against fragmentation has been addressed by a few groups, e.g. at Stockholm, Caen and KVI.

A scaling law to estimate TCS for uracil, water and other large molecules are also being investigated by different authors (e.g. [103, 106] and Olson EPJD 2019).

**Current and future challenges.** From a large set of data on ion-atom and ion-molecular collisions, it appears that the theoretical techniques, based on the CDW-EIS and various versions of it, fairly explain the data-sets particularly for simple light target atoms. However, for large molecules including nucleobases the back-scattering phenomenon is yet to be understood, since one often finds deviation of theory for ejected electron emission in large scattering angles. In case of such large molecules many electron correlation, size effect or any collective effect need to be included in the models. In view of their potential applications in diverse fields like radiobiology or medical imaging there is an effort to develop Monte Carlo numerical codes of charged particle transport and energy loss. Two such approaches by Champion and Garcia can be found in EPJD 71 (130) 2017; and Rad Phys Chem 130, (371) 2017. In spite of having many measurements carried out one finds a lack of accurate experimental data on total energy loss of charged particles in water, particularly around the Bragg peak. Such measurement will automatically include the contribution of the ionization, EC and fragmentation in the total energy loss. Whether the use of water to simulate the biological medium is correct or not needs to be answered experimentally. In practical front, the challenging task is to carry out experiments which must be tuned to include the realistic environment around the target molecules. For example most of the ion-collision experiments are carried out with isolated biomolecules in vapor phase. In reality the nucleobases are parts of the DNA/RNA present in biological matters along with liquid water.

**Advances in science and technology to meet challenges.** In certain class of experiments one uses the clusters of biomolecules, water-clusters or liquid drops. For example, the study of fragmentation of clusters of 5Br-uracil indicates clustering effect, by triggering new pathways for fragmentation, e.g. the loss of the OH group (PCCP 19, 19807, (2017)). Therefore, to explore the interaction dynamics of these biologically active molecules surrounded by an environment, such as, solvent molecules, water, alcohol, or other smaller bio-molecules is an experimentally challenging task. To this end, a bio-molecular ion beam facility, comprising of an electro-spray ion source and an ion-trap with a cooling buffer-gas, capable of delivering low energy internally cold molecular-ions, could be used as injector to a storage ring. Such cross-beam experiments involving accelerators are being developed in different laboratories worldwide (e.g. Stockholm, Aarhus, RIKEN).

Metal nanoparticles are proposed to be candidates as sensitizers in cancer treatments in hadron-therapy [104]. The injection of such nanoparticles into tumors increase the biological effectiveness due to the enhancement of low energy electrons or radicals. Collective plasmon excitation in the inserted metal is a possible mechanism for such enhancement [107]. In reality this is extremely challenging experiment. The initial experiments, which are in progress involve different halo-uracils as target, such as, bromouracil, iodouracil etc. In benchmark system, such as, $C_{60}$ it has been observed that, nearly 50% of the electron emission and hence similar fraction of energy loss can be accounted by the collective excitation alone. Such collective excitations are dealt theoretically by a few groups: Eric Suraud et al (Toulouse, France) and Solovyov and co-workers (Frankfurt group) (e.g. see [105], EPJD 66, 254 (2012), JPCS 490, 012159 (2014)).

From radiation biology point of view the contribution of the ICD process, to the DNA-strand breakage needs to be investigated in more details, particularly its role in case of heavy-ion collisions.

The last, but not the least point relates to the ion-atom collisions. In case of electron emission for ion-atom or ion-molecule collisions, the deviation of the models for backward electron emission is yet to be understood. Observed double frequency in interference oscillation in backward e-emission from $H_2$ compared to the forward emission is yet to be understood. In case of interference experiment, DDCS for molecule is compared with that for the atomic DDCS. However, only in one experiment such explicit comparison was possible i.e. by using atomic H [98], but for other atomic targets, e.g. N or O atoms, such experiments are awaited.

**Concluding remarks.** The mature field of ion-molecule interaction has taken a new shape of interdisciplinary science due to constant contributions by genre of researchers across different branches of science i.e. plasma- and astrophysics, biology, chemistry and radiobiology.

New discoveries, such as, ICD in photo-ionization and e-interference in molecular double slit have kept the field vibrant. The theme of ion-molecule collision continues to offer an active area of research which enriches our basic understanding of large bio-molecules, PAH molecules, fullerenes and clusters. The future research may aim towards the interaction with biomolecules which is attached to an environment and with nano-inserted DNA/RNA molecules- which is, however, a challenging task. The development of a range of sophisticated equipment, ion-traps, ion-sources, storage-rings, ion-beam facility will continue to push the field of molecular sciences.

## Acknowledgments

I would like to thank my students, colleagues and R Rivarola and C Champion for long-standing theory-experiment collaborations.
against fragmentation has been addressed by a few groups, e.g. at Stockholm, Caen and KVI.

A scaling law to estimate TCS for uracil, water and other large molecules are also being investigated by different authors (e.g. [103, 106] and Olson EPJD 2019).

**Current and future challenges.** From a large set of data on ion-atom and ion-molecular collisions, it appears that the theoretical techniques, based on the CDW-EIS and various versions of it, fairly explain the data-sets particularly for simple light target atoms. However, for large molecules including nucleobases the back-scattering phenomenon is yet to be understood, since one often finds deviation of theory for ejected electron emission in large scattering angles. In case of such large molecules many electron correlation, size effect or any collective effect need to be included in the models. In view of their potential applications in diverse fields like radiobiology or medical imaging there is an effort to develop Monte Carlo numerical codes of charged particle transport and energy loss. Two such approaches by Champion and Garcia can be found in EPJD 71 (130) 2017; and Rad Phys Chem 130, (371) 2017. In spite of having many measurements carried out one finds a lack of accurate experimental data on total energy loss of charged particles in water, particularly around the Bragg peak. Such measurement will automatically include the contribution of the ionization, EC and fragmentation in the total energy loss. Whether the use of water to simulate the biological medium is correct or not needs to be answered experimentally. In practical front, the challenging task is to carry out experiments which must be tuned to include the realistic environment around the target molecules. For example most of the ion-collision experiments are carried out with isolated biomolecules in vapor phase. In reality the nucleobases are parts of the DNA/RNA present in biological matters along with liquid water.

**Advances in science and technology to meet challenges.** In certain class of experiments one uses the clusters of biomolecules, water-clusters or liquid drops. For example, the study of fragmentation of clusters of 5Br-uracil indicates clustering effect, by triggering new pathways for fragmentation, e.g. the loss of the OH group (PCCP 19, 19807, (2017)). Therefore, to explore the interaction dynamics of these biologically active molecules surrounded by an environment, such as, solvent molecules, water, alcohol, or other smaller bio-molecules is an experimentally challenging task. To this end, a bio-molecular ion beam facility, comprising of an electro-spray ion source and an ion-trap with a cooling buffer-gas, capable of delivering low energy internally cold molecular-ions, could be used as injector to a storage ring. Such cross-beam experiments involving accelerators are being developed in different laboratories worldwide (e.g. Stockholm, Aarhus, RIKEN).

Metal nanoparticles are proposed to be candidates as sensitizers in cancer treatments in hadron-therapy [104]. The injection of such nanoparticles into tumors increase the biological effectiveness due to the enhancement of low energy electrons or radicals. Collective plasmon excitation in the inserted metal is a possible mechanism for such enhancement [107]. In reality this is extremely challenging experiment. The initial experiments, which are in progress involve different halo-uracils as target, such as, bromouracil, iodouracil etc. In benchmark system, such as, $C_{60}$ it has been observed that, nearly 50% of the electron emission and hence similar fraction of energy loss can be accounted by the collective excitation alone. Such collective excitations are dealt theoretically by a few groups: Eric Suraud et al (Toulouse, France) and Solovyov and co-workers (Frankfurt group) (e.g. see [105], EPJD 66, 254 (2012), JPCS 490, 012159 (2014)).

From radiation biology point of view the contribution of the ICD process, to the DNA-strand breakage needs to be investigated in more details, particularly its role in case of heavy-ion collisions.

The last, but not the least point relates to the ion-atom collisions. In case of electron emission for ion-atom or ion-molecule collisions, the deviation of the models for backward electron emission is yet to be understood. Observed double frequency in interference oscillation in backward e-emission from $H_2$ compared to the forward emission is yet to be understood. In case of interference experiment, DDCS for molecule is compared with that for the atomic DDCS. However, only in one experiment such explicit comparison was possible i.e. by using atomic H [98], but for other atomic targets, e.g. N or O atoms, such experiments are awaited.

**Concluding remarks.** The mature field of ion-molecule interaction has taken a new shape of interdisciplinary science due to constant contributions by genre of researchers across different branches of science i.e. plasma- and astrophysics, biology, chemistry and radiobiology.

New discoveries, such as, ICD in photo-ionization and e-interference in molecular double slit have kept the field vibrant. The theme of ion-molecule collision continues to offer an active area of research which enriches our basic understanding of large bio-molecules, PAH molecules, fullerenes and clusters. The future research may aim towards the interaction with biomolecules which is attached to an environment and with nano-inserted DNA/RNA molecules- which is, however, a challenging task. The development of a range of sophisticated equipment, ion-traps, ion-sources, storage-rings, ion-beam facility will continue to push the field of molecular sciences.

## Acknowledgments

I would like to thank my students, colleagues and R Rivarola and C Champion for long-standing theory-experiment collaborations.
# 10. Ion-ion collisions in the intermediate velocity regime

Emily Lamour

INSP—Sorbonne University, France

**Status.** Ion-ion collisions provide a unique scenario for testing our knowledge of fundamental electronic processes such as capture, ionization and excitation. Their study is also motivated by the fact that they are strongly correlated to the ion energy transfer in various plasma conditions.

Whereas ion-ion experiments for high-energy physics (like the experiments at CERN) are currently carried out, ion-ion collisions for atomic physics have been so far performed mainly in the context of magnetically confined plasmas [108]. There, in the low velocity regime, typically at center-of-mass energies of a few keV up to a few 100 keV, cross section measurements of the charge transfer process [109, 110] (by far the dominant process) were performed with light ions (up to oxygen) for collisions with bare, hydrogen- or helium-like ions, or with low-charged ions for the heavy systems like Bi and Pb, where charge states of up to 4 + have been used.

Investigation of the intermediate velocity regime (the pink area in figure 16) is more complicated due to the fact that, there, all the primary electronic processes (EC, loss and excitation) reach their optimum probability leading to the maximum of the ion stopping power and, consequently, to the strongest effects on material modifications. A few ion-plasma experiments, motivated by their consequences in the inertial confinement plasma fusion physics, have been carried out with swift heavy ions in hydrogen or deuterium low-density plasmas and, later on, in laser-generated carbon plasma of one percent solid state density. Evidences for drastic differences in ion stopping power when ions interact with either neutral or ionized matter have been clearly established (see for instance, [111]). Nevertheless, to extract direct information on elementary process modifications is almost impossible since many charge states may be present at the same time in the plasma. Likewise, in simple ion—(neutral) atom collisions, the presence of many electrons makes the determination of experimental cross sections of a single elementary collision process extremely difficult. It can be achieved only in very specific cases: for instance, taking full advantages of the spin-selectivity in excited state populations, the single $1s \rightarrow 2p$ excitation cross section has been measured for collisions between 13.6 MeV/u Ar$^{16+}$ ions and neutral atoms (from He to Xe) [112]. From a theoretical point of view, none of the present most sophisticated available calculations is able to treat all the processes together on the same footing pointing to a fundamental issue in our understanding of elementary atomic interactions. This circumstance gives rise to a paradoxical situation where, for this velocity regime, cross sections are very hard to predict, while their knowledge is of critical importance. A significant test of theories can only be performed if the presence of numerous electrons can be avoided (beside the simplest case of a proton on hydrogen collision). Alternatively, the effect of other electrons

<figure><img src="image_19.png" /><figcaption>Figure 16. Cross sections of elementary atomic collision processes for the system p → H as a function of the proton energy. The brown line is the stopping power (refer to the right y-axis) for protons in aluminum. The pink area marks the intermediate collision regime.</figcaption></figure>

participating to the processes must be explored. In this context, our knowledge of the intermediate collision regime is really limited. There is a lack of measurements and available theoretical calculations are at their limit of validity. In other words, this regime corresponds to a real 'terra incognita' for atomic physics.

With ion-ion collision experiments, we deal with 'clean plasmas' of well-known charge states, we have the ability to investigate a large variety of systems and the possibility to easily scan the charge state of each ion partner. Nevertheless, the realization of these experiments remains a real challenge involving several steps that have to be solved in order to perform absolute cross section measurements.

**Current and future challenges.** The intermediate regime is reached when the relative target-projectile velocity is of the same order as the ones of the active electrons in its initial state. For instance, in the case of the symmetric collision Ar$^{Q+}$ on Ar$^{q+}$, it occurs at a collision velocity around 8 MeV/u.

Besides the possibility to reach the pure three-body problem (bare ion on hydrogenic target) as a benchmark, the role of additional electrons bounded to the target and/or to the projectile -one by one- should allow quantifying several effects such as:

1. closure and/or opening of different channels: such as capture channels, that are open for bare projectiles but may be closed (or less likely) for other charge states;

2. electron-electron interactions: besides correlations, the presence of additional electrons can also directly increase (anti-screening) or decrease (screening) the mechanism probabilities;

3. multi-electron processes: often neglected, they can become as large as single processes in some cases (see, for instance [112]);
# 10. Ion-ion collisions in the intermediate velocity regime

Emily Lamour

INSP—Sorbonne University, France

**Status.** Ion-ion collisions provide a unique scenario for testing our knowledge of fundamental electronic processes such as capture, ionization and excitation. Their study is also motivated by the fact that they are strongly correlated to the ion energy transfer in various plasma conditions.

Whereas ion-ion experiments for high-energy physics (like the experiments at CERN) are currently carried out, ion-ion collisions for atomic physics have been so far performed mainly in the context of magnetically confined plasmas [108]. There, in the low velocity regime, typically at center-of-mass energies of a few keV up to a few 100 keV, cross section measurements of the charge transfer process [109, 110] (by far the dominant process) were performed with light ions (up to oxygen) for collisions with bare, hydrogen- or helium-like ions, or with low-charged ions for the heavy systems like Bi and Pb, where charge states of up to 4 + have been used.

Investigation of the intermediate velocity regime (the pink area in figure 16) is more complicated due to the fact that, there, all the primary electronic processes (EC, loss and excitation) reach their optimum probability leading to the maximum of the ion stopping power and, consequently, to the strongest effects on material modifications. A few ion-plasma experiments, motivated by their consequences in the inertial confinement plasma fusion physics, have been carried out with swift heavy ions in hydrogen or deuterium low-density plasmas and, later on, in laser-generated carbon plasma of one percent solid state density. Evidences for drastic differences in ion stopping power when ions interact with either neutral or ionized matter have been clearly established (see for instance, [111]). Nevertheless, to extract direct information on elementary process modifications is almost impossible since many charge states may be present at the same time in the plasma. Likewise, in simple ion—(neutral) atom collisions, the presence of many electrons makes the determination of experimental cross sections of a single elementary collision process extremely difficult. It can be achieved only in very specific cases: for instance, taking full advantages of the spin-selectivity in excited state populations, the single $1s \rightarrow 2p$ excitation cross section has been measured for collisions between 13.6 MeV/u Ar$^{16+}$ ions and neutral atoms (from He to Xe) [112]. From a theoretical point of view, none of the present most sophisticated available calculations is able to treat all the processes together on the same footing pointing to a fundamental issue in our understanding of elementary atomic interactions. This circumstance gives rise to a paradoxical situation where, for this velocity regime, cross sections are very hard to predict, while their knowledge is of critical importance. A significant test of theories can only be performed if the presence of numerous electrons can be avoided (beside the simplest case of a proton on hydrogen collision). Alternatively, the effect of other electrons

<figure><img src="image_20.png" /><figcaption>Figure 16. Cross sections of elementary atomic collision processes for the system p → H as a function of the proton energy. The brown line is the stopping power (refer to the right y-axis) for protons in aluminum. The pink area marks the intermediate collision regime.</figcaption></figure>

participating to the processes must be explored. In this context, our knowledge of the intermediate collision regime is really limited. There is a lack of measurements and available theoretical calculations are at their limit of validity. In other words, this regime corresponds to a real 'terra incognita' for atomic physics.

With ion-ion collision experiments, we deal with 'clean plasmas' of well-known charge states, we have the ability to investigate a large variety of systems and the possibility to easily scan the charge state of each ion partner. Nevertheless, the realization of these experiments remains a real challenge involving several steps that have to be solved in order to perform absolute cross section measurements.

**Current and future challenges.** The intermediate regime is reached when the relative target-projectile velocity is of the same order as the ones of the active electrons in its initial state. For instance, in the case of the symmetric collision Ar$^{Q+}$ on Ar$^{q+}$, it occurs at a collision velocity around 8 MeV/u.

Besides the possibility to reach the pure three-body problem (bare ion on hydrogenic target) as a benchmark, the role of additional electrons bounded to the target and/or to the projectile -one by one- should allow quantifying several effects such as:

1. closure and/or opening of different channels: such as capture channels, that are open for bare projectiles but may be closed (or less likely) for other charge states;

2. electron-electron interactions: besides correlations, the presence of additional electrons can also directly increase (anti-screening) or decrease (screening) the mechanism probabilities;

3. multi-electron processes: often neglected, they can become as large as single processes in some cases (see, for instance [112]);
4. Coulomb forces acting on the electron cloud in the entrance and exit pathway of the collision (effect related to the total charge of the collision partners).

Therefore, these kind of studies should provide original data on the quantum dynamics of *N*-body systems.

So far, no experiment has been performed in this regime mainly due to experimental issues, among which the requirement of (i) very high ion beam intensities of good optical quality with a perfect charge state control of the both ion beams, (ii) the control of the overlap between the ion beams and (iii) the high energy ion detector with a good count rate capability (up to 1 MHz) that need to be, in particular, radiation resistant. Additionally, an efficient cross beam arrangement running under ultra-high vacuum conditions is needed with the possibility to slightly change the energy of the low-energy ions in the interaction zone to tag the true events from the ones coming from collisions with the remaining atoms in the residual gas. Obviously, to properly analyze the collision products, powerful charge-state dispersion systems coupled to ion detectors are required for multi-coincidence measurements.

*Advances in science and technology to meet challenges.* For the low-energy channel, an ion source connected to a beam transport line provides currently ions in the keV/u energy range. The line needs to be well-adapted to shape the beam and clean it from the non-desired charge state just prior to the collision zone (for background reduction). This beam constitutes a target of a rather dilute density (a few 10¹⁴ cm³ maximum). Therefore, for the high energy channel, very intense beams are mandatory.

The forthcoming availability of MeV energy and stable ion beams of high optical quality at French and German Large Scale Facilities, GANIL/SPIRAL2/S3 [113] and FAIR/CRYRING ([114, 117], see section 19), opens now real opportunities towards the study of the intermediate collision regime. In fact, two experimental approaches have to be considered depending on the facility used. With SPIRAL2/S3, very intense ion beams between 10¹² and 10¹⁴ particles per second of medium Z number (from He to Ar) will be delivered allowing a 'single-pass experiment' arrangement. In this case, the stripping of very intense ion beams for reaching the desired charge state raises the issue of the resistance of the stripper (a thin solid foil) to the ion energy deposition. This can be overcome by using a rotating stripper so that the beam power is distributed over a much larger volume [115]. With

the CRYRING ion storage ring, the effective target density is increased simply due to the revolution frequency of the MeV/u ion beam what we call a 'multi-pass experiment' arrangement. CRYRING is equipped with an electron cooler operating with an ultracold electron beam, allowing to provide ion beams of very high-optical quality. With this facility, MeV/u ions heavier than the ones provided by SPIRAL2 (presumably up to U) will be stored allowing the study of asymmetric collision systems. For the heaviest ions stored at energies in the region of ~10 MeV/u or less, we also enter the realm where the formation of a quasi-molecule during the collision with an electric field from the combined nuclear charge of $Z_{\text{target}} + Z_{\text{projectile}} > 174$ can be formed allowing the spontaneous creation of electron-positron pairs (supercritical field) [116]. This offers the possibility to investigate the most controlled environment where fully relativistic QED calculations are required to study atomic processes in the presence of extreme electromagnetic fields (i.e. exceeding the critical Schwinger limit of $2 \times 10^{16} \text{ V cm}^{-1}$) [117].

