# Roadmap on photonic, electronic and atomic collision physics: III. Heavy particles: with zero to relativistic speeds

Friedrich Aumayr, Kiyoshi Ueda, Emma Sokell, Stefan Schippers, Hossein Sadeghpour, Frédéric Merkt, Thomas Gallagher, F Barry Dunning, Paul Scheier, Olof Echt, et al.

► To cite this version:

Friedrich Aumayr, Kiyoshi Ueda, Emma Sokell, Stefan Schippers, Hossein Sadeghpour, et al. Roadmap on photonic, electronic and atomic collision physics: III. Heavy particles: with zero to relativistic speeds. Journal of Physics B: Atomic, Molecular and Optical Physics, 2019, 52 (17), pp.171003. 10.1088/1361-6455/ab26ea. hal-02374535

HAL Id: hal-02374535

https://hal.science/hal-02374535

Submitted on 27 May 2024

**HAL** is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire **HAL**, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_1.png" /></figure>
# Roadmap on photonic, electronic and atomic collision physics: III. Heavy particles: with zero to relativistic speeds

Friedrich Aumayr, Kiyoshi Ueda, Emma Sokell, Stefan Schippers, Hossein Sadeghpour, Frédéric Merkt, Thomas Gallagher, F Barry Dunning, Paul Scheier, Olof Echt, et al.

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Friedrich Aumayr, Kiyoshi Ueda, Emma Sokell, Stefan Schippers, Hossein Sadeghpour, et al. Roadmap on photonic, electronic and atomic collision physics: III. Heavy particles: with zero to relativistic speeds. Journal of Physics B: Atomic, Molecular and Optical Physics, 2019, 52 (17), pp.171003. 10.1088/1361-6455/ab26ea. hal-02374535

HAL Id: hal-02374535

https://hal.science/hal-02374535v1

Submitted on 27 May 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>
## Roadmap

# Roadmap on photonic, electronic and atomic collision physics: III. Heavy particles: with zero to relativistic speeds

Friedrich Aumayr<sup>1,27,28</sup>, Kiyoshi Ueda<sup>2,27</sup>, Emma Sokell<sup>3,27</sup>, Stefan Schippers<sup>4,27</sup>, Hossein Sadeghpour<sup>5,27</sup>, Frédéric Merkt<sup>6,7</sup>, Thomas F Gallagher<sup>8</sup>, F Barry Dunning<sup>9</sup>, Paul Scheier<sup>10</sup>, Olof Echt<sup>10</sup>, Tom Kirchner<sup>11</sup>, Stephan Fritzsche<sup>12,13,14</sup>, Andrey Surzhykov<sup>15,16</sup>, Xinwen Ma<sup>17</sup>, Roberto Rivarola<sup>18</sup>, Omar Fojon<sup>18</sup>, Lokesh Tribedi<sup>19</sup>, Emily Lamour<sup>20</sup>, José R Crespo López-Urrutia<sup>21</sup>, Yuri A Litvinov<sup>14</sup>, Vladimir Shabaev<sup>22</sup>, Henrik Cederquist<sup>23</sup>, Henning Zettergren<sup>23</sup>, Marika Schleberger<sup>24</sup>, Richard A Wilhelm<sup>1</sup>, Toshiyuki Azuma<sup>25</sup>, Philippe Boduch<sup>26</sup>, Henning T Schmidt<sup>23</sup> and Thomas Stöhlker<sup>12,13,14</sup>

<sup>1</sup> TU Wien, Institute of Applied Physics, A-1040 Vienna, Austria

<sup>2</sup> Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

<sup>3</sup> School of Physics, University College Dublin, Dublin, Ireland

<sup>4</sup> Justus-Liebig-Universität Gießen, I. Physikalisches Institut, 35392 Giessen, Germany

<sup>5</sup> ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, United States of America

<sup>6</sup> Department of Chemistry and Applied Biosciences, ETH Zürich, CH-8093 Zurich, Switzerland

<sup>7</sup> Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands

<sup>8</sup> Department of Physics, University of Virginia, Charlottesville, VA 22904, United States of America

<sup>9</sup> Department of Physics and Astronomy, Rice University MS61, Houston TX 77005, United States of America

