = 40.09(5) keV, we found that the probability of a two-photon decay via nuclear excitation is surprisingly large, PNETP = 3.5 × 10-9, when compared with the overall and continuous two-photon emission. In order to verify the proposed mechanism, we suggest to observe the delayed emission of the nuclear fluorescence γ2 photons at the current GSI Heavy-Ion Research Facility in Darmstadt. The initial 1s2s 1S0 state can be efficiently produced in the collisions of lithiumlike ions of the given isotope with N2 gas target via the selective K-shell ionization. The x-ray emission will be measured in coincidences with the detection of the up-charged (heliumlike) ions, whose efficiency is near to 100%. This experimental setup therefore enables one to measure a very clean spectrum of the two-photon decay. In order to observe the delayed nuclear fluorescence photons γ2, a high efficiency in-vacuum x-ray detector need to be installed in order to cover a solid angle as large as possible. Moreover, fast transitions, that will mostly decay in the vicinity of the gas-target, will be shielded in order to reduce the background in the measurement of the delayed photons. At the experimental storage ring (ESR) at GSI beams of ≥ 108 cooled ions can be provided in such a bunch and stored for collisions with the gas-jet target and with areal densities above 1014 cm-2. Because of the high revolution frequencies of ions in the storage ring (about 2 MHz) and, hence, a steadily recurring interaction of the ions and target electrons, a very high luminosity can be achieved. From a more detailed analysis, we therefore expect to stimulate up to few hundreds NETP fluorescence photons per day of beamtime. Indeed, a successful observation and characterization of the NETP process appears feasible already with present-day technology. Moreover, once the new FAIR accelerator complex has been built, the experiment will profit from a much higher luminosity as well as from the ability of measuring closer to the ion beam.
Andrey V. Volotka1,2 and Stephan Fritzsche1,2
1 Helmholtz-Institute Jena, Jena, Germany
2 Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität, Jena, Germany
Prof. Dr. Stephan Fritzsche
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