*Concluding remarks.* When a few MeV/u ions collide with a few keV/u ions, a hitherto unexplored collision regime is reached: the regime where the ion energy transfer is at its maximum. There, measurements and reliable theoretical predictions are completely lacking. With the performances of the new upcoming facilities in France and Germany, a complete experimental program of ion-ion collisions is now clearly conceivable involving a large variety of collision systems with the possibility to tune both the projectile and target charge state over a wide range up to bare ion on hydrogenic target. There is no doubt that original experimental data on the quantum dynamics of *N*-body systems are expected.

## Acknowledgments

This work is not and will not be feasible without the full ASUR team at INSP, our colleagues from CIMAP (Caen, France) and from the Atomic Physics group at GSI and Jena University (Germany). We thank the GANIL staff and the Atomic Physic group at Giessen (Germany). This work is supported by the French National Agency under the two contracts ANR-13-IS04-0007 and 10-EQPX-0046 as well as by the Laboratory of Excellence Plas@Par (Plasma à Paris).
4. Coulomb forces acting on the electron cloud in the entrance and exit pathway of the collision (effect related to the total charge of the collision partners).

Therefore, these kind of studies should provide original data on the quantum dynamics of N-body systems.

So far, no experiment has been performed in this regime mainly due to experimental issues, among which the requirement of (i) very high ion beam intensities of good optical quality with a perfect charge state control of the both ion beams, (ii) the control of the overlap between the ion beams and (iii) the high energy ion detector with a good count rate capability (up to 1 MHz) that need to be, in particular, radiation resistant. Additionally, an efficient cross beam arrangement running under ultra-high vacuum conditions is needed with the possibility to slightly change the energy of the low-energy ions in the interaction zone to tag the true events from the ones coming from collisions with the remaining atoms in the residual gas. Obviously, to properly analyze the collision products, powerful charge-state dispersion systems coupled to ion detectors are required for multi-coincidence measurements.

*Advances in science and technology to meet challenges.* For the low-energy channel, an ion source connected to a beam transport line provides currently ions in the keV/u energy range. The line needs to be well-adapted to shape the beam and clean it from the non-desired charge state just prior to the collision zone (for background reduction). This beam constitutes a target of a rather dilute density (a few 10¹⁴ cm³ maximum). Therefore, for the high energy channel, very intense beams are mandatory.

The forthcoming availability of MeV energy and stable ion beams of high optical quality at French and German Large Scale Facilities, GANIL/SPIRAL2/S3 [113] and FAIR/CRYRING ([114, 117], see section 19), opens now real opportunities towards the study of the intermediate collision regime. In fact, two experimental approaches have to be considered depending on the facility used. With SPIRAL2/S3, very intense ion beams between 10¹² and 10¹⁴ particles per second of medium Z number (from He to Ar) will be delivered allowing a 'single-pass experiment' arrangement. In this case, the stripping of very intense ion beams for reaching the desired charge state raises the issue of the resistance of the stripper (a thin solid foil) to the ion energy deposition. This can be overcome by using a rotating stripper so that the beam power is distributed over a much larger volume [115]. With

the CRYRING ion storage ring, the effective target density is increased simply due to the revolution frequency of the MeV/u ion beam what we call a 'multi-pass experiment' arrangement. CRYRING is equipped with an electron cooler operating with an ultracold electron beam, allowing to provide ion beams of very high-optical quality. With this facility, MeV/u ions heavier than the ones provided by SPIRAL2 (presumably up to U) will be stored allowing the study of asymmetric collision systems. For the heaviest ions stored at energies in the region of ~10 MeV/u or less, we also enter the realm where the formation of a quasi-molecule during the collision with an electric field from the combined nuclear charge of $Z_{\text{target}} + Z_{\text{projectile}} > 174$ can be formed allowing the spontaneous creation of electron-positron pairs (supercritical field) [116]. This offers the possibility to investigate the most controlled environment where fully relativistic QED calculations are required to study atomic processes in the presence of extreme electromagnetic fields (i.e. exceeding the critical Schwinger limit of $2 \times 10^{16} \text{ V cm}^{-1}$) [117].

*Concluding remarks.* When a few MeV/u ions collide with a few keV/u ions, a hitherto unexplored collision regime is reached: the regime where the ion energy transfer is at its maximum. There, measurements and reliable theoretical predictions are completely lacking. With the performances of the new upcoming facilities in France and Germany, a complete experimental program of ion-ion collisions is now clearly conceivable involving a large variety of collision systems with the possibility to tune both the projectile and target charge state over a wide range up to bare ion on hydrogenic target. There is no doubt that original experimental data on the quantum dynamics of N-body systems are expected.

## Acknowledgments

This work is not and will not be feasible without the full ASUR team at INSP, our colleagues from CIMAP (Caen, France) and from the Atomic Physics group at GSI and Jena University (Germany). We thank the GANIL staff and the Atomic Physic group at Giessen (Germany). This work is supported by the French National Agency under the two contracts ANR-13-IS04-0007 and 10-EQPX-0046 as well as by the Laboratory of Excellence Plas@Par (Plasma à Paris).
# HIGHLY CHARGED IONS

## 11. Frequency metrology with trapped and stored HCIs

José R Crespo López-Urrutia

Max-Planck-Institut für Kernphysik, Germany

**Status.** Arguably, all interactions in the Standard Model of physics leave their watermark on the electronic wave function. The question is, can one access those effects through precision measurements? Until now, the answer in atomic physics has often been yes; witnesses are atomic clocks, hyperfine anomalies, Mössbauer-based general relativity tests, atomic parity non-conservation and many other examples. An even wider landscape of possibilities is reviewed in [118]. For the most accurate method in science, frequency metrology, the introduction of the frequency comb as well as the use of atoms and singly charged ions as clock references [119], with laser cooling techniques bringing them into the Doppler-free motional ground state are enabling stupendous and steady gains in accuracy. With frequency (ν) determinations in optical transitions by far surpassing in their accuracies that of classical microwave atomic clocks, novel methods of optical frequency metrology (OFM) are starting to contribute to fundamental and applied research in manifold ways. At the level of $\Delta\nu/\nu \approx 10^{-18}$ recently demonstrated [120], universally reproducible atomic frequency standards are also equally sensitive to various physical aspects of their environment and become the finest physical sensors available.

Until recently, HCIs stayed outside those developments, since directly laser cooling them is not possible. Fundamental studies with HCI in the field of QED in extreme fields, nuclear-size effects and the like had the advantage of the high powers of the atomic number Z with which those effects scale up with the charge state (see, e.g. [121, 122]). Astrophysics benefited from controlled spectroscopic studies in the laboratory [123], and atomic structure theory was stringently benchmarked [124]. However, HCI spectroscopy in electron beam ion traps [124], merged-beam setups and storage rings was intrinsically limited by Doppler-borne broadening and shifts to an accuracy typically worse than one part-per-million, more than ten orders of magnitude away from state-of-the-art OFM. None of the proposed techniques including the use of free-electron lasers and highly monochromatic synchrotron radiation could suppress this drawback of those devices.

Very recently, with the introduction of sympathetic laser cooling [125] in a cryogenic radio-frequency trap (see figure 17) at the Max-Planck-Institut für Kernphysik (MPIK), HCI cooling to the motional ground state has nonetheless become achievable, breaking the present barriers. In addition, this step has suddenly increased the variety of species available for OFM by a large factor, since many isoelectronic sequences in HCI possess narrow optical transitions suitable for laser excitation from the electronic ground state. Many

<figure><img src="image_20.png" /><figcaption>Figure 17. Invisible, a sympathetically cooled Ar$^{13+}$ ion occupies the left side of a Coulomb crystal of laser-cooled Be$^{+}$ ions. Bringing down the translational temperature of the HCI by nearly eight orders of magnitude, this key step prepares the ion for subsequent ground-state cooling followed by quantum-logic spectroscopy in a cryogenic radio-frequency trap (Image: MPIK).</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Figure 18. Frequency metrology with HCI: an electron beam ion trap emits HCI that are decelerated, bunched, and injected into a linear radio-frequency trap, where sympathetic cooling with a previously prepared Coulomb crystal of several Be$^{+}$ ions takes place. Then, an ensemble of one single HCI with one single Be$^{+}$ ion is prepared and cooled to its motional ground state. Resonant excitation of forbidden transitions in the HCI, and detection of those excitations by means of quantum-logic spectroscopy follow. In this method, interrogation of the Raman side-band transitions of Be$^{+}$ yields the state of the HCI (Image: MPIK).</figcaption></figure>

applications in fundamental research will benefit from this advance [124, 126].

Moreover, HCI have high ionization potentials and can therefore be excited by lasers from the extreme ultraviolet to the x-ray region without being photoionized, making narrow electronic transitions at such high frequencies of the electromagnetic field possible (figure 18). In this way, supported by rapid advances in the generation of narrow-band lasers in those spectral regions based on high-harmonic generation, extreme frequency metrology (XFM) will find in HCI [127] adequate frequency standards for reference and stabilization beyond the few that potential nuclear clocks could provide.

**Current and future challenges.** From a scientific point of view, the foremost task is testing the basic theories that support our understanding of nature, such as QED, general
# HIGHLY CHARGED IONS

## 11. Frequency metrology with trapped and stored HCIs

José R Crespo López-Urrutia

Max-Planck-Institut für Kernphysik, Germany

**Status.** Arguably, all interactions in the Standard Model of physics leave their watermark on the electronic wave function. The question is, can one access those effects through precision measurements? Until now, the answer in atomic physics has often been yes; witnesses are atomic clocks, hyperfine anomalies, Mössbauer-based general relativity tests, atomic parity non-conservation and many other examples. An even wider landscape of possibilities is reviewed in [118]. For the most accurate method in science, frequency metrology, the introduction of the frequency comb as well as the use of atoms and singly charged ions as clock references [119], with laser cooling techniques bringing them into the Doppler-free motional ground state are enabling stupendous and steady gains in accuracy. With frequency (ν) determinations in optical transitions by far surpassing in their accuracies that of classical microwave atomic clocks, novel methods of optical frequency metrology (OFM) are starting to contribute to fundamental and applied research in manifold ways. At the level of $\Delta\nu/\nu \approx 10^{-18}$ recently demonstrated [120], universally reproducible atomic frequency standards are also equally sensitive to various physical aspects of their environment and become the finest physical sensors available.

Until recently, HCIs stayed outside those developments, since directly laser cooling them is not possible. Fundamental studies with HCI in the field of QED in extreme fields, nuclear-size effects and the like had the advantage of the high powers of the atomic number Z with which those effects scale up with the charge state (see, e.g. [121, 122]). Astrophysics benefited from controlled spectroscopic studies in the laboratory [123], and atomic structure theory was stringently benchmarked [124]. However, HCI spectroscopy in electron beam ion traps [124], merged-beam setups and storage rings was intrinsically limited by Doppler-borne broadening and shifts to an accuracy typically worse than one part-per-million, more than ten orders of magnitude away from state-of-the-art OFM. None of the proposed techniques including the use of free-electron lasers and highly monochromatic synchrotron radiation could suppress this drawback of those devices.

Very recently, with the introduction of sympathetic laser cooling [125] in a cryogenic radio-frequency trap (see figure 17) at the Max-Planck-Institut für Kernphysik (MPIK), HCI cooling to the motional ground state has nonetheless become achievable, breaking the present barriers. In addition, this step has suddenly increased the variety of species available for OFM by a large factor, since many isoelectronic sequences in HCI possess narrow optical transitions suitable for laser excitation from the electronic ground state. Many

<figure><img src="image_21.png" /><figcaption>Figure 17. Invisible, a sympathetically cooled Ar$^{13+}$ ion occupies the left side of a Coulomb crystal of laser-cooled Be$^{+}$ ions. Bringing down the translational temperature of the HCI by nearly eight orders of magnitude, this key step prepares the ion for subsequent ground-state cooling followed by quantum-logic spectroscopy in a cryogenic radio-frequency trap (Image: MPIK).</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Figure 18. Frequency metrology with HCI: an electron beam ion trap emits HCI that are decelerated, bunched, and injected into a linear radio-frequency trap, where sympathetic cooling with a previously prepared Coulomb crystal of several Be$^{+}$ ions takes place. Then, an ensemble of one single HCI with one single Be$^{+}$ ion is prepared and cooled to its motional ground state. Resonant excitation of forbidden transitions in the HCI, and detection of those excitations by means of quantum-logic spectroscopy follow. In this method, interrogation of the Raman side-band transitions of Be$^{+}$ yields the state of the HCI (Image: MPIK).</figcaption></figure>

applications in fundamental research will benefit from this advance [124, 126].

Moreover, HCI have high ionization potentials and can therefore be excited by lasers from the extreme ultraviolet to the x-ray region without being photoionized, making narrow electronic transitions at such high frequencies of the electromagnetic field possible (figure 18). In this way, supported by rapid advances in the generation of narrow-band lasers in those spectral regions based on high-harmonic generation, extreme frequency metrology (XFM) will find in HCI [127] adequate frequency standards for reference and stabilization beyond the few that potential nuclear clocks could provide.

**Current and future challenges.** From a scientific point of view, the foremost task is testing the basic theories that support our understanding of nature, such as QED, general
relativity, the standard model of physics, parity non-
conservation, cosmology and the Dark Matter question
appear. Atomic physics and frequency metrology are
already yielding deeper and deeper insights into those, and
presumably an extension to higher photon energies will open
new possibilities to contribute to these fields. However, our
ability to benchmark theoretical developments against the
most accurate results from OFM still encounters a conundrum
that is both hindrance and opportunity, namely the limitations
of our knowledge about the atomic nucleus. A very good
example is the proton radius issue, where the superior
sensitivity of laser techniques has challenged long standing
high-energy electron scattering results, albeit not all problems
have been solved yet. QED in stable, bound systems is the
most accurate theory of physics, but further advances will
require a better understanding of nuclear-size contributions to
the experimentally determined atomic transition frequencies.
On the other side, proposed combinations of such
measurements can provide exactly that information on the
nucleus, thus facilitating tests of nuclear theory and deeper
benchmarking of QED. This would be more propitious than at
first sight: as the primordial quantum-field theory, any
improvements in its methods will lead to advances in other
parts of the standard model both from the point of view of the
mathematical methodology in use as well as from the better
understanding of perturbations that affect measurements at
high and low momentum transfer.

*Advances in science and technology to meet challenges.*

Exquisite methods of OFM [119] have been developed in the
last decade by pioneering groups worldwide. Transferring
those to the newly accessible HCI [125] will undoubtedly
become a task for the next few years. Auspiciously, ground-
state cooling of HCI via sympathetic cooling, and quantum-
logic spectroscopy with HCI have just been achieved by a
collaboration of the QUEST group (Schmidt) at the
Physikalisch-Technische Bundesanstalt (PTB) in
Braunschweig and MPIK. This step makes HCI available
for the application of OFM at the highest levels of accuracy
now available. Other groups pursuing this route will also
profit from it.

With this clear path for OFM with HCI already in the
near future, the quest for an extension into the XFM domain is
still pending [127]. Frequency combs in the VUV and XUV
have already been demonstrated by a few groups. Attempts to
make them available for uses with HCI are already underway.
Perspectives for their application include in principle all what
has already been shown to work in the optical region, plus
fields of research which intrinsically require high photon
energies. One interesting example for long-term research is
the study of nuclear transitions unaffected by solid-state

effects, this means, using isolated HCI as targets being the
carriers of the nuclei of interest. Potentially, HCI impervious
to the x rays needed to excite low-lying nuclear levels, as in
Mössbauer transitions, up to 100 keV could be prepared and
cooled. The extremely narrow linewidths of those x-ray
transitions would enable even more sensitive probes of
nuclear forces and fundamental physics.

Another fruitful approach to fundamental physics with
HCI is their use in high-precision Penning traps (see related
references to recent work of various groups in [118, 124]).
This has delivered outstanding tests of QED through studies
of the bound-electron *g* factor and atomic mass determina-
tions that are sensitive to the binding energies of nuclei and
their surrounding electronic shell to a level which is rapidly
becoming competitive with standard x-ray spectroscopy of
HCI. Furthermore, in combination with rare-isotope beam
facilities, Penning traps that are already workhorses of nuclear
physics will also experience a stupendous push in accuracy
from the application of sympathetic laser cooling techniques
to the trapped HCI, and quantum logic techniques.

*Concluding remarks.* Beyond our daily perspective, HCI
constitute the bulk of baryonic matter for the majority of the
chemical elements in the universe. Due to their properties,
they control radiation transport in stellar cores, and are the
strongest spectral emitters in x-ray astrophysics from stellar
corona to black hole and active galactic nuclei environments.
As isolated quantum systems, they are excellent probes for
fundamental interactions with the triple advantage of strongly
scaled-up QED and nuclear-size effects, simpler electronic
structure than atoms, and extreme suppression of sensitivity to
spurious external perturbations of the electromagnetic field.
Nowadays, their use in the laboratory is becoming easier, with
smaller and more practical sources showing their performance
exactly for those purposes.

Now, tamed for XFM by means of re-trapping followed by
sympathetic cooling, their variety will constitute an invaluable
advantage for fundamental and applied research. The periodic
table acquires height with the ionic charge state; on the pathways
across these largely pristine ranges, new spots at high vantages
will offer broad scopes and far sights of the physics landscape.
Leaving them unexplored would be a lost opportunity.

Acknowledgments

Stimulating discussions with J Berengut, K Blaum, D Budker,
A Derevianko, V Flambaum, M Kozlov, M Safronova, P O
Schmidt, and other colleagues driving this field with their
ideas are gratefully acknowledged.
relativity, the standard model of physics, parity non-conservation, cosmology and the Dark Matter question appear. Atomic physics and frequency metrology are already yielding deeper and deeper insights into those, and presumably an extension to higher photon energies will open new possibilities to contribute to these fields. However, our ability to benchmark theoretical developments against the most accurate results from OFM still encounters a conundrum that is both hindrance and opportunity, namely the limitations of our knowledge about the atomic nucleus. A very good example is the proton radius issue, where the superior sensitivity of laser techniques has challenged long standing high-energy electron scattering results, albeit not all problems have been solved yet. QED in stable, bound systems is the most accurate theory of physics, but further advances will require a better understanding of nuclear-size contributions to the experimentally determined atomic transition frequencies. On the other side, proposed combinations of such measurements can provide exactly that information on the nucleus, thus facilitating tests of nuclear theory and deeper benchmarking of QED. This would be more propitious than at first sight: as the primordial quantum-field theory, any improvements in its methods will lead to advances in other parts of the standard model both from the point of view of the mathematical methodology in use as well as from the better understanding of perturbations that affect measurements at high and low momentum transfer.

*Advances in science and technology to meet challenges.*

Exquisite methods of OFM [119] have been developed in the last decade by pioneering groups worldwide. Transferring those to the newly accessible HCI [125] will undoubtedly become a task for the next few years. Auspiciously, ground-state cooling of HCI via sympathetic cooling, and quantum-logic spectroscopy with HCI have just been achieved by a collaboration of the QUEST group (Schmidt) at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig and MPIK. This step makes HCI available for the application of OFM at the highest levels of accuracy now available. Other groups pursuing this route will also profit from it.