<sup>10</sup> Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, A-6020, Innsbruck, Austria

<sup>11</sup> Department of Physics and Astronomy, York University, Toronto, Ontario, M3J 1P3, Canada

<sup>12</sup> Helmholtz Institute Jena, D-07743 Jena, Germany

<sup>13</sup> Theoretisch-Physikalisches Institut, Friedrich-Schiller Universität Jena, D-07743 Jena, Germany

<sup>14</sup> GSI Helmholtz Centre for Heavy Ion Research, D-64291 Darmstadt, Germany

<sup>15</sup> Technische Universität Braunschweig, Institut für Mathematische Physik, D-38106 Braunschweig, Germany

<sup>16</sup> Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Germany

<sup>17</sup> Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, People's Republic of China

<sup>18</sup> Instituto de Física Rosario CONICET-UNR, 2000 Rosario, Argentina

<sup>19</sup> Tata Institute of Fundamental Research, Mumbai 400005, India

<sup>20</sup> Institut des NanoSciences de Paris, CNRS, Sorbonne University, Paris, F-75005, France

<sup>21</sup> Max-Planck-Institut für Kernphysik, D-69117 Heidelberg, Germany

<sup>22</sup> Department of Physics, St. Petersburg State University, 199034 St. Petersburg, Russia

<sup>23</sup> Department of Physics, Stockholm University, AlbaNova, SE-106 91, Stockholm, Sweden

<sup>24</sup> Universität Duisburg-Essen, Fakultät für Physik and Cenide, D-47057 Duisburg, Germany

<sup>25</sup> Atomic, Molecular, and Optical Physics Laboratory, RIKEN, Wako, 351-0198, Japan

<sup>26</sup> CIMAP-GANIL/University of Caen-Normandie UNICAEN, France

<sup>27</sup> Guest editors of the roadmap
## Roadmap

# Roadmap on photonic, electronic and atomic collision physics: III. Heavy particles: with zero to relativistic speeds

Friedrich Aumayr<sup>1,27,28</sup>, Kiyoshi Ueda<sup>2,27</sup>, Emma Sokell<sup>3,27</sup>, Stefan Schippers<sup>4,27</sup>, Hossein Sadeghpour<sup>5,27</sup>, Frédéric Merkt<sup>6,7</sup>, Thomas F Gallagher<sup>8</sup>, F Barry Dunning<sup>9</sup>, Paul Scheier<sup>10</sup>, Olof Echt<sup>10</sup>, Tom Kirchner<sup>11</sup>, Stephan Fritzsche<sup>12,13,14</sup>, Andrey Surzhykov<sup>15,16</sup>, Xinwen Ma<sup>17</sup>, Roberto Rivarola<sup>18</sup>, Omar Fojon<sup>18</sup>, Lokesh Tribedi<sup>19</sup>, Emily Lamour<sup>20</sup>, José R Crespo López-Urrutia<sup>21</sup>, Yuri A Litvinov<sup>14</sup>, Vladimir Shabaev<sup>22</sup>, Henrik Cederquist<sup>23</sup>, Henning Zettergren<sup>23</sup>, Marika Schleberger<sup>24</sup>, Richard A Wilhelm<sup>1</sup>, Toshiyuki Azuma<sup>25</sup>, Philippe Boduch<sup>26</sup>, Henning T Schmidt<sup>23</sup> and Thomas Stöhlker<sup>12,13,14</sup>

<sup>1</sup> TU Wien, Institute of Applied Physics, A-1040 Vienna, Austria

<sup>2</sup> Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

<sup>3</sup> School of Physics, University College Dublin, Dublin, Ireland

<sup>4</sup> Justus-Liebig-Universität Gießen, I. Physikalisches Institut, 35392 Giessen, Germany

<sup>5</sup> ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, United States of America

<sup>6</sup> Department of Chemistry and Applied Biosciences, ETH Zürich, CH-8093 Zurich, Switzerland

<sup>7</sup> Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands

<sup>8</sup> Department of Physics, University of Virginia, Charlottesville, VA 22904, United States of America

<sup>9</sup> Department of Physics and Astronomy, Rice University MS61, Houston TX 77005, United States of America