With this clear path for OFM with HCI already in the near future, the quest for an extension into the XFM domain is still pending [127]. Frequency combs in the VUV and XUV have already been demonstrated by a few groups. Attempts to make them available for uses with HCI are already underway. Perspectives for their application include in principle all what has already been shown to work in the optical region, plus fields of research which intrinsically require high photon energies. One interesting example for long-term research is the study of nuclear transitions unaffected by solid-state

effects, this means, using isolated HCI as targets being the carriers of the nuclei of interest. Potentially, HCI impervious to the x rays needed to excite low-lying nuclear levels, as in Mössbauer transitions, up to 100 keV could be prepared and cooled. The extremely narrow linewidths of those x-ray transitions would enable even more sensitive probes of nuclear forces and fundamental physics.

Another fruitful approach to fundamental physics with HCI is their use in high-precision Penning traps (see related references to recent work of various groups in [118, 124]). This has delivered outstanding tests of QED through studies of the bound-electron *g* factor and atomic mass determinations that are sensitive to the binding energies of nuclei and their surrounding electronic shell to a level which is rapidly becoming competitive with standard x-ray spectroscopy of HCI. Furthermore, in combination with rare-isotope beam facilities, Penning traps that are already workhorses of nuclear physics will also experience a stupendous push in accuracy from the application of sympathetic laser cooling techniques to the trapped HCI, and quantum logic techniques.

*Concluding remarks.* Beyond our daily perspective, HCI constitute the bulk of baryonic matter for the majority of the chemical elements in the universe. Due to their properties, they control radiation transport in stellar cores, and are the strongest spectral emitters in x-ray astrophysics from stellar coronae to black hole and active galactic nuclei environments. As isolated quantum systems, they are excellent probes for fundamental interactions with the triple advantage of strongly scaled-up QED and nuclear-size effects, simpler electronic structure than atoms, and extreme suppression of sensitivity to spurious external perturbations of the electromagnetic field. Nowadays, their use in the laboratory is becoming easier, with smaller and more practical sources showing their performance exactly for those purposes.

Now, tamed for XFM by means of re-trapping followed by sympathetic cooling, their variety will constitute an invaluable advantage for fundamental and applied research. The periodic table acquires height with the ionic charge state; on the pathways across these largely pristine ranges, new spots at high vantages will offer broad scopes and far sights of the physics landscape. Leaving them unexplored would be a lost opportunity.

## Acknowledgments

Stimulating discussions with J Berengut, K Blaum, D Budker, A Derevianko, V Flambaum, M Kozlov, M Safronova, P O Schmidt, and other colleagues driving this field with their ideas are gratefully acknowledged.
## 12. Highly-charged radionuclides

Yuri A Litvinov

GSI Helmholtz Center, Germany

**Status.** Highly-charged radionuclides (HCR) are systems with none or just a few atomic electrons, like, for instance, hydrogen- (H-like), helium- (He-like) or lithium-like (Li-like) ions. These are well-defined nucleus plus lepton(s) systems with well-defined quantum numbers. Studies of isolated HCRs shall help understanding complicated processes involving HCRs in stellar hot and dense objects.

The first major research subject with HCRs is devoted to studies of nuclear decay properties [128]. Here, decay channels known in neutral atoms can disappear, like for instance orbital EC is disabled in fully-ionized nuclides, while new decay channels may open up. One example of the latter is the bound-state beta decay ($\beta_b$). Different from an ordinary $\beta^-$ decay, the electron is not emitted into continuum but occupies one of the free bound orbitals. To date, $\beta_b$ decay has been measured for 5 nuclides ($^{163}$Dy$^{63+}$, $^{187}$Re$^{87+}$, $^{205}$Hg$^{80+}$, $^{206,207}$Tl$^{81+}$), providing—among other important results—the first $\beta_b/\beta^-$ ratio that can be compared to time-mirrored EC/$\beta^+$ ratios [128]. Very demanding is the measurement of the $\beta_b$ of $^{205}$Tl$^{81+}$, which is important for the determination of the pp-solar neutrino capture probability into the 2.3 keV state of $^{205}$Pb and can also be used to constrain the very end of the s-process (slow neutron capture) nucleosynthesis.

Excellent examples illustrating the importance of the interplay of atomic and nuclear structure in describing weak decays are provided by first experiments addressing allowed Gamow-Teller EC decays in H- and He-like ions [129]. The EC decay rate in H-like $^{140}$Pr$^{58+}$ and $^{142}$Pm$^{60+}$ ions was found to be about 50% larger than in the respective He-like ions. This result is explained by considering the conservation of the total (nucleus + leptons) angular momentum and the defined helicity of the emitted electron neutrino [129]. A surprising consequence of the latter is the disabled Gamow-Teller $1^+ \rightarrow 2^+ + \text{EC}$ transitions in H-like $^{122}$I$^{52+}$ ions [129]. By selecting specific nuclei and transitions, forbidden decays and other subtle effects in weak decay can be addressed in the future. One specific example is $^{111}$Sn, where, by studying $\beta$ decay rate in bare and H-like ions, first direct measurement of electron screening in $\beta$ decay can be achieved [129].

Concerning the electromagnetic decays, the atomic charge state can also have a significant influence on the decay rate. It is straightforward that the de-excitation of nuclei via internal conversion (IC) is disabled in fully-ionized nuclides. A new decay mode, the bound-state internal conversion (BIC) [130], can open up in HCRs. Here, an excited nuclear state resonantly transfers its excitation energy to a bound electron which is excited to a bound atomic level at a higher energy. The time-reversed processes for IC and BIC are respectively the nuclear excitation by electron capture/transition (NEEC/T). The latter exotic decay modes are being searched for many decades. They may play an essential role in the population of nuclear excited states in

plasmas, which in turn are the reason for the so-called stellar enhancement factors in nucleosynthesis modeling. Furthermore, an effective induced de-excitation of a nuclear isomer through NEEC/T process is one of the dreams for the application of nuclear isomers for energy storage. A first observation of the NEEC process has been reported in 2018 [131] and calls for an independent verification. Suggestions for searches of other exotic decay modes, like Pauli-forbidden transitions and bound electron-positron de-excitations, have been proposed and await their realization [132].

The second research subject is DR on HCRs [129]. The DR spectra of the in-flight generated Li-like $^{237}$U$^{89+}$ and $^{234}$Pa$^{87+}$ ions have been obtained [133]. The resonant nature of the DR process, which is sensitive to nuclear quantum numbers, might be used to select/purify nuclides of interest from unresolved contaminants [133]. This may be employed to investigate the lowest-energy isomeric states ($^{229}$Th, $^{235}$U) [134]. The experimental verification of the existence of the 'nuclear clock' isomeric state in $^{229}$Th [135] makes its future extraction and trapping highly relevant. It is also interesting to measure the lifetime of $^{229}$Th isomeric state dependent on the atomic charge state, that is with enabled/disabled hyperfine splitting (HFS).

The last application of HCRs addressed here are the astrophysical reactions, where the nuclear reaction rate is deduced through normalizing to the significantly better known theoretical atomic K-REC cross-section. The first proton capture reactions were performed on $^{94}$Ru$^{44+}$ and $^{124}$Xe$^{54+}$ stable nuclides [136]. In the latter case, the center of mass energy as low as 6 MeV/$u$ has been achieved [137] thus approaching the Gamow window of the astrophysical p-process (proton capture process). The available experimental data are scarce and such investigations are therefore highly demanded.

**Current and future challenges.** Experimentally, precision investigations on HCRs are complicated since the exotic nuclides have to be produced in a specific high atomic charge state and then be purified from inevitable contaminants [128, 129]. Furthermore, except for very short lifetimes, all experiments require HCRs to be stored for an extended period of time in a preserved atomic charge state. The experimental studies with HCRs are presently routinely conducted at heavy-ion storage rings. We note though, that there are proposals for studying decays of HCRs in electron-beam ion traps (EBITs). Therefore, the main challenges are connected with the development of trapping devices, EBITs and storage rings, connected to radioactive-ion beam facilities. Furthermore, different experiments require different energies and sophisticated beam manipulations. All experiments count on excellent quality of electron-cooled ion beams.

To keep HCRs stored, the detectors must be non-destructive or intercept reaction products at special locations defined by the storage ring ion-optics. Since the experiments are conducted on rare ion species, an essential goal is to improve sensitivity and efficiency of detectors, ideally up to ultimate sensitivity to individual ions and 100% efficiency. One example of the latter is illustrated in figure 19, where the
# 12. Highly-charged radionuclides

Yuri A Litvinov

GSI Helmholtz Center, Germany

**Status.** Highly-charged radionuclides (HCR) are systems with none or just a few atomic electrons, like, for instance, hydrogen- (H-like), helium- (He-like) or lithium-like (Li-like) ions. These are well-defined nucleus plus lepton(s) systems with well-defined quantum numbers. Studies of isolated HCRs shall help understanding complicated processes involving HCRs in stellar hot and dense objects.

The first major research subject with HCRs is devoted to studies of nuclear decay properties [128]. Here, decay channels known in neutral atoms can disappear, like for instance orbital EC is disabled in fully-ionized nuclides, while new decay channels may open up. One example of the latter is the bound-state beta decay ($\beta_b$). Different from an ordinary $\beta^-$ decay, the electron is not emitted into continuum but occupies one of the free bound orbitals. To date, $\beta_b$ decay has been measured for 5 nuclides ($^{163}$Dy$^{63+}$, $^{187}$Re$^{87+}$, $^{205}$Hg$^{80+}$, $^{206,207}$Tl$^{81+}$), providing—among other important results—the first $\beta_b/\beta^-$ ratio that can be compared to time-mirrored EC/$\beta^+$ ratios [128]. Very demanding is the measurement of the $\beta_b$ of $^{205}$Tl$^{81+}$, which is important for the determination of the pp-solar neutrino capture probability into the 2.3 keV state of $^{205}$Pb and can also be used to constrain the very end of the s-process (slow neutron capture) nucleosynthesis.

Excellent examples illustrating the importance of the interplay of atomic and nuclear structure in describing weak decays are provided by first experiments addressing allowed Gamow-Teller EC decays in H- and He-like ions [129]. The EC decay rate in H-like $^{140}$Pr$^{58+}$ and $^{142}$Pm$^{60+}$ ions was found to be about 50% larger than in the respective He-like ions. This result is explained by considering the conservation of the total (nucleus + leptons) angular momentum and the defined helicity of the emitted electron neutrino [129]. A surprising consequence of the latter is the disabled Gamow-Teller $1^+ \rightarrow 2^+ + \text{EC}$ transitions in H-like $^{122}$I$^{52+}$ ions [129]. By selecting specific nuclei and transitions, forbidden decays and other subtle effects in weak decay can be addressed in the future. One specific example is $^{111}$Sn, where, by studying $\beta$ decay rate in bare and H-like ions, first direct measurement of electron screening in $\beta$ decay can be achieved [129].

Concerning the electromagnetic decays, the atomic charge state can also have a significant influence on the decay rate. It is straightforward that the de-excitation of nuclei via internal conversion (IC) is disabled in fully-ionized nuclides. A new decay mode, the bound-state internal conversion (BIC) [130], can open up in HCRs. Here, an excited nuclear state resonantly transfers its excitation energy to a bound electron which is excited to a bound atomic level at a higher energy. The time-reversed processes for IC and BIC are respectively the nuclear excitation by electron capture/transition (NEEC/T). The latter exotic decay modes are being searched for many decades. They may play an essential role in the population of nuclear excited states in

plasmas, which in turn are the reason for the so-called stellar enhancement factors in nucleosynthesis modeling. Furthermore, an effective induced de-excitation of a nuclear isomer through NEEC/T process is one of the dreams for the application of nuclear isomers for energy storage. A first observation of the NEEC process has been reported in 2018 [131] and calls for an independent verification. Suggestions for searches of other exotic decay modes, like Pauli-forbidden transitions and bound electron-positron de-excitations, have been proposed and await their realization [132].

The second research subject is DR on HCRs [129]. The DR spectra of the in-flight generated Li-like $^{237}$U$^{89+}$ and $^{234}$Pa$^{87+}$ ions have been obtained [133]. The resonant nature of the DR process, which is sensitive to nuclear quantum numbers, might be used to select/purify nuclides of interest from unresolved contaminants [133]. This may be employed to investigate the lowest-energy isomeric states ($^{229}$Th, $^{235}$U) [134]. The experimental verification of the existence of the 'nuclear clock' isomeric state in $^{229}$Th [135] makes its future extraction and trapping highly relevant. It is also interesting to measure the lifetime of $^{229}$Th isomeric state dependent on the atomic charge state, that is with enabled/disabled hyperfine splitting (HFS).

The last application of HCRs addressed here are the astrophysical reactions, where the nuclear reaction rate is deduced through normalizing to the significantly better known theoretical atomic K-REC cross-section. The first proton capture reactions were performed on $^{94}$Ru$^{44+}$ and $^{124}$Xe$^{54+}$ stable nuclides [136]. In the latter case, the center of mass energy as low as 6 MeV/$u$ has been achieved [137] thus approaching the Gamow window of the astrophysical p-process (proton capture process). The available experimental data are scarce and such investigations are therefore highly demanded.

**Current and future challenges.** Experimentally, precision investigations on HCRs are complicated since the exotic nuclides have to be produced in a specific high atomic charge state and then be purified from inevitable contaminants [128, 129]. Furthermore, except for very short lifetimes, all experiments require HCRs to be stored for an extended period of time in a preserved atomic charge state. The experimental studies with HCRs are presently routinely conducted at heavy-ion storage rings. We note though, that there are proposals for studying decays of HCRs in electron-beam ion traps (EBITs). Therefore, the main challenges are connected with the development of trapping devices, EBITs and storage rings, connected to radioactive-ion beam facilities. Furthermore, different experiments require different energies and sophisticated beam manipulations. All experiments count on excellent quality of electron-cooled ion beams.

To keep HCRs stored, the detectors must be non-destructive or intercept reaction products at special locations defined by the storage ring ion-optics. Since the experiments are conducted on rare ion species, an essential goal is to improve sensitivity and efficiency of detectors, ideally up to ultimate sensitivity to individual ions and 100% efficiency. One example of the latter is illustrated in figure 19, where the
<figure><img src="image_22.png" /><figcaption>Figure 19. Two electron capture decays of H-like $^{142}$Pm$^{60+}$ ions measured by a resonant Schottky detector in the ESR at GSI [129]. The disappearance of each $^{142}$Pm$^{60+}$ ion and a correlated in time appearance of daughter $^{142}$Nd$^{60+}$ ion is seen. The curved traces correspond to the electron cooling of the recoil energy due to the neutrino emission. The lengths of the curved traces and the sign provide information on the direction and longitudinal component of the recoil momentum [129]. Reprinted from [129] Copyright 2013, with permission from Elsevier.</figcaption></figure>

novel resonant non-destructive Schottky detector is applied to detect EC decays of each stored H-like $^{142}$Pm$^{60+}$ ion [129].

For the particle detectors, the electron-cooled beams have tiny sizes so as the hit area on the detectors. Furthermore, the experiments at lower energies need detectors to be located directly in the ultra-high vacuum environment of a storage ring which is often a severe technological challenge [136, 137].

The relevant center-of-mass energies for astrophysical p-process are 2–6 MeV/u. Efficient slowing down to these energies of HCRs produced at high energies is yet a challenge [117]. Ultra-pure, thin, internal gas-jet targets are needed. The handling of low-energy beams interacting with gas targets, background due to Rutherford scattering, cooling efficiency, duty cycles, etc are still to be investigated. If successful, even lower energies relevant for, e.g. rp-process (rapid proton capture process) can be envisioned. So far only proton capture reactions were addressed. However, all kinds of proton and alpha induced reactions are of high interest.

Advances in science and technology to meet challenges.
Presently there are only two operational heavy-ion storage
rings capable of performing relevant experiments. These are
the experimental storage ring (ESR) at GSI in Darmstadt and
the experimental cooler-storage ring at IMPCAS in Lanzhou
[128, 129]. However, both rings are designed for a routine
operation at high, several hundred MeV/u, energies. Although
the ESR is capable of slowing the ions down to energies as low
as 3 MeV/u, there is an obvious need for dedicated low-energy
storage rings. At GSI, the CRYRING@ESR project is being
finalized ([117], section 19). Several pilot experiments have
been approved to run in the near future.

In addition to ESR and CRYRING, the new-generation
Facility for Antiproton and Ion Research (FAIR) will add
collector ring and high-energy storage ring (HESR) ([128, 129],
section 19). Mainly due to significantly increased secondary
beam intensities from the new powerful radioactive ion-beam
facility Super-FRS, various studies of decays of HCRs will
become possible, especially for nuclides relevant for astrophy-
sics. Furthermore, the HITRAP facility will enable HCRs at rest
 subsection 19). With all these new trapping devices, GSI/FAIR
will offer HCRs in a wide range of energies from about at rest
(HITRAP) throughout to about 5 GeV/u (HESR) (section 19).

In China, High-Intensity Accelerator Facility (HIAF) is
being planned [138]. This complex will include several
storage rings and versatile experimental capabilities.

A unique project to install a low-energy storage ring at ISOLDE/CERN has been proposed [134]. Such a ring would enable a broad range of experiments with HCRs. One distinct advantage of the project is that HCRs are injected into the ring at the required energy omitting the inefficient deceleration process. In particular, the EC decay of H- and He-like $^7$Be would be measured, which is important for constraining the Solar neutrino flux [134]. The project is presently postponed.

A new storage ring facility R3 has been constructed
behind the fragment separator at RIKEN in Japan. Atomic
mass measurements and lifetimes of very exotic HCRs are
planned there [138].

*Concluding remarks.* The interest in HCRs is found at the intersection of atomic, nuclear, and plasma physics. The precision investigations with HCRs allow for investigating basic phenomena under very clean experimental conditions where the atomic charge state and the corresponding quantum numbers are well-defined. Thus, the complex processes found in hot and dense plasmas can be constrained.

Addressed here are the decays of HCRs, which are
extremely sensitive to the interplay of atomic and nuclear
structure. Furthermore, DR and reaction studies on HCRs have
huge discovery potential. Left aside are atomic mass measure-
ments [138]. All measurements will profit dramatically from
new possibilities offered by the next-generation accelerator
complexes. Especially the low-energy storage rings and traps
will boost the research field in near future [117, 134].

Acknowledgments

This short paper is dedicated to my friends Paul Kienle and
Fritz Bosch who passed away much too early. It is based on
previous publications of our colleagues from several storage
ring collaborations. To all of them I am deeply obliged.
Discussions with K Blaum, C Brandau, I Dillmann, H Geis-
sel, J Glorius, C Kozhuharov, R Reifarth, M S Sanjari, M
Steck, Th Stöhkler, D Schneider, P M Walker, P J Woods, T
Yamaguchi and Y H Zhang are greatly appreciated. This
work is supported by the European Research Council (ERC)
under the EU Horizon 2020 research and innovation pro-
gramme (ERC CG 682841 ‘ASTRUm’).
<figure><img src="image_23.png" /><figcaption>Figure 19. Two electron capture decays of H-like $^{142}$Pm$^{60+}$ ions measured by a resonant Schottky detector in the ESR at GSI [129]. The disappearance of each $^{142}$Pm$^{60+}$ ion and a correlated in time appearance of daughter $^{142}$Nd$^{60+}$ ion is seen. The curved traces correspond to the electron cooling of the recoil energy due to the neutrino emission. The lengths of the curved traces and the sign provide information on the direction and longitudinal component of the recoil momentum [129]. Reprinted from [129] Copyright 2013, with permission from Elsevier.</figcaption></figure>

novel resonant non-destructive Schottky detector is applied to detect EC decays of each stored H-like $^{142}$Pm$^{60+}$ ion [129].

For the particle detectors, the electron-cooled beams have tiny sizes so as the hit area on the detectors. Furthermore, the experiments at lower energies need detectors to be located directly in the ultra-high vacuum environment of a storage ring which is often a severe technological challenge [136, 137].

The relevant center-of-mass energies for astrophysical p-process are 2–6 MeV/u. Efficient slowing down to these energies of HCRs produced at high energies is yet a challenge [117]. Ultra-pure, thin, internal gas-jet targets are needed. The handling of low-energy beams interacting with gas targets, background due to Rutherford scattering, cooling efficiency, duty cycles, etc are still to be investigated. If successful, even lower energies relevant for, e.g. rp-process (rapid proton capture process) can be envisioned. So far only proton capture reactions were addressed. However, all kinds of proton and alpha induced reactions are of high interest.

*Advances in science and technology to meet challenges.* Presently there are only two operational heavy-ion storage rings capable of performing relevant experiments. These are the experimental storage ring (ESR) at GSI in Darmstadt and the experimental cooler-storage ring at IMPCAS in Lanzhou [128, 129]. However, both rings are designed for a routine operation at high, several hundred MeV/u, energies. Although the ESR is capable of slowing the ions down to energies as low as 3 MeV/u, there is an obvious need for dedicated low-energy storage rings. At GSI, the CRYRING@ESR project is being finalized ([117], section 19). Several pilot experiments have been approved to run in the near future.

In addition to ESR and CRYRING, the new-generation Facility for Antiproton and Ion Research (FAIR) will add collector ring and high-energy storage ring (HESR) ([128, 129], section 19). Mainly due to significantly increased secondary beam intensities from the new powerful radioactive ion-beam facility Super-FRS, various studies of decays of HCRs will become possible, especially for nuclides relevant for astrophysics. Furthermore, the HITRAP facility will enable HCRs at rest (section 19). With all these new trapping devices, GSI/FAIR will offer HCRs in a wide range of energies from about at rest (HITRAP) throughout to about 5 GeV/u (HESR) (section 19).

In China, High-Intensity Accelerator Facility (HIAF) is being planned [138]. This complex will include several storage rings and versatile experimental capabilities.

A unique project to install a low-energy storage ring at ISOLDE/CERN has been proposed [134]. Such a ring would enable a broad range of experiments with HCRs. One distinct advantage of the project is that HCRs are injected into the ring at the required energy omitting the inefficient deceleration process. In particular, the EC decay of H- and He-like $^7$Be would be measured, which is important for constraining the Solar neutrino flux [134]. The project is presently postponed.

A new storage ring facility R3 has been constructed behind the fragment separator at RIKEN in Japan. Atomic mass measurements and lifetimes of very exotic HCRs are planned there [138].

*Concluding remarks.* The interest in HCRs is found at the intersection of atomic, nuclear, and plasma physics. The precision investigations with HCRs allow for investigating basic phenomena under very clean experimental conditions where the atomic charge state and the corresponding quantum numbers are well-defined. Thus, the complex processes found in hot and dense plasmas can be constrained.

Addressed here are the decays of HCRs, which are extremely sensitive to the interplay of atomic and nuclear structure. Furthermore, DR and reaction studies on HCRs have huge discovery potential. Left aside are atomic mass measurements [138]. All measurements will profit dramatically from new possibilities offered by the next-generation accelerator complexes. Especially the low-energy storage rings and traps will boost the research field in near future [117, 134].

## Acknowledgments

This short paper is dedicated to my friends Paul Kienle and Fritz Bosch who passed away much too early. It is based on previous publications of our colleagues from several storage ring collaborations. To all of them I am deeply obliged. Discussions with K Blaum, C Brandau, I Dillmann, H Geisel, J Glorius, C Kozhuharov, R Reifarth, M S Sanjari, M Steck, Th Stöhkler, D Schneider, P M Walker, P J Woods, T Yamaguchi and Y H Zhang are greatly appreciated. This work is supported by the European Research Council (ERC) under the EU Horizon 2020 research and innovation programme (ERC CG 682841 'ASTRUm').
## 13. QED in strong fields

Vladimir Shabaev

St. Petersburg State University, Russia

**Status.** Basic principles of QED were formulated to the beginning of 1930s by merging quantum mechanics with special relativity. The discovery of the Lamb shift in 1947 stimulated theorists to complete the creation of QED by developing the renormalization technique. Till the beginning of 1980s tests of QED were mainly restricted to light atomic systems where the calculations were performed in the weak-field approximation, which corresponds to small values of the parameter $\alpha Z$ ($\alpha$ is the fine structure constant and Z is the nuclear charge number). A unique opportunity to test QED in a strong-field regime, which requires calculations without any expansion in $\alpha Z$, appeared when high-precision experiments with heavy few-electron ions became feasible.

High-precision tests of QED effects with HCIs were first performed for the binding energies. The ground state Lamb shift in H-like uranium, which is defined as a difference between the exact energy and the point-nucleus Dirac energy, was measured to amount 460.2(4.6) eV [139]. The comparison of this experiment with the theoretical result, 463.99(39) eV (see [140] and references therein), provides a test of QED at the strong Coulomb field on a 2% level. Higher accuracy was achieved in experiments with Li-like ions. The present status of theory [141] and experiment [142] for the 2p<sub>1/2</sub>–2s transition energy in Li-like uranium provides a test of QED on a 0.2% level. For both H- and Li-like uranium ions the theoretical uncertainty is presently defined by some uncalculated contributions of two-loop QED diagrams (figure 20) and by an uncertainty of the nuclear charge radius.

To date we have a number of high-precision measurements of the HFS in heavy H-like ions (see, e.g. [143] and references therein). The main goal of these experiments was to test QED in a unique combination of strong electric and magnetic fields. But, because of a large theoretical uncertainty due to the nuclear magnetization distribution correction (so called Bohr–Weisskopf effect), it turned out that the QED tests are possible only via studying a specific difference of the HFS values of H- and Li-like ions [144]. The recent measurements of this difference in Bi [143] revealed a large discrepancy between experiment and theory. This discrepancy was explained in [145] by an incorrect value of the nuclear magnetic moment which was widely used in literature. New calculations of the magnetic shielding factor and new measurements of the nuclear magnetic moment in <sup>209</sup>Bi(NO<sub>3</sub>)<sub>3</sub> and <sup>209</sup>BiF<sub>6</sub> [145] lead to good agreement between theory and experiment. However, more precise measurements of the nuclear magnetic moments and the HFS values are needed to provide stringent QED tests.

High-precision measurements of the g factor of H- and Li-like low- and middle-Z ions (see, e.g. [146] and references therein) have provided stringent tests of the QED effects in presence of a magnetic field. Combined with the related theoretical predictions, these experiments have also provided the most precise determination of the electron mass [146].

<figure><img src="image_23.png" /><figcaption>Figure 20. One-electron two-loop Feynman diagrams which contribute to the Lamb shift. The double line represents an electron propagating in the Coulomb field. The wavy line indicates a virtual photon.</figcaption></figure>

Recently [147], the isotope shift of the g factor of Li-like calcium ions was measured. This experiment allowed the first test of the relativistic theory of the nuclear recoil effect on the g factor of highly charged Li-like ions.

One of the most interesting and intriguing issues of modern fundamental physics is related to tests of QED at supercritical fields. According to the QED theory, a static and spatially uniform electric field should create electron–positron pairs, provided its strength is close to the Schwinger limit, $E = 1.3 \times 10^{16}$ V cm<sup>-1</sup>. One might expect that the desired field can be achieved using strong laser fields. Recent developments of the laser technologies have triggered a great interest to calculations of the pair production in strong fields, especially for the case of colliding laser pulses. However, the maximal field strength which can be achieved by modern lasers is by 3–4 orders of magnitude smaller than the Schwinger limit. Another access to QED at supercritical fields can be gained in Coulomb field created by an extended nucleus with the nuclear charge number exceeding the critical value, $Z_c = 173$. At this critical value, the 1s level should ‘dive’ into the negative energy Dirac continuum. If the 1s level was empty, its diving results in spontaneous creation of two positrons. Since there is no nuclei with so high Z, the only way to access the supercritical regime is to study low-energy collisions of heavy ions with the total nuclear charge larger than the critical value. The corresponding experiments were performed many years ago at GSI (Darmstadt). However, for a number of reasons [148], these experiments could not prove or disprove the spontaneous pair creation. Plans to return to investigations of this phenomenon at FAIR (Germany), HIAF (China), and NICA (Russia) facilities have triggered new theoretical studies of relativistic quantum dynamics at low-energy heavy-ion collisions.

**Current and future challenges.** Despite the great progress in the Lamb shift experiments with heavy few-electron ions, further work on improving the precision of the 1s Lamb shift in heavy H-like ions is needed. The nearest principal goal consists in
## 13. QED in strong fields

Vladimir Shabaev

St. Petersburg State University, Russia

**Status.** Basic principles of QED were formulated to the beginning of 1930s by merging quantum mechanics with special relativity. The discovery of the Lamb shift in 1947 stimulated theorists to complete the creation of QED by developing the renormalization technique. Till the beginning of 1980s tests of QED were mainly restricted to light atomic systems where the calculations were performed in the weak-field approximation, which corresponds to small values of the parameter $\alpha Z$ ($\alpha$ is the fine structure constant and Z is the nuclear charge number). A unique opportunity to test QED in a strong-field regime, which requires calculations without any expansion in $\alpha Z$, appeared when high-precision experiments with heavy few-electron ions became feasible.

High-precision tests of QED effects with HCIs were first performed for the binding energies. The ground state Lamb shift in H-like uranium, which is defined as a difference between the exact energy and the point-nucleus Dirac energy, was measured to amount 460.2(4.6) eV [139]. The comparison of this experiment with the theoretical result, 463.99(39) eV (see [140] and references therein), provides a test of QED at the strong Coulomb field on a 2% level. Higher accuracy was achieved in experiments with Li-like ions. The present status of theory [141] and experiment [142] for the 2p<sub>1/2</sub>–2s transition energy in Li-like uranium provides a test of QED on a 0.2% level. For both H- and Li-like uranium ions the theoretical uncertainty is presently defined by some uncalculated contributions of two-loop QED diagrams (figure 20) and by an uncertainty of the nuclear charge radius.

To date we have a number of high-precision measurements of the HFS in heavy H-like ions (see, e.g. [143] and references therein). The main goal of these experiments was to test QED in a unique combination of strong electric and magnetic fields. But, because of a large theoretical uncertainty due to the nuclear magnetization distribution correction (so called Bohr–Weisskopf effect), it turned out that the QED tests are possible only via studying a specific difference of the HFS values of H- and Li-like ions [144]. The recent measurements of this difference in Bi [143] revealed a large discrepancy between experiment and theory. This discrepancy was explained in [145] by an incorrect value of the nuclear magnetic moment which was widely used in literature. New calculations of the magnetic shielding factor and new measurements of the nuclear magnetic moment in <sup>209</sup>Bi(NO<sub>3</sub>)<sub>3</sub> and <sup>209</sup>BiF<sub>6</sub> [145] lead to good agreement between theory and experiment. However, more precise measurements of the nuclear magnetic moments and the HFS values are needed to provide stringent QED tests.

High-precision measurements of the g factor of H- and Li-like low- and middle-Z ions (see, e.g. [146] and references therein) have provided stringent tests of the QED effects in presence of a magnetic field. Combined with the related theoretical predictions, these experiments have also provided the most precise determination of the electron mass [146].

<figure><img src="image_24.png" /><figcaption>Figure 20. One-electron two-loop Feynman diagrams which contribute to the Lamb shift. The double line represents an electron propagating in the Coulomb field. The wavy line indicates a virtual photon.</figcaption></figure>

Recently [147], the isotope shift of the g factor of Li-like calcium ions was measured. This experiment allowed the first test of the relativistic theory of the nuclear recoil effect on the g factor of highly charged Li-like ions.

One of the most interesting and intriguing issues of modern fundamental physics is related to tests of QED at supercritical fields. According to the QED theory, a static and spatially uniform electric field should create electron–positron pairs, provided its strength is close to the Schwinger limit, $E = 1.3 \times 10^{16} \text{ V cm}^{-1}$. One might expect that the desired field can be achieved using strong laser fields. Recent developments of the laser technologies have triggered a great interest to calculations of the pair production in strong fields, especially for the case of colliding laser pulses. However, the maximal field strength which can be achieved by modern lasers is by 3–4 orders of magnitude smaller than the Schwinger limit. Another access to QED at supercritical fields can be gained in Coulomb field created by an extended nucleus with the nuclear charge number exceeding the critical value, $Z_c = 173$. At this critical value, the 1s level should ‘dive’ into the negative energy Dirac continuum. If the 1s level was empty, its diving results in spontaneous creation of two positrons. Since there is no nuclei with so high Z, the only way to access the supercritical regime is to study low-energy collisions of heavy ions with the total nuclear charge larger than the critical value. The corresponding experiments were performed many years ago at GSI (Darmstadt). However, for a number of reasons [148], these experiments could not prove or disprove the spontaneous pair creation. Plans to return to investigations of this phenomenon at FAIR (Germany), HIAF (China), and NICA (Russia) facilities have triggered new theoretical studies of relativistic quantum dynamics at low-energy heavy-ion collisions.

**Current and future challenges.** Despite the great progress in the Lamb shift experiments with heavy few-electron ions, further work on improving the precision of the 1s Lamb shift in heavy H-like ions is needed. The nearest principal goal consists in
gaining the 1 eV accuracy in the 1s Lamb shift in H-like
uranium. The Lamb shift in heavy H-like ions should be
considered as the main reference point for QED tests at strong
fields. This is due to the simplicity of H-like ions compared to
few-electron ions as well as the simplicity of the Lamb shift
compared to other QED effects. These tests are needed to prove
the non-perturbative QED methods, which then can be applied
to calculations of other important properties of HCIs. From the
theoretical side, to improve the accuracy of the ground-state
Lamb shift, the last two diagrams in figure 20 have to be
calculated beyond the free-electron-loop approximation. Also
the rigorous evaluations of the second-order two- and three-
electron QED contributions in highly charged Be-like ions are
urgently needed to meet the experimental accuracy achieved in
recent measurements of the transition energies.

Accurate measurements of the HFS transition energies in H- and Li-like ions must be accompanied by independent high-precision determinations of the nuclear magnetic moments. From the theoretical side, the corresponding calculations for B-like ions including all second-order two- and more-electron contributions are required. Together with the corresponding calculations for H- and Li-like ions, these calculations can also be used for tests of QED in a combination of the strongest electric and magnetic fields.

High-precision measurements of the g factors of heavy H-, Li-, and B-like ions are anticipated in the near future at the Max-Planck Institut fuer Kernphysik (MPIK) in Heidelberg and at the HITRAP/FAIR facilities in Darmstadt. Combined with the related theoretical predictions, these measurements should provide stringent tests of QED at strong fields. It was recently shown that the study of the g factors of H- and Li-like lead ions can provide a test of the QED nuclear recoil effect on a few-percent level. This would give the first test of QED at strong-coupling regime beyond the Furry picture. Measurements of the g factor of ions with non-zero nuclear spin will result in the most precise determinations of the nuclear magnetic moments. Also an independent determination of the fine structure constant from the g-factor experiments with heavy H- and B-like ions is feasible, provided the corresponding theoretical calculations are performed to the required accuracy.

The study of QED at supercritical fields created in low-
energy heavy-ion collisions demands developments of

theoretical methods which allow to investigate in all details
such processes as pair production, electron excitation and
ionization, charge transfer, and x-ray emission. Special
attention should be paid to calculations focused on finding
signatures of the ‘diving’ scenario which inevitably leads to
the spontaneous pair production.

Advances in science and technology to meet challenges.

The progress in high-precision QED calculations of HCIs was
always stimulated by the related progress in experiment. No
doubts that any further substantial progress on the Lamb shift
experiments with heavy ions, which is one of the main topics
of a number of nowadays conferences and workshops, will
motivate theorists to advance the calculations of two-loop
QED contributions in ions with one and more electrons.
Precise measurements of the g factors of heavy few-electron
ions at MPIK in Heidelberg and at GSI/FAIR in Darmstadt
will stimulate theoretical calculations of the corresponding
higher-order QED and nuclear effects. The recent advances in
calculations of the pair-creation probabilities in low-energy
heavy-ion collisions beyond the monopole approximation
give a hope for further developments of theoretical two-center
methods, which are needed to study in details the quantum
dynamics of electrons in strong and supercritical fields.

*Concluding remarks.* High-precision measurements with HCIs, combined with the corresponding theoretical calculations, provide stringent tests of non-perturbative QED methods. These theory and experiment can be also used for the most precise determinations of the electron mass, nuclear magnetic moments, nuclear radii, etc. They have also a potential for an independent determination of the fine structure constant. The study of quantum dynamics of electrons in low-energy heavy ion collisions can provide a unique possibility for tests of QED in supercritical regime.

Acknowledgments

This work was supported by the Russian Science Foundation
(Grant No. 17-12-01097).
gaining the 1 eV accuracy in the 1s Lamb shift in H-like
uranium. The Lamb shift in heavy H-like ions should be
considered as the main reference point for QED tests at strong
fields. This is due to the simplicity of H-like ions compared to
few-electron ions as well as the simplicity of the Lamb shift
compared to other QED effects. These tests are needed to prove
the non-perturbative QED methods, which then can be applied
to calculations of other important properties of HCIs. From the
theoretical side, to improve the accuracy of the ground-state
Lamb shift, the last two diagrams in figure 20 have to be
calculated beyond the free-electron-loop approximation. Also
the rigorous evaluations of the second-order two- and three-
electron QED contributions in highly charged Be-like ions are
urgently needed to meet the experimental accuracy achieved in
recent measurements of the transition energies.

Accurate measurements of the HFS transition energies in H- and Li-like ions must be accompanied by independent high-precision determinations of the nuclear magnetic moments. From the theoretical side, the corresponding calculations for B-like ions including all second-order two- and more-electron contributions are required. Together with the corresponding calculations for H- and Li-like ions, these calculations can also be used for tests of QED in a combination of the strongest electric and magnetic fields.

High-precision measurements of the g factors of heavy H-, Li-, and B-like ions are anticipated in the near future at the Max-Planck Institut fuer Kernphysik (MPIK) in Heidelberg and at the HITRAP/FAIR facilities in Darmstadt. Combined with the related theoretical predictions, these measurements should provide stringent tests of QED at strong fields. It was recently shown that the study of the g factors of H- and Li-like lead ions can provide a test of the QED nuclear recoil effect on a few-percent level. This would give the first test of QED at strong-coupling regime beyond the Furry picture. Measurements of the g factor of ions with non-zero nuclear spin will result in the most precise determinations of the nuclear magnetic moments. Also an independent determination of the fine structure constant from the g-factor experiments with heavy H- and B-like ions is feasible, provided the corresponding theoretical calculations are performed to the required accuracy.

The study of QED at supercritical fields created in low-
energy heavy-ion collisions demands developments of

theoretical methods which allow to investigate in all details
such processes as pair production, electron excitation and
ionization, charge transfer, and x-ray emission. Special
attention should be paid to calculations focused on finding
signatures of the ‘diving’ scenario which inevitably leads to
the spontaneous pair production.

Advances in science and technology to meet challenges.

The progress in high-precision QED calculations of HCIs was
always stimulated by the related progress in experiment. No
doubts that any further substantial progress on the Lamb shift
experiments with heavy ions, which is one of the main topics
of a number of nowadays conferences and workshops, will
motivate theorists to advance the calculations of two-loop
QED contributions in ions with one and more electrons.
Precise measurements of the g factors of heavy few-electron
ions at MPIK in Heidelberg and at GSI/FAIR in Darmstadt
will stimulate theoretical calculations of the corresponding
higher-order QED and nuclear effects. The recent advances in
calculations of the pair-creation probabilities in low-energy
heavy-ion collisions beyond the monopole approximation
give a hope for further developments of theoretical two-center
methods, which are needed to study in details the quantum
dynamics of electrons in strong and supercritical fields.