<sup>10</sup> Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, A-6020, Innsbruck, Austria

<sup>11</sup> Department of Physics and Astronomy, York University, Toronto, Ontario, M3J 1P3, Canada

<sup>12</sup> Helmholtz Institute Jena, D-07743 Jena, Germany

<sup>13</sup> Theoretisch-Physikalisches Institut, Friedrich-Schiller Universität Jena, D-07743 Jena, Germany

<sup>14</sup> GSI Helmholtz Centre for Heavy Ion Research, D-64291 Darmstadt, Germany

<sup>15</sup> Technische Universität Braunschweig, Institut für Mathematische Physik, D-38106 Braunschweig, Germany

<sup>16</sup> Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Germany

<sup>17</sup> Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, People's Republic of China

<sup>18</sup> Instituto de Física Rosario CONICET-UNR, 2000 Rosario, Argentina

<sup>19</sup> Tata Institute of Fundamental Research, Mumbai 400005, India

<sup>20</sup> Institut des NanoSciences de Paris, CNRS, Sorbonne University, Paris, F-75005, France

<sup>21</sup> Max-Planck-Institut für Kernphysik, D-69117 Heidelberg, Germany

<sup>22</sup> Department of Physics, St. Petersburg State University, 199034 St. Petersburg, Russia

<sup>23</sup> Department of Physics, Stockholm University, AlbaNova, SE-106 91, Stockholm, Sweden

<sup>24</sup> Universität Duisburg-Essen, Fakultät für Physik and Cenide, D-47057 Duisburg, Germany

<sup>25</sup> Atomic, Molecular, and Optical Physics Laboratory, RIKEN, Wako, 351-0198, Japan

<sup>26</sup> CIMAP-GANIL/University of Caen-Normandie UNICAEN, France

<sup>27</sup> Guest editors of the roadmap
<figure><img src="image_2.png" /></figure>

CrossMark

Abstract

We publish three Roadmaps on photonic, electronic and atomic collision physics in order to celebrate the 60th anniversary of the ICPEAC conference. Roadmap III focusses on heavy particles: with zero to relativistic speeds. Modern theoretical and experimental approaches provide detailed insight into the wide range of many-body interactions involving projectiles and targets of varying complexity ranging from simple atoms, through molecules and clusters, complex biomolecules and nanoparticles to surfaces and crystals. These developments have been driven by technological progress and future developments will expand the horizon of the systems that can be studied. This Roadmap aims at looking back along the road, explaining the evolution of the field, and looking forward, collecting nineteen contributions from leading scientists in the field.

Keywords: heavy particles, many-body interactions, clusters, complex biomolecules

(Some figures may appear in colour only in the online journal)

Contents

<table><tr><td>INTRODUCTION</td><td>4</td></tr><tr><td>RYDBERG ATOMS AND COLD COLLISIONS</td><td>6</td></tr><tr><td>1. High Rydberg states and ion chemistry</td><td>6</td></tr><tr><td>2. Resonant energy transfer with Rydberg atoms</td><td>8</td></tr><tr><td>3. Studies involving high-n Rydberg atoms</td><td>10</td></tr><tr><td>4. Chemistry close to 0 K</td><td>12</td></tr><tr><td>COLLISIONS INVOLVING HEAVY PROJECTILES</td><td>14</td></tr><tr><td>5. Non-relativistic ion-atom collision theory</td><td>14</td></tr><tr><td>6. Correlation and polarization phenomena in relativistic ion-atom collisions</td><td>16</td></tr><tr><td>7. Experimental investigations on ion-atom collisions</td><td>18</td></tr><tr><td>8. Interference effects in ion-molecule collisions</td><td>21</td></tr><tr><td>9. Ion-molecule collisions—large molecules</td><td>23</td></tr><tr><td>10. Ion-ion collisions in the intermediate velocity regime</td><td>25</td></tr><tr><td>HIGHLY CHARGED IONS</td><td>27</td></tr><tr><td>11. Frequency metrology with trapped and stored HCIs</td><td>27</td></tr><tr><td>12. Highly-charged radionuclides</td><td>29</td></tr><tr><td>13. QED in strong fields</td><td>31</td></tr><tr><td>14. Interactions of HCIs with clusters</td><td>33</td></tr><tr><td>15. Interaction of HCIs with surfaces and 2D materials</td><td>35</td></tr></table>