*Concluding remarks.* High-precision measurements with HCIs, combined with the corresponding theoretical calculations, provide stringent tests of non-perturbative QED methods. These theory and experiment can be also used for the most precise determinations of the electron mass, nuclear magnetic moments, nuclear radii, etc. They have also a potential for an independent determination of the fine structure constant. The study of quantum dynamics of electrons in low-energy heavy ion collisions can provide a unique possibility for tests of QED in supercritical regime.

Acknowledgments

This work was supported by the Russian Science Foundation
(Grant No. 17-12-01097).
# 14. Interactions of HCIs with clusters

Henrik Cederquist and Henning Zettergren

Stockholm University, Sweden

**Status.** The title 'Interactions of HCIs with clusters' makes most ICPEAC participants think about situations where atomic ions, stripped of many of its electrons, collide with some neutral aggregation of matter—a cluster. Typically, ICPEAC-clusters have consisted of metal atoms [149], noble gas atoms [150], or small molecules [151]. Carbon clusters and in particular $C_{60}$ have also often been used as targets. A recent trend is to study interactions with clusters of larger molecules where the bonds between the individual molecules are much weaker than within the molecules themselves.

Examples are loosely bound clusters of biomolecules [152], clusters of $C_{60}$ [153] or PAHs—Polycyclic Aromatic Hydrocarbon molecules [154]. The interest in the latter two targets is partly motivated by astrophysical observation of characteristic emission in the micrometer wavelength region, where $C_{60}$, PAHs and other aromatic molecules are known—or expected to—play important roles. Here we will mainly focus on collisions between slow highly charged, positive, ions and neutral clusters of molecules. In this context a collision is slow when the velocity of the ion is lower than typical velocities of the outermost target electrons. As indicated in figure 21, one or several electrons may be transferred from the cluster to the ion already at large distances. The higher the charge state, *q*, the larger the ion-cluster distance at which electron transfer processes may occur and the larger the cluster ionization cross section. The essence of this behavior is well described by over-the-barrier models in which one considers the potential energy barrier for an electron moving in the electric field created by the ion, the active electron itself, and the ionized cluster (see [155] and references therein). These considerations become particularly simple for surfaces and spherical or close to spherical targets and it has been shown that $C_{60}$ can be modeled as a classical metal sphere [155]. The same model also explains the high charge mobility within clusters of fullerenes and the ultrafast (sub-femtosecond) timescales for such processes [155, 156]. At a first glance, one would expect that distant electron transfer processes would lead to very little heating of the cluster, but with HCIs strong heating of individual molecules emitted from clusters have been observed [154]. This is most likely due to heating during cluster Coulomb-explosion processes [154]. In penetrating collisions, the incoming HCI is first neutralized and may then transfer considerable amounts of energy in electronic and nuclear stopping processes as it passes through the cluster. In particular, the projectile may knock out single atoms in prompt Rutherford-like atom-atom scattering processes (sub-femtosecond timescale). This gives highly reactive molecular fragments, which are likely to bind to other molecules or fragments in the cluster breakup phase (see [157] and references therein). The fast knockout processes are non-statistical in nature as the knockout atom is removed before local excitations (at the

<figure><img src="image_24.png" /><figcaption>Figure 21. Schematic of distant and penetrating (close) collisions between a highly charged ion and a cluster of $C_{60}$ fullerenes. Distant collisions lead mainly to charge transfer with little heating of the target, but in penetrating collisions much more damage can be inflicted through nuclear and electronic stopping processes.</figcaption></figure>

knockout site) have time to distribute over the whole molecule. Here, a key point for the survival of molecular-growth products is that the excess energy is shared among many of the molecules in the cluster. This scenario is supported by close agreement between experimental results and classical molecular dynamics (MD) simulations assuming neutral projectiles. In these simulations, trajectories of all individual atoms in the system are followed for a few picoseconds and the agreement with the experimental results then indicate that growth products survive also on typical experimental time scales of microseconds (see [157] and references therein). Given the interest from the astrophysics community for, for example, carbon-based molecules and their formation and destruction in interstellar space, planetary atmospheres and supernova shock waves—and for understanding fundamental molecular growth processes as such—it is of great interest to study the long-term stabilities of such fragments and to study how they react with neutral, charged, and multiply charged molecules or clusters. Related to this, it will be most interesting to investigate the role of the incident ion charge in situations like the one depicted in figure 21.

**Current and future challenges.** So far, most ion-cluster collision studies have been performed with keV atomic ions colliding with thermal neutral cluster targets and where distributions of cluster sizes always have been rather wide. One challenge is thus to perform experiments with size-selected clusters. Such experiments will make it possible to control internal cluster temperatures and to study how size-selected clusters interact with atoms, molecules, or other clusters in completely new velocity domains using merged-beams techniques. A further challenge on the experimental side concerns spectroscopic studies of molecular growth products resulting from close interactions between clusters of molecules and ions in both high and low charge states. On the theoretical side, long-term goals are to simulate knockout driven intra-cluster reactions in a wide range of systems using
# 14. Interactions of HCIs with clusters

Henrik Cederquist and Henning Zettergren

Stockholm University, Sweden

**Status.** The title 'Interactions of HCIs with clusters' makes most ICPEAC participants think about situations where atomic ions, stripped of many of its electrons, collide with some neutral aggregation of matter—a cluster. Typically, ICPEAC-clusters have consisted of metal atoms [149], noble gas atoms [150], or small molecules [151]. Carbon clusters and in particular $C_{60}$ have also often been used as targets. A recent trend is to study interactions with clusters of larger molecules where the bonds between the individual molecules are much weaker than within the molecules themselves.

Examples are loosely bound clusters of biomolecules [152], clusters of $C_{60}$ [153] or PAHs—Polycyclic Aromatic Hydrocarbon molecules [154]. The interest in the latter two targets is partly motivated by astrophysical observation of characteristic emission in the micrometer wavelength region, where $C_{60}$, PAHs and other aromatic molecules are known—or expected to—play important roles. Here we will mainly focus on collisions between slow highly charged, positive, ions and neutral clusters of molecules. In this context a collision is slow when the velocity of the ion is lower than typical velocities of the outermost target electrons. As indicated in figure 21, one or several electrons may be transferred from the cluster to the ion already at large distances. The higher the charge state, *q*, the larger the ion-cluster distance at which electron transfer processes may occur and the larger the cluster ionization cross section. The essence of this behavior is well described by over-the-barrier models in which one considers the potential energy barrier for an electron moving in the electric field created by the ion, the active electron itself, and the ionized cluster (see [155] and references therein). These considerations become particularly simple for surfaces and spherical or close to spherical targets and it has been shown that $C_{60}$ can be modeled as a classical metal sphere [155]. The same model also explains the high charge mobility within clusters of fullerenes and the ultrafast (sub-femtosecond) timescales for such processes [155, 156]. At a first glance, one would expect that distant electron transfer processes would lead to very little heating of the cluster, but with HCIs strong heating of individual molecules emitted from clusters have been observed [154]. This is most likely due to heating during cluster Coulomb-explosion processes [154]. In penetrating collisions, the incoming HCI is first neutralized and may then transfer considerable amounts of energy in electronic and nuclear stopping processes as it passes through the cluster. In particular, the projectile may knock out single atoms in prompt Rutherford-like atom-atom scattering processes (sub-femtosecond timescale). This gives highly reactive molecular fragments, which are likely to bind to other molecules or fragments in the cluster breakup phase (see [157] and references therein). The fast knockout processes are non-statistical in nature as the knockout atom is removed before local excitations (at the

<figure><img src="image_25.png" /><figcaption>Figure 21. Schematic of distant and penetrating (close) collisions between a highly charged ion and a cluster of $C_{60}$ fullerenes. Distant collisions lead mainly to charge transfer with little heating of the target, but in penetrating collisions much more damage can be inflicted through nuclear and electronic stopping processes.</figcaption></figure>

knockout site) have time to distribute over the whole molecule. Here, a key point for the survival of molecular-growth products is that the excess energy is shared among many of the molecules in the cluster. This scenario is supported by close agreement between experimental results and classical molecular dynamics (MD) simulations assuming neutral projectiles. In these simulations, trajectories of all individual atoms in the system are followed for a few picoseconds and the agreement with the experimental results then indicate that growth products survive also on typical experimental time scales of microseconds (see [157] and references therein). Given the interest from the astrophysics community for, for example, carbon-based molecules and their formation and destruction in interstellar space, planetary atmospheres and supernova shock waves—and for understanding fundamental molecular growth processes as such—it is of great interest to study the long-term stabilities of such fragments and to study how they react with neutral, charged, and multiply charged molecules or clusters. Related to this, it will be most interesting to investigate the role of the incident ion charge in situations like the one depicted in figure 21.

**Current and future challenges.** So far, most ion-cluster collision studies have been performed with keV atomic ions colliding with thermal neutral cluster targets and where distributions of cluster sizes always have been rather wide. One challenge is thus to perform experiments with size-selected clusters. Such experiments will make it possible to control internal cluster temperatures and to study how size-selected clusters interact with atoms, molecules, or other clusters in completely new velocity domains using merged-beams techniques. A further challenge on the experimental side concerns spectroscopic studies of molecular growth products resulting from close interactions between clusters of molecules and ions in both high and low charge states. On the theoretical side, long-term goals are to simulate knockout driven intra-cluster reactions in a wide range of systems using
<figure><img src="image_25.png" /><figcaption>Figure 22. Mass spectra from collisions between 400 keV Xe$^{20+}$ ions and neutral $[C_{60}]_k$ clusters. The red data is for experimental conditions that give, on average, larger cluster sizes $k$ than the blue data. Reprinted from [158], with the permission of AIP Publishing.</figcaption></figure>

quantum mechanics instead of classical force fields, and to include the effects of electronic excitations and the incident ion charge state in the simulations. These are extremely challenging tasks but some steps in this direction have already been taken [157].

Studies of ions interacting with aggregates of carbon-based matter relates to one of the main issues in fullerene research: How are the classical fullerenes predominantly formed and why is it that $C_{60}$ and $C_{70}$ become so dominant in so many different types of experimental situations and in nature? In figure 22, which is adapted from [158], parts of mass spectra recorded for collisions between 400 keV Xe$^{20+}$ and small (blue spectrum) and large (red spectrum) neutral clusters of $k C_{60}$ molecules, $[C_{60}]_k$, are shown. In both cases there are broad size-distributions of neutral clusters before the collision but with a larger average target cluster size in the experiment yielding the red spectrum. The much wider distribution of reaction products in the red spectrum is particularly striking. There are also enhanced intensities for so called magic fullerenes like, for examples, $C_{84}^+$ and $C_{70}^+$. These results are consistent with a picture in which hot large giant fullerenes form in confined hot carbon plasma along projectile ion trajectories through the cluster. The $C_{60}$ molecules that are not directly struck by the projectile mostly remain intact initially and are then either evaporated from the heated system or react with, e.g. carbon atoms or molecules from the plasma. Hot giant fullerenes may then decay by fragmentation and photon emission and some of them will shrink towards smaller sizes including, for examples, $C_{84}^+$, $C_{78}^+$, $C_{70}^+$, and $C_{60}^+$. Such magic fullerenes have somewhat higher stabilities than their neighbors. It has been suggested, however, that the large abundances of $C_{60}$ in many different situations rather is due to exceptionally fast radiative cooling

processes. Products like $[C_{60}]_3^+$ in figure 22 are due to multiple ionization of much larger $[C_{60}]_k$ clusters followed by emissions of many intact $C_{60}$ molecules. A current challenge is to investigate molecular growth starting from much smaller carbon-based molecular building blocks and also to study the conditions for $C_{60}$-formation as functions of cluster size, cluster charge, mass and velocity, a future challenge is to study how internally cold cluster ions in different charge states interact with neutrals and with other ions at subthermal and higher collision energies.

**Advances in science and technology to meet challenges.** It is of great interest to improve, e.g. the experiment behind the spectra in figure 22. As has already been indicated above, this can be done by colliding size-selected $[C_{60}]_k^+$ clusters and clusters of other carbon-bearing molecules with atomic targets. This will yield cluster-size specific distributions of reaction products and, in addition, possibilities to register several reaction products in coincidence for each cluster size. Furthermore, one could prepare beams of ultracold $[C_{60}]_k^+$ clusters inside HNDs, which would lead to a much better definition of the cluster structure than in earlier experiments. By placing a gas target on injection lines of cryogenic electrostatic ion storage devices it will become possible to study stabilities and photo-absorption properties of fragments and molecular growth products resulting from single collisions in the target gas. In some ion storage devices, it may also become possible to study interactions between internally cold complex (cluster) ions of opposite charge states using merged beams techniques. Interactions between highly charged *atomic ions* and internally cold clusters of molecules can be performed in single-pass merged beams experiments.

**Concluding remarks.** We foresee highly interesting developments where molecular growth processes, and in particular the $C_{60}$ formation mechanism are investigated with control of cluster size, charge, internal energy, structure, and velocity for different masses of the target. In these studies, the charge will be carried into the collision by the cluster and it will be crucial to be able to handle the system charge in simulations of reaction processes. Stabilities and optical properties of molecular growth products will be studied with cryogenic electrostatic ion storage devices. In the near future, these devices will allow studies of pairwise interactions between molecular clusters using merged-beams techniques.

## Acknowledgments

This work was supported by the Swedish Research Council through Grants No. 2015-04990 and 2016-0418. Michael Gatchell, Stockholm University and Innsbruck University is gratefully acknowledged for his input and for discussions
<figure><img src="image_26.png" /><figcaption>Figure 22. Mass spectra from collisions between 400 keV Xe$^{20+}$ ions and neutral $[C_{60}]_k$ clusters. The red data is for experimental conditions that give, on average, larger cluster sizes $k$ than the blue data. Reprinted from [158], with the permission of AIP Publishing.</figcaption></figure>

quantum mechanics instead of classical force fields, and to include the effects of electronic excitations and the incident ion charge state in the simulations. These are extremely challenging tasks but some steps in this direction have already been taken [157].

Studies of ions interacting with aggregates of carbon-based matter relates to one of the main issues in fullerene research: How are the classical fullerenes predominantly formed and why is it that $C_{60}$ and $C_{70}$ become so dominant in so many different types of experimental situations and in nature? In figure 22, which is adapted from [158], parts of mass spectra recorded for collisions between 400 keV Xe$^{20+}$ and small (blue spectrum) and large (red spectrum) neutral clusters of $k$ $C_{60}$ molecules, $[C_{60}]_k$, are shown. In both cases there are broad size-distributions of neutral clusters before the collision but with a larger average target cluster size in the experiment yielding the red spectrum. The much wider distribution of reaction products in the red spectrum is particularly striking. There are also enhanced intensities for so called magic fullerenes like, for examples, $C_{84}^+$ and $C_{70}^+$. These results are consistent with a picture in which hot large giant fullerenes form in confined hot carbon plasma along projectile ion trajectories through the cluster. The $C_{60}$ molecules that are not directly struck by the projectile mostly remain intact initially and are then either evaporated from the heated system or react with, e.g. carbon atoms or molecules from the plasma. Hot giant fullerenes may then decay by fragmentation and photon emission and some of them will shrink towards smaller sizes including, for examples, $C_{84}^+$, $C_{78}^+$, $C_{70}^+$, and $C_{60}^+$. Such magic fullerenes have somewhat higher stabilities than their neighbors. It has been suggested, however, that the large abundances of $C_{60}$ in many different situations rather is due to exceptionally fast radiative cooling

processes. Products like $[C_{60}]_3^+$ in figure 22 are due to multiple ionization of much larger $[C_{60}]_k$ clusters followed by emissions of many intact $C_{60}$ molecules. A current challenge is to investigate molecular growth starting from much smaller carbon-based molecular building blocks and also to study the conditions for $C_{60}$-formation as functions of cluster size, cluster charge, mass and velocity, a future challenge is to study how internally cold cluster ions in different charge states interact with neutrals and with other ions at subthermal and higher collision energies.

*Advances in science and technology to meet challenges.* It is of great interest to improve, e.g. the experiment behind the spectra in figure 22. As has already been indicated above, this can be done by colliding *size-selected* $[C_{60}]_k^+$ clusters and clusters of other carbon-bearing molecules with atomic targets. This will yield cluster-size specific distributions of reaction products and, in addition, possibilities to register several reaction products in coincidence for each cluster size. Furthermore, one could prepare beams of ultracold $[C_{60}]_k^+$ clusters inside HNDs, which would lead to a much better definition of the cluster structure than in earlier experiments. By placing a gas target on injection lines of cryogenic electrostatic ion storage devices it will become possible to study stabilities and photo-absorption properties of fragments and molecular growth products resulting from single collisions in the target gas. In some ion storage devices, it may also become possible to study interactions between internally cold complex (cluster) ions of opposite charge states using merged beams techniques. Interactions between highly charged *atomic ions* and internally cold clusters of molecules can be performed in single-pass merged beams experiments.

*Concluding remarks.* We foresee highly interesting developments where molecular growth processes, and in particular the $C_{60}$ formation mechanism are investigated with control of cluster size, charge, internal energy, structure, and velocity for different masses of the target. In these studies, the charge will be carried into the collision by the cluster and it will be crucial to be able to handle the system charge in simulations of reaction processes. Stabilities and optical properties of molecular growth products will be studied with cryogenic electrostatic ion storage devices. In the near future, these devices will allow studies of pairwise interactions between molecular clusters using merged-beams techniques.

## Acknowledgments

This work was supported by the Swedish Research Council through Grants No. 2015-04990 and 2016-0418. Michael Gatchell, Stockholm University and Innsbruck University is gratefully acknowledged for his input and for discussions
# 15. Interaction of HCIs with surfaces and 2D materials

Marika Schleberger<fnref n="1" /> and Richard A Wilhelm<fnref n="2" />

**Status.** Nowadays, the modification of solids with ion beams represents the backbone in semi-conductor manufacturing with respect to tuning electrical properties by implantation and shaping surface structures by ion lithography. However, the ever-smaller layer thicknesses and lateral dimensions in modern electronics demands new approaches [159]. Reducing the ion's kinetic energy to confine energy deposition to only a few atomic layers seems to be a straightforward solution, but serious challenges arise from the broad energy spread of the ion sources and when it comes to beam focus at these low energies.

Slow HCIs carry an additional potential energy, which can be even larger than the kinetic energy [160]. Upon neutralization, HCI deposit a large amount of the potential energy in a shallow region at the material's surface and thus feature an ideal tool to tailor properties of surfaces and 2D materials without the need to go to ultralow kinetic energies [161]. It was shown on surfaces of wide band-gap insulators that HCI can induce extremely large sputtering yields of a few thousand atoms per ion or even induce local phase transitions on the nanoscale depending on material properties [162]. For insulators the modification mechanisms are well described by the formation of an inelastic thermal spike, surface melting, and resolidification; or by electronically stimulated desorption (DIET). In general, HCI neutralization leads to heating of the electronic subsystem of the material. A coupling between electrons and phonons heats the lattice on a later time scale. This two-temperature model (TTM) provides an extremely powerful description of the initial energy deposition processes, while details of the electrical and thermal properties of the material play a decisive role for the outcome of the ion impact. This also is the reason why metal surfaces are typically not prone to nano-structuring by HCI, because the deposited energy in the electronic subsystem dissipates in the material before electron-phonon coupling can effectively set in.

When moving towards 2D materials supported by arbitrary substrates, new phenomena already emerge as the non-perfectly matched electronic and lattice subsystems of the substrate decouple the 2D layer [163]. Quantum confinement effects for the excited electrons prevent energy dissipation in the third dimension. This points towards an even more efficient potential energy-driven process leading to modifications similar to those for bulk insulators, and the few experiments conducted so far support this assumption [164, 165]. In the purely freestanding case of 2D materials, where a substrate is entirely absent, one may expect that even metal-like materials become prone to HCI modifications due to quantum confinement effects. However, this has not yet been observed experimentally [166]. In their freestanding

<figure><img src="image_26.png" /><figcaption>Figure 23. HCI irradiation of surfaces from bulk materials revealed efficient nanostructuring. Possible processes are surface melting (described by TTM), DIET, or Coulomb explosion (CE) depending on the ion's kinetic and potential energies. 3D insulators (I), semi-conductors (S), and metals (M) show different susceptibility to HCI driven modification, whereas further research for 2D materials is needed. In the future, more complex integrated multi-coincidence spectroscopy and *in situ* microscopy in combination with refined theoretical descriptions will reveal details on the interaction mechanisms.</figcaption></figure>

state. 2D materials also constitute a perfect model system to study the material in an (ion-induced) highly non-equilibrium state in unprecedented detail [167]. While the TTM allows for a powerful description of the processes in a thermodynamic sense only, a detailed and quantifiable atomistic model is still missing due to the complexity of the neutralization processes and subsequent surface electron and atom dynamics.

**Current and future challenges.** One of the greatest challenges in HCI irradiation and spectroscopy with 2D materials lies currently in the fact that HCI beams are only available as broad beams. Additionally, the presence of surface contaminations becomes increasingly important. Because 2D materials are surface-only materials, adsorbed hydrocarbons, residuals either from wet-chemical transfer or from the growth substrate despite chemical etching, all affect available measurement techniques, i.e. scanning probe and electron microscopy, spectroscopy of the scattered/ transmitted ions, sputtered target recoils, as well as emitted electrons and photons, see figure 23.

Another important problem and research issue are defects in 2D materials. Those have a great influence on the material's structural, optical, and electronic properties, and even sometimes dominate them. The presence of intrinsic defects, i.e. single and multi-atomic vacancies, small and extended rotational defects, grain boundaries, foreign atoms, creases, wrinkles, etc needs to be controlled during all steps of sample preparation, i.e. material growth, transfer onto a substrate, onto another 2D material and/or onto a supportive

<footnote n="1">¹Universität Duisburg-Essen, Germany</footnote>

<footnote n="2">²TU Wien, Austria</footnote>
## 15. Interaction of HCIs with surfaces and 2D materials

Marika Schleberger<fnref n="1" /> and Richard A Wilhelm<fnref n="2" />

**Status.** Nowadays, the modification of solids with ion beams represents the backbone in semi-conductor manufacturing with respect to tuning electrical properties by implantation and shaping surface structures by ion lithography. However, the ever-smaller layer thicknesses and lateral dimensions in modern electronics demands new approaches [159]. Reducing the ion's kinetic energy to confine energy deposition to only a few atomic layers seems to be a straightforward solution, but serious challenges arise from the broad energy spread of the ion sources and when it comes to beam focus at these low energies.

Slow HCIs carry an additional potential energy, which can be even larger than the kinetic energy [160]. Upon neutralization, HCI deposit a large amount of the potential energy in a shallow region at the material's surface and thus feature an ideal tool to tailor properties of surfaces and 2D materials without the need to go to ultralow kinetic energies [161]. It was shown on surfaces of wide band-gap insulators that HCI can induce extremely large sputtering yields of a few thousand atoms per ion or even induce local phase transitions on the nanoscale depending on material properties [162]. For insulators the modification mechanisms are well described by the formation of an inelastic thermal spike, surface melting, and resolidification; or by electronically stimulated desorption (DIET). In general, HCI neutralization leads to heating of the electronic subsystem of the material. A coupling between electrons and phonons heats the lattice on a later time scale. This two-temperature model (TTM) provides an extremely powerful description of the initial energy deposition processes, while details of the electrical and thermal properties of the material play a decisive role for the outcome of the ion impact. This also is the reason why metal surfaces are typically not prone to nano-structuring by HCI, because the deposited energy in the electronic subsystem dissipates in the material before electron-phonon coupling can effectively set in.

When moving towards 2D materials supported by arbitrary substrates, new phenomena already emerge as the non-perfectly matched electronic and lattice subsystems of the substrate decouple the 2D layer [163]. Quantum confinement effects for the excited electrons prevent energy dissipation in the third dimension. This points towards an even more efficient potential energy-driven process leading to modifications similar to those for bulk insulators, and the few experiments conducted so far support this assumption [164, 165]. In the purely freestanding case of 2D materials, where a substrate is entirely absent, one may expect that even metal-like materials become prone to HCI modifications due to quantum confinement effects. However, this has not yet been observed experimentally [166]. In their freestanding

<figure><img src="image_27.png" /><figcaption>Figure 23. HCI irradiation of surfaces from bulk materials revealed efficient nanostructuring. Possible processes are surface melting (described by TTM), DIET, or Coulomb explosion (CE) depending on the ion's kinetic and potential energies. 3D insulators (I), semi-conductors (S), and metals (M) show different susceptibility to HCI driven modification, whereas further research for 2D materials is needed. In the future, more complex integrated multi-coincidence spectroscopy and *in situ* microscopy in combination with refined theoretical descriptions will reveal details on the interaction mechanisms.</figcaption></figure>

state. 2D materials also constitute a perfect model system to study the material in an (ion-induced) highly non-equilibrium state in unprecedented detail [167]. While the TTM allows for a powerful description of the processes in a thermodynamic sense only, a detailed and quantifiable atomistic model is still missing due to the complexity of the neutralization processes and subsequent surface electron and atom dynamics.

**Current and future challenges.** One of the greatest challenges in HCI irradiation and spectroscopy with 2D materials lies currently in the fact that HCI beams are only available as broad beams. Additionally, the presence of surface contaminations becomes increasingly important. Because 2D materials are surface-only materials, adsorbed hydrocarbons, residuals either from wet-chemical transfer or from the growth substrate despite chemical etching, all affect available measurement techniques, i.e. scanning probe and electron microscopy, spectroscopy of the scattered/ transmitted ions, sputtered target recoils, as well as emitted electrons and photons, see figure 23.

Another important problem and research issue are defects in 2D materials. Those have a great influence on the material's structural, optical, and electronic properties, and even sometimes dominate them. The presence of intrinsic defects, i.e. single and multi-atomic vacancies, small and extended rotational defects, grain boundaries, foreign atoms, creases, wrinkles, etc needs to be controlled during all steps of sample preparation, i.e. material growth, transfer onto a substrate, onto another 2D material and/or onto a supportive

<footnote n="1">¹Universität Duisburg-Essen, Germany</footnote>

<footnote n="2">²TU Wien, Austria</footnote>
grid in case of a suspended sheet. This is why currently homogeneous, defect-free 2D materials cannot easily be produced on the mm-scale.

Some 2D materials are even not stable in air, as e.g. black phosphorous or silicene, and thus require a complicated in-vacuum transfer to an HCI facility and to an analysis device. On top of this, some 2D materials are highly susceptible to damage by electronic excitations, beneficial for HCI induced modification, but hampering atomically resolved electron-based microscopy. In principle, suspended 2D materials allow direct spectroscopy of the ion still in a non-equilibrium state after transmission through the material together with the spectroscopy of emitted secondary particles i.e. sputtered atoms, electrons, and photons. Spectroscopy of (quasi-) particles from the interaction process with a suspended 2D material can give, for the first time, experimental access to the dynamics of ion-induced electronic processes on the femto-second time-scale. However, the current challenge lies in the measurement of all particle energies and momenta, ideally in coincidence, plus the determination of energy retained in the material. To probe even longer time scales, i.e. atomic dynamics in the layer after the ion transmission, a truly time-resolved ion scattering spectroscopy would be needed.

Apart from the experimental difficulties also theory faces serious challenges. The models for ion-solid interaction nowadays adequately describe equilibrium processes, whereas the impact of an HCI on a surface represents a highly perturbative non-equilibrium process. In this regime only little is known about the dynamics of the ion neutralization as well as the kinetic energy loss. However, to model and predict the energy deposition of HCI in various materials, challenges in simulating multi-electron processes must be overcome.

***Advances in science and technology to meet challenges.*** To meet the challenges, the integration of HCI facilities into an ultra-high-vacuum (UHV) set-up will be necessary. Currently, some labs are pursuing this path. Further, the combination of HCI beams with electron-based microscopes would allow true *in situ* measurements minimizing the influence of surface adsorbates, even though volatile hydrocarbon molecules are always abundant even in UHV. For small area 2D materials or crystalline grains, the development of focused HCI devices with beam spot sizes well below 1 µm will advantageous. Some first efforts have been undertaken until now, but further development is heavily needed in this field.

To further complement spectroscopic measurements with data from emitted secondary particles, a reaction microscope

setup suitable to hold a suspended 2D sample will be necessary. To measure the energy retained in the material, a bolometer-type temperature measurement at liquid He temperature could be performed and thus making the full kinematics of energy deposition and emission by the projectile and secondary particles accessible.

To disentangle processes during the ion impact on the material such as its neutralization and primary energy deposition, from processes on much longer time scales, such as atom sputtering and thermalization, a truly time-resolved methodology is required. Whether this will rely on absolute time-resolution or on a stroboscopic technique is currently under debate.

In case of highly perturbative interaction phenomena, new theoretical methods for their description must be developed. The most promising methodologies are based on TD-DFT and hybrid models, i.e. MD simulations for large simulation cells coupled to an electronic temperature bath. While MD can capture atomic motion in large cells for an extended period of time (several nanoseconds), TD-DFT can give ab-initio information on the energy deposition into the electronic system by charge state dependent ion stopping and neutralization. Coupling TD-DFT and MD goes beyond the Born-Oppenheimer-Approximation and therefore represents a powerful tool for situations where the electronic and atomic subsystems are strongly coupled on similar time-scales [168].

***Concluding remarks.*** Over recent years HCI-surface interaction studies have moved from 3D to 2D and thus increased drastically in complexity with respect to sample manufacturing, handling, analysis, and ion spectroscopic methodologies, see figure 23. The combination of an increasing number of all-UHV and *in situ* methods, 2D material complexity, as well as multi-coincidence techniques will continue in the future. While simulations will soon be able to describe HCI-surface interaction from the sub-fs to the ns time regime, the next disruptive step in experiments will be the development of truly time-resolved ion-scattering techniques.

## Acknowledgments

MS acknowledges funding by the DFG SFB1242 'Non-Equilibrium Dynamics of Condensed Matter in the Time Domain', project C5. R W acknowledges support from the DFG through project WI 4691/1-1 (no. 322051344). We want to express our gratitude to A Reichert for contributing to the visualization.
grid in case of a suspended sheet. This is why currently homogeneous, defect-free 2D materials cannot easily be produced on the mm-scale.

Some 2D materials are even not stable in air, as e.g. black phosphorous or silicene, and thus require a complicated in-vacuum transfer to an HCI facility and to an analysis device. On top of this, some 2D materials are highly susceptible to damage by electronic excitations, beneficial for HCI induced modification, but hampering atomically resolved electron-based microscopy. In principle, suspended 2D materials allow direct spectroscopy of the ion still in a non-equilibrium state after transmission through the material together with the spectroscopy of emitted secondary particles i.e. sputtered atoms, electrons, and photons. Spectroscopy of (quasi-) particles from the interaction process with a suspended 2D material can give, for the first time, experimental access to the dynamics of ion-induced electronic processes on the femto-second time-scale. However, the current challenge lies in the measurement of all particle energies and momenta, ideally in coincidence, plus the determination of energy retained in the material. To probe even longer time scales, i.e. atomic dynamics in the layer after the ion transmission, a truly time-resolved ion scattering spectroscopy would be needed.

Apart from the experimental difficulties also theory faces serious challenges. The models for ion-solid interaction nowadays adequately describe equilibrium processes, whereas the impact of an HCI on a surface represents a highly perturbative non-equilibrium process. In this regime only little is known about the dynamics of the ion neutralization as well as the kinetic energy loss. However, to model and predict the energy deposition of HCI in various materials, challenges in simulating multi-electron processes must be overcome.

***Advances in science and technology to meet challenges.*** To meet the challenges, the integration of HCI facilities into an ultra-high-vacuum (UHV) set-up will be necessary. Currently, some labs are pursuing this path. Further, the combination of HCI beams with electron-based microscopes would allow true *in situ* measurements minimizing the influence of surface adsorbates, even though volatile hydrocarbon molecules are always abundant even in UHV. For small area 2D materials or crystalline grains, the development of focused HCI devices with beam spot sizes well below 1 µm will advantageous. Some first efforts have been undertaken until now, but further development is heavily needed in this field.

To further complement spectroscopic measurements with data from emitted secondary particles, a reaction microscope

setup suitable to hold a suspended 2D sample will be necessary. To measure the energy retained in the material, a bolometer-type temperature measurement at liquid He temperature could be performed and thus making the full kinematics of energy deposition and emission by the projectile and secondary particles accessible.

To disentangle processes during the ion impact on the material such as its neutralization and primary energy deposition, from processes on much longer time scales, such as atom sputtering and thermalization, a truly time-resolved methodology is required. Whether this will rely on absolute time-resolution or on a stroboscopic technique is currently under debate.

In case of highly perturbative interaction phenomena, new theoretical methods for their description must be developed. The most promising methodologies are based on TD-DFT and hybrid models, i.e. MD simulations for large simulation cells coupled to an electronic temperature bath. While MD can capture atomic motion in large cells for an extended period of time (several nanoseconds), TD-DFT can give ab-initio information on the energy deposition into the electronic system by charge state dependent ion stopping and neutralization. Coupling TD-DFT and MD goes beyond the Born-Oppenheimer-Approximation and therefore represents a powerful tool for situations where the electronic and atomic subsystems are strongly coupled on similar time-scales [168].

***Concluding remarks.*** Over recent years HCI-surface interaction studies have moved from 3D to 2D and thus increased drastically in complexity with respect to sample manufacturing, handling, analysis, and ion spectroscopic methodologies, see figure 23. The combination of an increasing number of all-UHV and *in situ* methods, 2D material complexity, as well as multi-coincidence techniques will continue in the future. While simulations will soon be able to describe HCI-surface interaction from the sub-fs to the ns time regime, the next disruptive step in experiments will be the development of truly time-resolved ion-scattering techniques.

## Acknowledgments

MS acknowledges funding by the DFG SFB1242 'Non-Equilibrium Dynamics of Condensed Matter in the Time Domain', project C5. R W acknowledges support from the DFG through project WI 4691/1-1 (no. 322051344). We want to express our gratitude to A Reichert for contributing to the visualization.
# 16. Interaction of HCIs with crystals/solids

Toshiyuki Azuma

RIKEN, Japan

**Status.** Ever since energetic heavy ions have been available, their interaction with solids has been an important topic to be explored. Energy transfer and damage to the solid are especially critical to material and biological sciences. HCIs in solids experience successive collisions with the constituent atoms of the solid, leading to the formation of tracks in the solid. This is a far cry from the single-collision conditions for ion-atom collisions in the gas phase. Nowadays a large amount of information has been compiled for ion-induced effects in solids including electronic excitation and elastic collisions. The traveling ions' behavior such as ionization, EC, and excitation has also been investigated in detail. Nevertheless, owing to the difficulty in observing the ion state in the solid in *situ*, many issues still remain unresolved.

For crystal targets, a very unique property known as channeling is available. By being guided by the crystal potential, traveling ions have a chance to pass through the open space of the crystal without hard collisions with atoms. This phenomenon has been widely applied as a powerful tool for diagnostics of crystal quality.

From the viewpoint of atomic collision physics, one of the most exciting phenomena in crystal targets is the Okorokov effect, often also called RCE. Ions passing through a periodic lattice (ordered rows or planes) of a crystal feel a time-dependent perturbation of the crystal potential. When one of the frequencies of the perturbation corresponds to the difference of internal energy levels of the ions, transitions may take place. Theoretical prediction of this effect can be traced back more than 50 years to an idea proposed by Okorokov [169]. Experimentally concrete observation was reported by Datz *et al* [170]. They observed this phenomenon by measuring the change of the charge state of H-like or He-like HCl ($Z = 5–9$) in the MeV/$u$ energy range channeling through a thin Au or Ag crystal at the resonance condition of the $1s–2p$ transition of the HCIs. The resonantly excited electron in the $2p$ state is more easily ionized by collisions with atoms in the crystal, leading to an enhancement of ionization under the resonance condition. The high ion energies used and the thinness of the crystals were two major reasons for the successful observation; otherwise charge exchange after resonance obscures the effect. In this experiment under the axial channeling condition, the ion energy was scanned to match the resonance condition, which was an experimentally difficult procedure for accelerator operation. They then proposed a new idea to satisfy the resonance conditions, what we now call 2D-RCE [171]. The excitation was induced by the two-dimensional periodic array of crystal strings under planar channeling conditions, where the resonance condition was achieved just by tilting the crystal with a rotating axis perpendicular to the crystal plane, enabling the precise scan of the resonance profile.

Since then, the experiments have made progress by adopting higher energy HCIs as shown in figure 24(a). In 1998 using HCIs with much higher energy, i.e. 390 MeV/$u$,

<figure><img src="image_27.png" /><figcaption>**Figure 24.** (a) Relationship between beam energy and atomic number required to observe the RCE process. The lines are calculated for the $1s–2p$ transition in H-like ions, and the $2s–2p_{1/2}$ and $2s–2p_{3/2}$ transitions in Li-like ions. (b) Schematic view of highly charged ions passing through a periodic structure of crystals. Reprinted figure with permission from [176], Copyright 2013 by the American Physical Society.</figcaption></figure>

supplied from the HIMAC synchrotron in Japan, this type of experiment was performed with H-like $Ar^{17+}$ combined with a thin Si crystal [172]. The oscillating frequency of the periodic crystal fields in the projectile's frame are equivalent to that of about 3 keV photons. The usual atomic collision processes, especially EC, are indeed suppressed and highly resolved resonance profiles with rich structure have been observed. From a series of successive experiments clear DC-Stark effects to the excited levels due to strong static crystal electric fields of the order of GeV/cm and the corresponding evolution of the wavefunction depending on the position of the ions in the crystal were revealed. At this stage, it was recognized that not only in the channeling condition but also in the non-channeling condition, such highly energetic ions can penetrate the crystal without suffering from severe collisions anymore. Taking full advantage of this fact, a great leap in the research happened. As shown in figure 24(b), in the non-channeling condition, ions have a chance to be excited by the three-dimensional periodic array of the crystal plane, which we call 3D-RCE [173]. This phenomenon was confirmed again by H-like $Ar^{17+}$ ions at an energy of 391 MeV/$u$ passing through a 1 µm thick silicon crystal, and resonance profiles observed by the charge state distribution or the x-ray emission yield are much narrower than those of planar channeling ions (2D-RCE) due to the absence of the large DC Stark shift caused by the planar potential.
16. Interaction of HCIs with crystals/solids

Toshiyuki Azuma

RIKEN, Japan

**Status.** Ever since energetic heavy ions have been available, their interaction with solids has been an important topic to be explored. Energy transfer and damage to the solid are especially critical to material and biological sciences. HCIs in solids experience successive collisions with the constituent atoms of the solid, leading to the formation of tracks in the solid. This is a far cry from the single-collision conditions for ion-atom collisions in the gas phase. Nowadays a large amount of information has been compiled for ion-induced effects in solids including electronic excitation and elastic collisions. The traveling ions' behavior such as ionization, EC, and excitation has also been investigated in detail. Nevertheless, owing to the difficulty in observing the ion state in the solid in *situ*, many issues still remain unresolved.

For crystal targets, a very unique property known as channeling is available. By being guided by the crystal potential, traveling ions have a chance to pass through the open space of the crystal without hard collisions with atoms. This phenomenon has been widely applied as a powerful tool for diagnostics of crystal quality.