<figure><img src="image_3.png" /></figure>

<footnote n="28">28 Author to whom any correspondence should be addressed.</footnote>
<figure><img src="image_3.png" /></figure>

CrossMark

Abstract

We publish three Roadmaps on photonic, electronic and atomic collision physics in order to celebrate the 60th anniversary of the ICPEAC conference. Roadmap III focusses on heavy particles: with zero to relativistic speeds. Modern theoretical and experimental approaches provide detailed insight into the wide range of many-body interactions involving projectiles and targets of varying complexity ranging from simple atoms, through molecules and clusters, complex biomolecules and nanoparticles to surfaces and crystals. These developments have been driven by technological progress and future developments will expand the horizon of the systems that can be studied. This Roadmap aims at looking back along the road, explaining the evolution of the field, and looking forward, collecting nineteen contributions from leading scientists in the field.

Keywords: heavy particles, many-body interactions, clusters, complex biomolecules

(Some figures may appear in colour only in the online journal)

Contents

<table><tr><td>INTRODUCTION</td><td>4</td></tr><tr><td>RYDBERG ATOMS AND COLD COLLISIONS</td><td>6</td></tr><tr><td>1. High Rydberg states and ion chemistry</td><td>6</td></tr><tr><td>2. Resonant energy transfer with Rydberg atoms</td><td>8</td></tr><tr><td>3. Studies involving high-n Rydberg atoms</td><td>10</td></tr><tr><td>4. Chemistry close to 0 K</td><td>12</td></tr><tr><td>COLLISIONS INVOLVING HEAVY PROJECTILES</td><td>14</td></tr><tr><td>5. Non-relativistic ion-atom collision theory</td><td>14</td></tr><tr><td>6. Correlation and polarization phenomena in relativistic ion-atom collisions</td><td>16</td></tr><tr><td>7. Experimental investigations on ion-atom collisions</td><td>18</td></tr><tr><td>8. Interference effects in ion-molecule collisions</td><td>21</td></tr><tr><td>9. Ion-molecule collisions—large molecules</td><td>23</td></tr><tr><td>10. Ion-ion collisions in the intermediate velocity regime</td><td>25</td></tr><tr><td>HIGHLY CHARGED IONS</td><td>27</td></tr><tr><td>11. Frequency metrology with trapped and stored HCIs</td><td>27</td></tr><tr><td>12. Highly-charged radionuclides</td><td>29</td></tr><tr><td>13. QED in strong fields</td><td>31</td></tr><tr><td>14. Interactions of HCIs with clusters</td><td>33</td></tr><tr><td>15. Interaction of HCIs with surfaces and 2D materials</td><td>35</td></tr></table>

<figure><img src="image_4.png" /></figure>

<footnote n="28">28 Author to whom any correspondence should be addressed.</footnote>
<table><thead><tr><th></th><th>Roadmap</th></tr></thead><tbody><tr><td>16. Interaction of HCIs with crystals/solids</td><td>37</td></tr><tr><td>17. COMs and irradiation effects in solid phase for astrophysics: radiolysis and radio-resistance of nucleobases</td><td>40</td></tr><tr><td>NEW FACILITIES FOR NEW CHALLENGES</td><td>42</td></tr><tr><td>18. Cryogenic electrostatic storage rings</td><td>42</td></tr><tr><td>19. Frontiers of extreme electromagnetic fields: atomic physics with HCIs at FAIR (SPARC collaboration)</td><td>44</td></tr></tbody></table>
<table><thead><tr><th></th><th>Roadmap</th></tr></thead><tbody><tr><td>16. Interaction of HCIs with crystals/solids</td><td>37</td></tr><tr><td>17. COMs and irradiation effects in solid phase for astrophysics: radiolysis and radio-resistance of nucleobases</td><td>40</td></tr><tr><td>NEW FACILITIES FOR NEW CHALLENGES</td><td>42</td></tr><tr><td>18. Cryogenic electrostatic storage rings</td><td>42</td></tr><tr><td>19. Frontiers of extreme electromagnetic fields: atomic physics with HCIs at FAIR (SPARC collaboration)</td><td>44</td></tr></tbody></table>
INTRODUCTION

Friedrich Aumayr¹, Kiyoshi Ueda², Emma Sokell³, Stefan Schippers⁴, Hossein Sadeghpour⁵

¹TU Wien, Austria

²Tohoku University, Japan

³University College Dublin, Ireland

⁴Justus-Liebig-Universität Gießen, Germany

⁵Harvard University, United States of America

To celebrate the 60th anniversary of the ICPEAC conference, we publish a series of three Roadmaps on photonic, electronic and atomic collision physics. One for each of the three classes of projectile that comprise the breadth of topics encompassed by ICPEAC; *I. Light-matter interaction*; *II. Electron and antimatter interactions*; and *III. Heavy particles: with zero to relativistic speeds*. Each of the Roadmaps is intended to provide an overview of the present status of the field, how it was arrived at and address current and future challenges faced by those working in the broad area of research. As with all IOP Roadmaps, the three articles have been authored collaboratively by leading researchers in the areas and each aims to provide an impression of current trends in the respective field of research.

Roadmap III: Heavy particles is dedicated to recent advances in collisions involving heavy particles, from highly relativistic ions to extremely cold atoms and molecules, from exotic Rydberg atoms to extremely highly-charged heavy ions, from simple atoms and molecules to clusters, large biomolecules, nanoparticles, novel 2D-materials, surfaces and solids. This field of research is at the heart of ICPEAC. The present Roadmap glimpses into the future of the field by explaining important and promising theoretical and experimental trends and developments. It comprises 19 contributions by leading scientists distributed over four topic sections: topic section 1 on Rydberg atoms and cold collisions, topic section 2 on collisions involving heavy projectiles, topic section 3 on highly-charged ions and topic section 4 on new facilities for new challenges.

In topic section 1, Merkt describes the use of molecular Rydberg states for ion chemistry using three examples, PFI-ZEKE and MQDT-assisted Rydberg spectroscopy for accessing a broad range of electronic, vibrational, rotational and hyperfine levels of the cation states and/or their energy intervals and a chip-based Rydberg-Stark deflector and decelerator for ion-molecule reactions within the Rydberg molecule. Gallagher looks back on the history of resonant energy transfer with Rydberg atoms, via dipole-dipole interactions without collisional motion, and discusses their applications from quantum gates and simulators to the construction of ultralong-range molecules. Dunning describes the current status of studies involving high-Rydberg atoms and future directions such as studying the dynamics of strongly-coupled Rydberg atoms, two-electron excited states (planetary atoms) and ultralong-range Rydberg molecules. Scheier and Echt discuss future directions of research using doped helium nanodroplets (HNDs). In particular they outline

the prospects of using up to 1 µm large, monodisperse droplets to synthesize and characterize novel structures like nanowires, Coulomb crystals or ligand-free catalysts.

In topic section 2, Kirchner sketches the path to a fully non-perturbative treatment of ion-atom collision processes. Advances in computational methods have already allowed us to answer some long-standing questions on the role of electron correlation effects in multiparticle dynamics. However, many electron systems will remain a challenge into the future. Fritzsche and Surzhykov show how high-resolution angle as well as polarization resolved studies in relativistic ion-atom collisions can lead to new insights into quantum dynamics in extremely strong fields if combined with advanced theoretical techniques. The FAIR facility will also make such polarization studies possible for negative-constantium dielectronic recombination (NCDR), a process in which a free electron is captured into a bound state of a heavy high-Z ion, while an electron-positron pair is emitted. Ma discusses the future challenges for experimental investigations of ion-atom collisions. On his list are new concepts to extract relative scattering phases from two-center interference patterns in ion-molecule collisions, as well as the incorporation of photon detection into reaction microscopes. Rivarola and Fojon further elaborate on these interference effects in ion-molecule collisions. From a theoretical point of view they suggest the investigation of the role of electron correlation not only in the description of molecular orbitals but also in the molecular continuum in the exit channels. Experimentally they propose a complete mapping of all resulting particles including the orientation of the molecular target. Tribedi deals with collisions between ions and very large molecules. In the case of larger molecules or clusters, the presence of further collision partners, to which energy can be transferred, leads to the appearance of new decay mechanisms such as interatomic Coulombic decay. In his contribution, he points out that it will be a great challenge in the future to conduct collision experiments with bio-molecules in their natural (liquid) environment. Such processes play an important role in radiation therapy, as well as in the use of metallic nanoparticles to enhance the biological effectiveness of ion irradiation via collective excitation effects. With her contribution Lamour opens a window into a hitherto unexplored collision regime, the interaction of ions with ions in the intermediate velocity regime. These experiments and reliable theoretical models are still completely missing, but will become feasible with the new upcoming facilities SPIRAL2 and FAIR in France and Germany, respectively.