From the viewpoint of atomic collision physics, one of the most exciting phenomena in crystal targets is the Okorokov effect, often also called RCE. Ions passing through a periodic lattice (ordered rows or planes) of a crystal feel a time-dependent perturbation of the crystal potential. When one of the frequencies of the perturbation corresponds to the difference of internal energy levels of the ions, transitions may take place. Theoretical prediction of this effect can be traced back more than 50 years to an idea proposed by Okorokov [169]. Experimentally concrete observation was reported by Datz *et al* [170]. They observed this phenomenon by measuring the change of the charge state of H-like or He-like HCl (Z = 5–9) in the MeV/u energy range channeling through a thin Au or Ag crystal at the resonance condition of the 1s–2p transition of the HCIs. The resonantly excited electron in the 2p state is more easily ionized by collisions with atoms in the crystal, leading to an enhancement of ionization under the resonance condition. The high ion energies used and the thinness of the crystals were two major reasons for the successful observation; otherwise charge exchange after resonance obscures the effect. In this experiment under the axial channeling condition, the ion energy was scanned to match the resonance condition, which was an experimentally difficult procedure for accelerator operation. They then proposed a new idea to satisfy the resonance conditions, what we now call 2D-RCE [171]. The excitation was induced by the two-dimensional periodic array of crystal strings under planar channeling conditions, where the resonance condition was achieved just by tilting the crystal with a rotating axis perpendicular to the crystal plane, enabling the precise scan of the resonance profile.

Since then, the experiments have made progress by adopting higher energy HCIs as shown in figure 24(a). In 1998 using HCIs with much higher energy, i.e. 390 MeV/u,

<figure><img src="image_28.png" /><figcaption>Figure 24. (a) Relationship between beam energy and atomic number required to observe the RCE process. The lines are calculated for the 1s–2p transition in H-like ions, and the 2s–2p<sup>1/2</sup> and 2s–2p<sup>3/2</sup> transitions in Li-like ions. (b) Schematic view of highly charged ions passing through a periodic structure of crystals.
Reprinted figure with permission from [176], Copyright 2013 by the American Physical Society.</figcaption></figure>

supplied from the HIMAC synchrotron in Japan, this type of experiment was performed with H-like Ar<sup>17+</sup> combined with a thin Si crystal [172]. The oscillating frequency of the periodic crystal fields in the projectile's frame are equivalent to that of about 3 keV photons. The usual atomic collision processes, especially EC, are indeed suppressed and highly resolved resonance profiles with rich structure have been observed. From a series of successive experiments clear DC-Stark effects to the excited levels due to strong static crystal electric fields of the order of GeV/cm and the corresponding evolution of the wavefunction depending on the position of the ions in the crystal were revealed. At this stage, it was recognized that not only in the channeling condition but also in the non-channeling condition, such highly energetic ions can penetrate the crystal without suffering from severe collisions anymore. Taking full advantage of this fact, a great leap in the research happened. As shown in figure 24(b), in the non-channeling condition, ions have a chance to be excited by the three-dimensional periodic array of the crystal plane, which we call 3D-RCE [173]. This phenomenon was confirmed again by H-like Ar<sup>17+</sup> ions at an energy of 391 MeV/u passing through a 1 µm thick silicon crystal, and resonance profiles observed by the charge state distribution or the x-ray emission yield are much narrower than those of planar channeling ions (2D-RCE) due to the absence of the large DC Stark shift caused by the planar potential.
The HCIs traveling through a crystal target feel a variety of periodic crystal fields including higher harmonic components simultaneously. The direction of research then naturally headed for double resonances using these different oscillating fields. The double resonance is a key technique in many fields like quantum optics or pump-probe spectroscopy in chemistry, and it has become reality in the x-ray energy region. Under the same configuration of the ion trajectory and the crystal direction, the double resonance condition of 3D-RCE can be satisfied by scanning two parameters, rotation angles of the crystal, which are in a sense analogous to two-color energy tunable x-ray laser excitation. One example of successful double resonance experiments is selective production of the doubly excited state in He-like Ar<sup>16+</sup> ions [174]. The Ar<sup>16+</sup> ions were resonantly excited sequentially from the ground state to the 1s2p state and then the 2p<sup>2</sup> state by the (X-X) double resonance, which was confirmed by Auger electron emission. The other example is a demonstration of the Autler–Townes doublet as a novel type of coherent interaction of atoms not with photons but with a periodic crystal field [175]. It was observed by the (X-VUV) double resonance. The states strongly coupled in the VUV region were probed by the excitation in the x-ray region. The characteristic spectra are well interpreted by an analogy of the dressed atom concept often adopted for atom-photon interactions.

**Current and future challenges.** Figure 25 schematically shows that, as the energy of the HCl beam increases, the resonance peaks become sharpened due to the lack of the collisions of HCl with atoms in a crystal which are the usual origin of decoherence effects. The typical resonance width, Δ*E*/*E*, for RCE of a few 100 MeV/u HCIs is of the order of 10<sup>-3</sup>. This leads to a new idea that RCE may be a new tool for high precision spectroscopy of the Lamb shift in the energy levels of HCl to check the bound state quantum electro dynamics (BS-QED). To explore this feasibility, experiments using uranium (Z = 92) ions were started at the accelerator and storage-ring facility of the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany using the heavy-ion synchrotron (SIS) [176]. The 2s–2p<sub>3/2</sub> transition of 4.5 keV in 192 MeV/u Li-like U<sup>89+</sup> ions was excited, and the resonance profiles were measured by the de-excitation x-ray yield. Clear resonances with a width of 4.4 eV were demonstrated. However, it was also realized that the resonance width was affected by the energy distribution of the provided ion beam. Then, narrowing of the ion velocity was achieved by introducing the electron cooling technique. The He-like U<sup>90+</sup> ions extracted from SIS were injected into an ESR ion storage ring, where the stored ions merged with a mono-energetic electron beam for electron cooling. The resulting Li-like U<sup>89+</sup> ions produced via EC were extracted and guided to the crystal target. As a result, the resonance width was narrowed down to 1.4 eV with a Lorentzian distribution. The next challenge in the near future is to determine the absolute energy within 1 ppm. Recent HFS measurements of Bi ions stored in the ESR ring was successful in determining the ion absolute energy by

<figure><img src="image_28.png" /><figcaption>Figure 25. Narrowing of the relative resonance width *E*/*E*<sub>res</sub> for the ions with higher energy.</figcaption></figure>

precisely measuring the electrode voltage for the electron cooler [177]. This technique will be adopted in the coming experiments.

A new synchrotron SIS100 is under construction in the ongoing FAIR project as introduced in section 19 in this Roadmap. This will provide 1 GeV/u uranium beams, making it within reach to determine the contribution of the 1s Lamb-shift (~460 eV) in the 1s–2p<sub>3/2</sub> transition of 140 keV using the RCE technique. A HESR is also planned for storing cooled beams at energies of up to a few GeV/u, and this may open a chance to perform new RCE experiments. This technique is in principle can be applied for any specific ions or transition levels. Especially, the double resonance technique will be useful to prepare metastable states. Alignment of HCIs by taking an advantage of the linearly-polarized nature of the perturbation of the crystal potential will be applied to high-Z ions, where the relativistic effect like the Breit interaction plays a significant role in polarization of the emitted x-rays. Nuclear excitation of low-lying levels of nuclei including nuclear quadrupole resonance is also within scope.

Apart from RCE with high-energy ions, an alternative approach to suppress decoherence is using the surface channeling condition where ions at glancing incidence to the crystal surface experience mirror reflection above the surface to avoid the collision process with surface atoms. This idea was indeed verified by two groups [178], and extensive application of this technique is expected.

**Advances in science and technology to meet challenges.** As already described, critical new techniques and devices were introduced, when important progresses in dynamics and spectroscopy were made, like higher energy ion accelerators, electron cooling techniques, and extremely thin crystals with good quality. In the future this trend will never change.
The HCIs traveling through a crystal target feel a variety of periodic crystal fields including higher harmonic components simultaneously. The direction of research then naturally headed for double resonances using these different oscillating fields. The double resonance is a key technique in many fields like quantum optics or pump-probe spectroscopy in chemistry, and it has become reality in the x-ray energy region. Under the same configuration of the ion trajectory and the crystal direction, the double resonance condition of 3D-RCE can be satisfied by scanning two parameters, rotation angles of the crystal, which are in a sense analogous to two-color energy tunable x-ray laser excitation. One example of successful double resonance experiments is selective production of the doubly excited state in He-like Ar<sup>16+</sup> ions [174]. The Ar<sup>16+</sup> ions were resonantly excited sequentially from the ground state to the 1s2p state and then the 2p<sup>2</sup> state by the (X-X) double resonance, which was confirmed by Auger electron emission. The other example is a demonstration of the Autler–Townes doublet as a novel type of coherent interaction of atoms not with photons but with a periodic crystal field [175]. It was observed by the (X-VUV) double resonance. The states strongly coupled in the VUV region were probed by the excitation in the x-ray region. The characteristic spectra are well interpreted by an analogy of the dressed atom concept often adopted for atom-photon interactions.

**Current and future challenges.** Figure 25 schematically shows that, as the energy of the HCl beam increases, the resonance peaks become sharpened due to the lack of the collisions of HCl with atoms in a crystal which are the usual origin of decoherence effects. The typical resonance width, Δ*E*/*E*, for RCE of a few 100 MeV/u HCIs is of the order of 10<sup>-3</sup>. This leads to a new idea that RCE may be a new tool for high precision spectroscopy of the Lamb shift in the energy levels of HCl to check the bound state quantum electro dynamics (BS-QED). To explore this feasibility, experiments using uranium (Z = 92) ions were started at the accelerator and storage-ring facility of the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany using the heavy-ion synchrotron (SIS) [176]. The 2s–2p<sub>3/2</sub> transition of 4.5 keV in 192 MeV/u Li-like U<sup>89+</sup> ions was excited, and the resonance profiles were measured by the de-excitation x-ray yield. Clear resonances with a width of 4.4 eV were demonstrated. However, it was also realized that the resonance width was affected by the energy distribution of the provided ion beam. Then, narrowing of the ion velocity was achieved by introducing the electron cooling technique. The He-like U<sup>90+</sup> ions extracted from SIS were injected into an ESR ion storage ring, where the stored ions merged with a mono-energetic electron beam for electron cooling. The resulting Li-like U<sup>89+</sup> ions produced via EC were extracted and guided to the crystal target. As a result, the resonance width was narrowed down to 1.4 eV with a Lorentzian distribution. The next challenge in the near future is to determine the absolute energy within 1 ppm. Recent HFS measurements of Bi ions stored in the ESR ring was successful in determining the ion absolute energy by

<figure><img src="image_29.png" /><figcaption>Figure 25. Narrowing of the relative resonance width *E*/*E*<sub>res</sub> for the ions with higher energy.</figcaption></figure>

precisely measuring the electrode voltage for the electron cooler [177]. This technique will be adopted in the coming experiments.

A new synchrotron SIS100 is under construction in the ongoing FAIR project as introduced in section 19 in this Roadmap. This will provide 1 GeV/u uranium beams, making it within reach to determine the contribution of the 1s Lamb-shift (~460 eV) in the 1s–2p<sub>3/2</sub> transition of 140 keV using the RCE technique. A HESR is also planned for storing cooled beams at energies of up to a few GeV/u, and this may open a chance to perform new RCE experiments. This technique is in principle can be applied for any specific ions or transition levels. Especially, the double resonance technique will be useful to prepare metastable states. Alignment of HCIs by taking an advantage of the linearly-polarized nature of the perturbation of the crystal potential will be applied to high-Z ions, where the relativistic effect like the Breit interaction plays a significant role in polarization of the emitted x-rays. Nuclear excitation of low-lying levels of nuclei including nuclear quadrupole resonance is also within scope.

Apart from RCE with high-energy ions, an alternative approach to suppress decoherence is using the surface channeling condition where ions at glancing incidence to the crystal surface experience mirror reflection above the surface to avoid the collision process with surface atoms. This idea was indeed verified by two groups [178], and extensive application of this technique is expected.

**Advances in science and technology to meet challenges.** As already described, critical new techniques and devices were introduced, when important progresses in dynamics and spectroscopy were made, like higher energy ion accelerators, electron cooling techniques, and extremely thin crystals with good quality. In the future this trend will never change.
Finally, it is also noted that, as a new approach, magnetic resonance of traveling neutral alkali atoms were achieved in the microwave frequency region using artificial periodic structures [179]. This technique also has the potential for a variety of future applications.

*Concluding remarks.* Understanding of the interaction of HCI with crystals has been deepened dramatically for the last decades far beyond a diagnostics tool for crystal quality or damage. RCE utilizing a periodic crystal field has offered a new paradigm in atomic collisions involving other research

fields. Its significance will be strengthened in the future as an alternative approach to lasers for exploring spectroscopy and dynamics of HCI.

## Acknowledgments

I would like to acknowledge valuable collaborations with Y Nakano, Y Nakai, A Hatakeyama, K Komaki, Y Yamazaki, A Demian-Bräunning, T Stöhlker, and many coworkers.
Finally, it is also noted that, as a new approach, magnetic resonance of traveling neutral alkali atoms were achieved in the microwave frequency region using artificial periodic structures [179]. This technique also has the potential for a variety of future applications.

*Concluding remarks.* Understanding of the interaction of HCI with crystals has been deepened dramatically for the last decades far beyond a diagnostics tool for crystal quality or damage. RCE utilizing a periodic crystal field has offered a new paradigm in atomic collisions involving other research

fields. Its significance will be strengthened in the future as an alternative approach to lasers for exploring spectroscopy and dynamics of HCI.

## Acknowledgments

I would like to acknowledge valuable collaborations with Y Nakano, Y Nakai, A Hatakeyama, K Komaki, Y Yamazaki, A Demian-Bräunning, T Stöhlker, and many coworkers.
# 17. COMs and irradiation effects in solid phase for astrophysics: radiolysis and radio-resistance of nucleobases

Philippe Boduch

CIMAP-GANIL/University of Caen-Normandie UNICAEN, France

**Status.** For COMs, several theories claim that these molecules have possibly reached the early Earth via comets and meteorites [180]. Indeed, during the recent ROSETTA space mission, the simplest amino acid glycine, has been detected in the coma of comet 67P/Churyumov-Gerasimenko [181]. Additionally, analyses of carbonaceous meteorites found on Earth show a presence of COMs (e.g. nucleobases). That is a strong indication of existence of such molecules in outer space.

Concerning the formation of complex molecules, irradiation of ices containing simple molecules such as H₂O, CO, NH₃ can lead to the formation of COMs [182, 183]. Among COMs, nucleobases are particularly important. They are a part of DNA and are essential for the emergence of life, maybe due to exogenesis. Even if nucleobases have not yet been observed directly in space, their presence on meteorites on earth is a strong indication of their existence in space environments. Thus, it is important to study irradiation effects on such molecules in order to determine their radio-resistance.

**Current and future challenges.** All the nucleobases (adenine, uracil, cytosine, guanine and thymine) have been irradiated with swift heavy ions at GANIL (Caen, France) and GSI (Darmstadt, Germany) facilities in order to determine their destruction cross sections as a function of the electronic stopping power of the projectiles. The goal of these experiments with high energy projectiles is to simulate in laboratory the effect of cosmic rays on COMs embedded in icy mantles on dusty grains in Inter Stellar Media (ISM) or at the surface of comets. The samples have been irradiated at low temperature (around 10 K) and the irradiation induced modifications are followed *in situ* by Fourier transform infrared spectroscopy (FTIR). Figure 26 shows the evolution of the cytosine column density inside the sample as a function of the local dose (deposited energy per molecule) for 4 projectiles (Ca, Ni, Xe and U). The fact that all these curves fall together strongly suggests that the local dose is a key parameter and the evolution of the cytosine sample depends mainly on the deposited energy. The same result was obtained for all of the nucleobases (for adenine, see [184]). From the evolution of the column density as a function of the fluence, it is possible to determine the destruction cross section of the nucleobases for each projectile. We distinguish 2 kinds of nucleobases: (i) purine nucleobases (guanine and adenine) formed of two heterocyclic rings, and (ii) pyrimidine nucleobases (cytosine, uracil and thymine) which are formed by just one heterocyclic ring. The corresponding destruction cross sections are of the same order of magnitude

<figure><img src="image_29.png" /><figcaption>Figure 26. Evolution of the cytosine column density as a function of the local dose.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>Figure 27. Destruction cross section versus the electronic stopping power Se for adenine samples.</figcaption></figure>

(between 1 and $5 \times 10^{-13} \text{ cm}^2$ for the experiments performed at GSI with 190 MeV Calcium projectiles). Nevertheless, the destruction cross sections of purine nucleobases are smaller than for pyrimidine nucleobases. Guanine is the most radio-resistant nucleobase. This is in agreement with the fact that guanine is also the most abundant nucleobase detected in carbon-rich meteorites analyzed on earth ([185]). From all the experiments performed with swift heavy ions at GANIL and at GSI, it is possible to determine the evolution of the nucleobase destruction cross section as a function of the electronic stopping power. Figure 27 shows as example the results obtained for heavy ions at 2 different places (GSI and GANIL) with 2 different experimental setups for adenine, which are in good agreement. This is also the case for the
# 17. COMs and irradiation effects in solid phase for astrophysics: radiolysis and radio-resistance of nucleobases

Philippe Boduch

CIMAP-GANIL/University of Caen-Normandie UNICAEN, France

**Status.** For COMs, several theories claim that these molecules have possibly reached the early Earth via comets and meteorites [180]. Indeed, during the recent ROSETTA space mission, the simplest amino acid glycine, has been detected in the coma of comet 67P/Churyumov-Gerasimenko [181]. Additionally, analyses of carbonaceous meteorites found on Earth show a presence of COMs (e.g. nucleobases). That is a strong indication of existence of such molecules in outer space.

Concerning the formation of complex molecules, irradiation of ices containing simple molecules such as H₂O, CO, NH₃ can lead to the formation of COMs [182, 183]. Among COMs, nucleobases are particularly important. They are a part of DNA and are essential for the emergence of life, maybe due to exogenesis. Even if nucleobases have not yet been observed directly in space, their presence on meteorites on earth is a strong indication of their existence in space environments. Thus, it is important to study irradiation effects on such molecules in order to determine their radio-resistance.