In topic section 3, Crespo López-Urrutia bangs the drum for the use of highly charged ions (HCI) in fundamental high precision experiments. In particular, with the first demonstration of sympathetic laser cooling of HCI re-trapped in a cryogenic radio-frequency trap, and the rapid development of narrow-band lasers in the x-ray regime, extreme frequency metrology (XFM) will become possible with HCI as adequate frequency standards and excellent study cases for fundamental interactions. Litvinov sketches the possibilities for precision investigations of highly charged radionuclides. Their decay processes are extremely sensitive to the interplay
## INTRODUCTION

Friedrich Aumayr¹, Kiyoshi Ueda², Emma Sokell³, Stefan Schippers⁴, Hossein Sadeghpour⁵

¹TU Wien, Austria

²Tohoku University, Japan

³University College Dublin, Ireland

⁴Justus-Liebig-Universität Gießen, Germany

⁵Harvard University, United States of America

To celebrate the 60th anniversary of the ICPEAC conference, we publish a series of three Roadmaps on photonic, electronic and atomic collision physics. One for each of the three classes of projectile that comprise the breadth of topics encompassed by ICPEAC; *I. Light-matter interaction*; *II. Electron and antimatter interactions*; and *III. Heavy particles: with zero to relativistic speeds*. Each of the Roadmaps is intended to provide an overview of the present status of the field, how it was arrived at and address current and future challenges faced by those working in the broad area of research. As with all IOP Roadmaps, the three articles have been authored collaboratively by leading researchers in the areas and each aims to provide an impression of current trends in the respective field of research.

Roadmap III: Heavy particles is dedicated to recent advances in collisions involving heavy particles, from highly relativistic ions to extremely cold atoms and molecules, from exotic Rydberg atoms to extremely highly-charged heavy ions, from simple atoms and molecules to clusters, large biomolecules, nanoparticles, novel 2D-materials, surfaces and solids. This field of research is at the heart of ICPEAC. The present Roadmap glimpses into the future of the field by explaining important and promising theoretical and experimental trends and developments. It comprises 19 contributions by leading scientists distributed over four topic sections: topic section 1 on Rydberg atoms and cold collisions, topic section 2 on collisions involving heavy projectiles, topic section 3 on highly-charged ions and topic section 4 on new facilities for new challenges.

In topic section 1, Merkt describes the use of molecular Rydberg states for ion chemistry using three examples, PFI-ZEKE and MQDT-assisted Rydberg spectroscopy for accessing a broad range of electronic, vibrational, rotational and hyperfine levels of the cation states and/or their energy intervals and a chip-based Rydberg-Stark deflector and decelerator for ion-molecule reactions within the Rydberg molecule. Gallagher looks back on the history of resonant energy transfer with Rydberg atoms, via dipole-dipole interactions without collisional motion, and discusses their applications from quantum gates and simulators to the construction of ultralong-range molecules. Dunning describes the current status of studies involving high-Rydberg atoms and future directions such as studying the dynamics of strongly-coupled Rydberg atoms, two-electron excited states (planetary atoms) and ultralong-range Rydberg molecules. Scheier and Echt discuss future directions of research using doped helium nanodroplets (HNDs). In particular they outline

the prospects of using up to 1 µm large, monodisperse droplets to synthesize and characterize novel structures like nanowires, Coulomb crystals or ligand-free catalysts.

In topic section 2, Kirchner sketches the path to a fully non-perturbative treatment of ion-atom collision processes. Advances in computational methods have already allowed us to answer some long-standing questions on the role of electron correlation effects in multiparticle dynamics. However, many electron systems will remain a challenge into the future. Fritzsche and Surzhykov show how high-resolution angle as well as polarization resolved studies in relativistic ion-atom collisions can lead to new insights into quantum dynamics in extremely strong fields if combined with advanced theoretical techniques. The FAIR facility will also make such polarization studies possible for negative-constantium dielectronic recombination (NCDR), a process in which a free electron is captured into a bound state of a heavy high-Z ion, while an electron-positron pair is emitted. Ma discusses the future challenges for experimental investigations of ion-atom collisions. On his list are new concepts to extract relative scattering phases from two-center interference patterns in ion-molecule collisions, as well as the incorporation of photon detection into reaction microscopes. Rivarola and Fojon further elaborate on these interference effects in ion-molecule collisions. From a theoretical point of view they suggest the investigation of the role of electron correlation not only in the description of molecular orbitals but also in the molecular continuum in the exit channels. Experimentally they propose a complete mapping of all resulting particles including the orientation of the molecular target. Tribedi deals with collisions between ions and very large molecules. In the case of larger molecules or clusters, the presence of further collision partners, to which energy can be transferred, leads to the appearance of new decay mechanisms such as interatomic Coulombic decay. In his contribution, he points out that it will be a great challenge in the future to conduct collision experiments with bio-molecules in their natural (liquid) environment. Such processes play an important role in radiation therapy, as well as in the use of metallic nanoparticles to enhance the biological effectiveness of ion irradiation via collective excitation effects. With her contribution Lamour opens a window into a hitherto unexplored collision regime, the interaction of ions with ions in the intermediate velocity regime. These experiments and reliable theoretical models are still completely missing, but will become feasible with the new upcoming facilities SPIRAL2 and FAIR in France and Germany, respectively.

In topic section 3, Crespo López-Urrutia bangs the drum for the use of highly charged ions (HCI) in fundamental high precision experiments. In particular, with the first demonstration of sympathetic laser cooling of HCI re-trapped in a cryogenic radio-frequency trap, and the rapid development of narrow-band lasers in the x-ray regime, extreme frequency metrology (XFM) will become possible with HCI as adequate frequency standards and excellent study cases for fundamental interactions. Litvinov sketches the possibilities for precision investigations of highly charged radionuclides. Their decay processes are extremely sensitive to the interplay
of atomic and nuclear structure and therefore promise a large
potential for new discoveries, once the next generation of
low-energy storage rings and traps becomes available.
Shabaev explains, how high precision experiments with HCIs
provide stringent tests for non-perturbative QED methods
leading to the most precise determination of electron mass,
nuclear magnetic moments, nuclear radii or even an
independent determination of the fine structure constant.
Cederquist and Zettergren describe the challenges and
prospects for ion-cluster collision studies. Improved control
over properties such as cluster size, charge and internal
energy will be the key to a more fundamental understanding.
Schleberger and Wilhelm motivate the reasons and explain
the challenges for moving from irradiation of 3D bulk to
novel 2D materials in HCI—surface interaction studies.
Modern multi-coincidence spectroscopies are already in use
to disentangle some of the basic interaction processes and the
development of truly time-resolved ion scattering techniques
will be the next step to study hollow atoms and 2D materials
in a highly non-equilibrium state in unprecedented detail.
Azuma briefly reviews the exciting phenomenon of resonant
coherent excitation (RCE) in ions traveling through periodic
crystals and suggests that RCE may become a new tool for
high precision spectroscopy and dynamics of HCI once new
high energy storage rings become available. Boduch
describes the latest efforts to simulate in the laboratory the
effect of cosmic rays on complex organic molecules (COMs)
embedded in icy mantles on dusty grains in interstellar media

or at the surface of comets. This is of particular interest since
such molecules might have reached the early Earth via comets
and meteorites contributing to the formation of life.