**Current and future challenges.** All the nucleobases (adenine, uracil, cytosine, guanine and thymine) have been irradiated with swift heavy ions at GANIL (Caen, France) and GSI (Darmstadt, Germany) facilities in order to determine their destruction cross sections as a function of the electronic stopping power of the projectiles. The goal of these experiments with high energy projectiles is to simulate in laboratory the effect of cosmic rays on COMs embedded in icy mantles on dusty grains in Inter Stellar Media (ISM) or at the surface of comets. The samples have been irradiated at low temperature (around 10 K) and the irradiation induced modifications are followed *in situ* by Fourier transform infrared spectroscopy (FTIR). Figure 26 shows the evolution of the cytosine column density inside the sample as a function of the local dose (deposited energy per molecule) for 4 projectiles (Ca, Ni, Xe and U). The fact that all these curves fall together strongly suggests that the local dose is a key parameter and the evolution of the cytosine sample depends mainly on the deposited energy. The same result was obtained for all of the nucleobases (for adenine, see [184]). From the evolution of the column density as a function of the fluence, it is possible to determine the destruction cross section of the nucleobases for each projectile. We distinguish 2 kinds of nucleobases: (i) purine nucleobases (guanine and adenine) formed of two heterocyclic rings, and (ii) pyrimidine nucleobases (cytosine, uracil and thymine) which are formed by just one heterocyclic ring. The corresponding destruction cross sections are of the same order of magnitude

<figure><img src="image_30.png" /><figcaption>Figure 26. Evolution of the cytosine column density as a function of the local dose.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>Figure 27. Destruction cross section versus the electronic stopping power Se for adenine samples.</figcaption></figure>

(between 1 and $5 \times 10^{-13} \text{ cm}^2$ for the experiments performed at GSI with 190 MeV Calcium projectiles). Nevertheless, the destruction cross sections of purine nucleobases are smaller than for pyrimidine nucleobases. Guanine is the most radio-resistant nucleobase. This is in agreement with the fact that guanine is also the most abundant nucleobase detected in carbon-rich meteorites analyzed on earth ([185]). From all the experiments performed with swift heavy ions at GANIL and at GSI, it is possible to determine the evolution of the nucleobase destruction cross section as a function of the electronic stopping power. Figure 27 shows as example the results obtained for heavy ions at 2 different places (GSI and GANIL) with 2 different experimental setups for adenine, which are in good agreement. This is also the case for the
cross sections for electron beams [186]. The cross sections follow a power law with electronic stopping $\sigma \approx A \cdot S_e^n$ with n typically around 1.2. This law can be used for astrophysics applications in order to determine the lifetime of nucleobases in ISM. In the case of adenine, the half-life found is around 10 million years [184]. This value is directly comparable to the typical lifetime of dense clouds in the ISM, clouds which are the birth place of stellar system. These results suggest that this type of molecules has a high survival probability and could be detected in ISM in the future.

**Technology to meet challenges.** To simulate the effect of cosmic rays on complex molecules and to perform such 'online' experiments with *in situ* analysis, it is mandatory to work at very low temperature in ultrahigh vacuum conditions to ensure a controlled preparation of the targets and a clean monitoring of its evolution under irradiation, in particular for mass spectrometry. In addition, contamination by water may influence cross section and sputter yield measurements. Recently, a new ultrahigh vacuum device has been built at CIMAP-GANIL (Caen, France). The performances of this new device are described in [187]. It is equipped with three spectrometers (FTIR, UV and Quadrupole Mass Spectroscope) and can be installed on several GANIL beam lines. This setup is open to the scientific community and will help to address new challenges about irradiation effects in ices, COMs, and other materials. These challenges are really numerous: for example, to study COMs irradiation in a more realistic situation. In ISM, grains are covered with a thin icy mantle mainly composed of H₂O molecules. In these conditions, it is important to study irradiation effects on COMs trapped in a water matrix at low temperature in order to characterize the effect of the matrix. A second challenge consists in increasing the size and the complexity of the

COMs. New experiments have been started on nucleotides (nucleobase + sugar). A sample of uridine (uracil + ribose) has been recently irradiated and the associated irradiation cross section will be compared with those obtained for uracil samples. This kind of studies will be extended to more complex molecules in the future, peptides for example. For astrophysics, polycyclic aromatic hydrocarbons (PAH) are really important complex molecules. They have been detected in space and represent an important source of carbon in space (up to 30%). Since carbon is the key element in evolution of prebiotic materials [188], it would be also really interesting to study the PAH radio-resistance and the associated radiolysis products in water matrix with different percentages.

**Concluding remarks.** Nucleobases are essential for the emergence of life. The analysis of nucleobase irradiation experiments shows that these molecules are rather radio-resistant and the associated life time indicates a high survival probability in ISM. Now, recent technical developments (see e.g. [189]) allow to continue these studies in more realistic conditions with water matrix and with more complex molecules.

## Acknowledgments

This work was supported by ANR IGLIAS project, Grant No. ANR-13-BS05-0004 of the French Agence Nationale de la Recherche. The author wants to thank the CIMAP-GANIL team: J M Ramillon, C Grygiel, I Monnet, A Domaracka, C Feierstein, E Balanzat, Y Ngono Ravache, F Levesque, A N Agnihotri, G Muniz, P Ada Bibang and H Rothard, E Dartois (ISMO laboratory), M Bender and D Severin (GSI) and G Strazzulla (INAF, Catania) for their really helpfull support.
cross sections for electron beams [186]. The cross sections follow a power law with electronic stopping $\sigma \approx A \cdot S_e^n$ with n typically around 1.2. This law can be used for astrophysics applications in order to determine the lifetime of nucleobases in ISM. In the case of adenine, the half-life found is around 10 million years [184]. This value is directly comparable to the typical lifetime of dense clouds in the ISM, clouds which are the birth place of stellar system. These results suggest that this type of molecules has a high survival probability and could be detected in ISM in the future.

**Technology to meet challenges.** To simulate the effect of cosmic rays on complex molecules and to perform such 'online' experiments with *in situ* analysis, it is mandatory to work at very low temperature in ultrahigh vacuum conditions to ensure a controlled preparation of the targets and a clean monitoring of its evolution under irradiation, in particular for mass spectrometry. In addition, contamination by water may influence cross section and sputter yield measurements. Recently, a new ultrahigh vacuum device has been built at CIMAP-GANIL (Caen, France). The performances of this new device are described in [187]. It is equipped with three spectrometers (FTIR, UV and Quadrupole Mass Spectroscope) and can be installed on several GANIL beam lines. This setup is open to the scientific community and will help to address new challenges about irradiation effects in ices, COMs, and other materials. These challenges are really numerous: for example, to study COMs irradiation in a more realistic situation. In ISM, grains are covered with a thin icy mantle mainly composed of H₂O molecules. In these conditions, it is important to study irradiation effects on COMs trapped in a water matrix at low temperature in order to characterize the effect of the matrix. A second challenge consists in increasing the size and the complexity of the

COMs. New experiments have been started on nucleotides (nucleobase + sugar). A sample of uridine (uracil + ribose) has been recently irradiated and the associated irradiation cross section will be compared with those obtained for uracil samples. This kind of studies will be extended to more complex molecules in the future, peptides for example. For astrophysics, polycyclic aromatic hydrocarbons (PAH) are really important complex molecules. They have been detected in space and represent an important source of carbon in space (up to 30%). Since carbon is the key element in evolution of prebiotic materials [188], it would be also really interesting to study the PAH radio-resistance and the associated radiolysis products in water matrix with different percentages.

**Concluding remarks.** Nucleobases are essential for the emergence of life. The analysis of nucleobase irradiation experiments shows that these molecules are rather radio-resistant and the associated life time indicates a high survival probability in ISM. Now, recent technical developments (see e.g. [189]) allow to continue these studies in more realistic conditions with water matrix and with more complex molecules.

## Acknowledgments

This work was supported by ANR IGLIAS project, Grant No. ANR-13-BS05-0004 of the French Agence Nationale de la Recherche. The author wants to thank the CIMAP-GANIL team: J M Ramillon, C Grygiel, I Monnet, A Domaracka, C Feierstein, E Balanzat, Y Ngono Ravache, F Levesque, A N Agnihotri, G Muniz, P Ada Bibang and H Rothard, E Dartois (ISMO laboratory), M Bender and D Severin (GSI) and G Strazzulla (INAF, Catania) for their really helpfull support.
NEW FACILITIES FOR NEW CHALLENGES

18. Cryogenic electrostatic storage rings

Henning T Schmidt

Stockholm University, Sweden

*Status.* With the introduction of ion-storage rings in atomic and molecular physics research in the late 1980s, the option to study ensembles of ions for extended time periods exceeding the µs range was for the first time combined with the efficient detection of decay/collision products offered by fast beams. While these relatively large (typically 50 m circumference) magnetic-confinement storage rings were mostly operated at MeV energies, some of the most prominent studies involved low-energy collisions between the stored ions and electrons in merged-beams configurations. The electron beams' original purpose was to cool the translational degrees of freedom of the stored ions, but at the same time they constituted an excellent target for electron-ion recombination studies. In molecular recombination the long-time storage and vibrational relaxation of the molecular ions were combined with the excellent electron-beam quality to provide unprecedented experimental conditions [190]. During the late 1990s with intense activities at the storage rings many experiments were performed, which only made use of the extended storage times and the ease with which products of interactions or spontaneous processes could be detected from an ion beam. It was realized that such experiments, which did not make use of the option of going to high (MeV) energies or to make use of electron cooling could be performed in simpler less costly devices. At the same time, a growing interest emerged in clusters and complex molecules, so that a development towards storage of higher mass particles was called for. For these new demands, a purely electrostatic ion-storage ring in an ultra-high vacuum environment was an ideal solution and this lead to the development of the ELISA storage ring in Aarhus [191].

Here a single example will represent all the pioneering ELISA experiments with complex systems: In studies of hot metal cluster anions with a large spread in internal energies, it was found that the spontaneous decay monitored through neutral product detection followed a power-law rather than an exponential [192]. ELISA was followed by other electrostatic rings where spontaneous processes and processes induced by interactions with photons or electrons are studied [193].

***Current and future challenges.*** The general advantage in all storage ring experiments is the combination of the temporally extended confinement, allowing the relaxation of excited state ions, and the efficient detection of reaction products. Concerning the relaxation, this is efficient for most metastable states in atomic systems with millisecond lifetimes and for vibrationally excited states of small molecular ions, where the few seconds of storage time easily available in room temperature rings are sufficient. In many cases, however, even *rotational* excitations

of molecular ions can have strong influence on the results of experimental investigations and if the fundamental properties are sought, one needs ways to accomplish control over the rotational degrees of freedom as well. The nature of this problem is two-fold. Rotational relaxation processes are generally quite slow, of the order of minutes even for the smallest molecules. Thus, very long storage times are needed. Furthermore, the excitation energies involved are so low that many rotational levels are occupied at room temperature, even if thermal equilibrium were to be attained. A central motivation behind the recently developed *cryogenic* electrostatic storage rings is that both these problems related to the rotational excitations are simultaneously addressed. Cooling the systems down to the 10 K temperature range makes the inner walls of the vacuum chambers act as efficient cryopumps for most of the gases otherwise present in the ultra-high vacuum systems. This way, residual-gas densities have been reached that are lower than one molecule per cubic millimeter. This extreme vacuum has led to storage lifetimes in cryogenic electrostatic rings of keV ion beams approaching one hour. With this, waiting for even the last steps of rotational cooling towards the ground state is within reach for many molecular systems. Evidently, the low temperature itself is also necessary for the thermally equilibrated molecular ions to have a high fraction of the population in the (few) lowest rotational levels. While the details are system dependent, the amount of rotational excitation is strongly decreased for all systems by going from room temperature to a cryogenic environment.

***Advances in science and technology to meet challenges.*** Recently, three cryogenic electrostatic storage ring facilities have become operational. These are the DESIREE (Double ElectroStatic Ion-Ring ExpEriment) at Stockholm University [194], the CSR (Cryogenic Storage Ring) at the Max-Planck Institute for Nuclear Physics in Heidelberg [195] and the RICE (RIKEN Cryogenic Electrostatic ring) at RIKEN, Japan [196]. Common to these are their principle constructions with an entire separate all-cryogenic vacuum chamber surrounded by in-vacuum thermal insulation. This ensures the very high vacuum and the long storage lifetimes. The three facilities differ strongly in other respects. RICE is with its 3.0 m circumference by far the smallest one. It is well suited for studies of spontaneous processes and for laser interaction with the stored ion beams. Furthermore, there are advanced plans for merging a beam of neutrals with the stored beam to study reactions between neutrals and positive ions at low and well-controlled energies [196]. Of the three, the CSR is the biggest system with a 35.1 m circumference. This large ring is equipped with an electron cooler for merged-beams ion-electron recombination studies, a merged neutral beam is being developed, and a reaction microscope is to be included [195]. DESIREE [194] (see figure 28) is special in being a double electrostatic ring and it consists of two 8.6 m circumference ion-storage rings. The design is based on the ability to merge beams of positive and negative ions stored in
# NEW FACILITIES FOR NEW CHALLENGES

## 18. Cryogenic electrostatic storage rings

Henning T Schmidt

Stockholm University, Sweden

**Status.** With the introduction of ion-storage rings in atomic and molecular physics research in the late 1980s, the option to study ensembles of ions for extended time periods exceeding the µs range was for the first time combined with the efficient detection of decay/collision products offered by fast beams. While these relatively large (typically 50 m circumference) magnetic-confinement storage rings were mostly operated at MeV energies, some of the most prominent studies involved low-energy collisions between the stored ions and electrons in merged-beams configurations. The electron beams' original purpose was to cool the translational degrees of freedom of the stored ions, but at the same time they constituted an excellent target for electron-ion recombination studies. In molecular recombination the long-time storage and vibrational relaxation of the molecular ions were combined with the excellent electron-beam quality to provide unprecedented experimental conditions [190]. During the late 1990s with intense activities at the storage rings many experiments were performed, which only made use of the extended storage times and the ease with which products of interactions or spontaneous processes could be detected from an ion beam. It was realized that such experiments, which did not make use of the option of going to high (MeV) energies or to make use of electron cooling could be performed in simpler less costly devices. At the same time, a growing interest emerged in clusters and complex molecules, so that a development towards storage of higher mass particles was called for. For these new demands, a purely electrostatic ion-storage ring in an ultra-high vacuum environment was an ideal solution and this lead to the development of the ELISA storage ring in Aarhus [191].

Here a single example will represent all the pioneering ELISA experiments with complex systems: In studies of hot metal cluster anions with a large spread in internal energies, it was found that the spontaneous decay monitored through neutral product detection followed a power-law rather than an exponential [192]. ELISA was followed by other electrostatic rings where spontaneous processes and processes induced by interactions with photons or electrons are studied [193].

**Current and future challenges.** The general advantage in all storage ring experiments is the combination of the temporally extended confinement, allowing the relaxation of excited state ions, and the efficient detection of reaction products. Concerning the relaxation, this is efficient for most metastable states in atomic systems with millisecond lifetimes and for vibrationally excited states of small molecular ions, where the few seconds of storage time easily available in room temperature rings are sufficient. In many cases, however, even rotational excitations

of molecular ions can have strong influence on the results of experimental investigations and if the fundamental properties are sought, one needs ways to accomplish control over the rotational degrees of freedom as well. The nature of this problem is two-fold. Rotational relaxation processes are generally quite slow, of the order of minutes even for the smallest molecules. Thus, very long storage times are needed. Furthermore, the excitation energies involved are so low that many rotational levels are occupied at room temperature, even if thermal equilibrium were to be attained. A central motivation behind the recently developed cryogenic electrostatic storage rings is that both these problems related to the rotational excitations are simultaneously addressed. Cooling the systems down to the 10 K temperature range makes the inner walls of the vacuum chambers act as efficient cryopumps for most of the gases otherwise present in the ultra-high vacuum systems. This way, residual-gas densities have been reached that are lower than one molecule per cubic millimeter. This extreme vacuum has led to storage lifetimes in cryogenic electrostatic rings of keV ion beams approaching one hour. With this, waiting for even the last steps of rotational cooling towards the ground state is within reach for many molecular systems. Evidently, the low temperature itself is also necessary for the thermally equilibrated molecular ions to have a high fraction of the population in the (few) lowest rotational levels. While the details are system dependent, the amount of rotational excitation is strongly decreased for all systems by going from room temperature to a cryogenic environment.

**Advances in science and technology to meet challenges.** Recently, three cryogenic electrostatic storage ring facilities have become operational. These are the DESIREE (Double ElectroStatic Ion-Ring ExpEriment) at Stockholm University [194], the CSR (Cryogenic Storage Ring) at the Max-Planck Institute for Nuclear Physics in Heidelberg [195] and the RICE (RIKEN Cryogenic Electrostatic ring) at RIKEN, Japan [196]. Common to these are their principle constructions with an entire separate all-cryogenic vacuum chamber surrounded by in-vacuum thermal insulation. This ensures the very high vacuum and the long storage lifetimes. The three facilities differ strongly in other respects. RICE is with its 3.0 m circumference by far the smallest one. It is well suited for studies of spontaneous processes and for laser interaction with the stored ion beams. Furthermore, there are advanced plans for merging a beam of neutrals with the stored beam to study reactions between neutrals and positive ions at low and well-controlled energies [196]. Of the three, the CSR is the biggest system with a 35.1 m circumference. This large ring is equipped with an electron cooler for merged-beams ion-electron recombination studies, a merged neutral beam is being developed, and a reaction microscope is to be included [195]. DESIREE [194] (see figure 28) is special in being a double electrostatic ring and it consists of two 8.6 m circumference ion-storage rings. The design is based on the ability to merge beams of positive and negative ions stored in
<figure><img src="image_31.png" /></figure>

Figure 28. DESIREE [194] at Stockholm University consists of two electrostatic ion-storage rings in a common cryogenic vacuum chamber and with a common straight section where beams of opposite charge polarity can be merged. With the low internal energies that can be attained by waiting for the ions to reach thermal equilibrium and the high degree of control of the inter-particle motion obtained from the merged-beams configuration, unprecedented control of all internal and external degrees of freedom can be obtained.

<figure><img src="image_32.png" /></figure>

Figure 29. Measured fractions of the OH⁻ ions not in the rotational ground state as function of time after injection in DESIREE (blue data points and curve). The green data points and curve show the same fraction but now a cw laser beam is merged with the ion beam for the first 260 s and tuned to a wavelength where non-ground state ions only can be photodetached [197].

the two rings and measure products of mutual neutralization and related processes. The long-time storage of both beams will make it possible to study pairs of ions of complex molecules close to thermal equilibrium with the cryogenic surroundings. While the merged-beams geometry provides the opportunity to control the *inter*-molecular degrees of freedom of the collision partners, the *intra*-molecular degrees of freedom are controlled by the low temperature and the long time storage.

For all the cryogenic storage rings, the ability to demonstrate rotational cooling and to which extent thermal

equilibrium may be reached are essential. In 2017 both the CSR and DESIREE teams reported the observation of stored beams of OH⁻ with well over 90% of the population in the lowest ($J=0$) quantum state [197]. Figure 29 displays data from a threshold photodetachment experiment in DESIREE. By comparing signal rates for wavelengths just above and just below the threshold for ground state photodetachment and using prior knowledge of the photodetachment cross sections, the fraction of OH⁻ ions *not* in the $J=0$ ground rotational level was deduced as function of time after ion injection. For the data set shown in green, the population of ions in excited rotational levels was reduced artificially by depletion through selective photodetachment. For the first 260 s after injection, this depletion laser was on resulting in an asymptotic excitation fraction of 3.6% ± 0.3% corresponding to a rotational temperature of 12.3 ± 0.2 K. After the laser light was blocked at $t = 260$ s the excitation fraction increased by absorption of thermal photons from the 13.5 ± 0.5 K temperature surroundings and by collisions with the few residual-gas molecules left. Finally an asymptotic excitation fraction of 18.1% ± 0.9%, corresponding to a rotational temperature of 20.6 ± 0.5 K, was reached. These results and similar findings in CSR holds great promise for future experiments in the here mentioned and any future cryogenic storage ring systems for experiments where cold molecular ions interact with light, electrons, neutral particles or other ions [194–197].

In parallel to the electrostatic ion-storage ring developments, compact electrostatic ion-beam traps have been developed in which fast-moving ions are confined between two opposing focusing electrostatic mirrors. Here we mention the recent studies from the Weizmann institute of ultraslow isomerization in $C_{10}$ molecular ions [198] and the first experiment with a cryogenic electrostatic storage device in which the He⁻ lifetime was accurately measured [199].

*Concluding remarks.* Novel cryogenic electrostatic ion-storage rings have become operational and cooling of the rotational degrees of freedom has been demonstrated. New insights from experiments with rotationally cold ions interacting with photons, electrons, neutral atoms and other cold ions are expected in the very near future.

## Acknowledgments

I want to acknowledge all colleagues at Stockholm University and elsewhere working on electrostatic ion-rings and traps for all their wonderful work, which is far beyond what can be represented here. I thank the Swedish Research council for its support for the DESIREE infrastructure (2017-00621) and my individual research grant (2018-04092).