In topic section 4, Schmidt describes the novel purely electrostatic and cryogenic ion-storage rings which have recently become operational. They allow experiments with rotationally cold ions and therefore offer unprecedented control of all internal and external degrees of freedom. Stöhlker outlines the challenging atomic physics program foreseen at FAIR. Since this future facility will offer beams of cooled HCI in energy regimes where no such experiments have so far been possible, it will substantially enlarge the research capabilities for the exploration of atomic matter within the realm of extreme and ultra-short duration electromagnetic fields.

Although the contributions to this Roadmap, outlined
above, come from a few selected researchers, we believe that
they are representative of many other related scientific
activities. The study of collision processes with heavy
projectiles is a broad field and offers great potential for new
discoveries in basic and applied research in the future.

Acknowledgments

KU acknowledges support from the five-star alliance and IMRAM project. ES thanks SFI and the EU CALIPSOplus programme for support.
of atomic and nuclear structure and therefore promise a large potential for new discoveries, once the next generation of low-energy storage rings and traps becomes available. Shabaev explains, how high precision experiments with HCs provide stringent tests for non-perturbative QED methods leading to the most precise determination of electron mass, nuclear magnetic moments, nuclear radii or even an independent determination of the fine structure constant. Cederquist and Zettergren describe the challenges and prospects for ion-cluster collision studies. Improved control over properties such as cluster size, charge and internal energy will be the key to a more fundamental understanding. Schleberger and Wilhelm motivate the reasons and explain the challenges for moving from irradiation of 3D bulk to novel 2D materials in HCI—surface interaction studies. Modern multi-coincidence spectroscopies are already in use to disentangle some of the basic interaction processes and the development of truly time-resolved ion scattering techniques will be the next step to study hollow atoms and 2D materials in a highly non-equilibrium state in unprecedented detail. Azuma briefly reviews the exciting phenomenon of resonant coherent excitation (RCE) in ions traveling through periodic crystals and suggests that RCE may become a new tool for high precision spectroscopy and dynamics of HCI once new high energy storage rings become available. Boduch describes the latest efforts to simulate in the laboratory the effect of cosmic rays on complex organic molecules (COMs) embedded in icy mantles on dusty grains in interstellar media

or at the surface of comets. This is of particular interest since such molecules might have reached the early Earth via comets and meteorites contributing to the formation of life.

In topic section 4, Schmidt describes the novel purely electrostatic and cryogenic ion-storage rings which have recently become operational. They allow experiments with rotationally cold ions and therefore offer unprecedented control of all internal and external degrees of freedom. Stohlker outlines the challenging atomic physics program foreseen at FAIR. Since this future facility will offer beams of cooled HCI in energy regimes where no such experiments have so far been possible, it will substantially enlarge the research capabilities for the exploration of atomic matter within the realm of extreme and ultra-short duration electromagnetic fields.

Although the contributions to this Roadmap, outlined above, come from a few selected researchers, we believe that they are representative of many other related scientific activities. The study of collision processes with heavy projectiles is a broad field and offers great potential for new discoveries in basic and applied research in the future.

## Acknowledgments

KU acknowledges support from the five-star alliance and IMRAM project. ES thanks SFI and the EU CALIPSOplus programme for support.
# RYDBERG ATOMS AND COLD COLLISIONS

## 1. High Rydberg states and ion chemistry

Frédéric Merkt

ETH Zurich, Switzerland; Free University of Amsterdam, The Netherlands

*Status.* This contribution focuses on the use of high Rydberg states of neutral molecular systems to characterize the structure, dynamics and reactivity of molecular cations. Rydberg states can be defined as the states of atoms and molecules having spectral positions $v_n$ that can be approximated by Rydberg's formula

$$v_n = E_1(\alpha^+) / h - cR_M / (n - d_l)^2. \quad (1)$$

In equation (1), $n$ is the principal quantum number, $\delta_l$ is the quantum defect of the series with electron orbital-angular-momentum quantum number $l$, $R_M$ is the mass-dependent Rydberg constant, $E_l(\alpha^+)$ represents the series limit as $n$ approaches infinity and thus the onset of the ionization continuum associated with the production of a singly charged ion in the quantum state $\alpha^+$ (see figure 1(a)). Equation (1) implies independent, separable motions of the Rydberg electron and the ion core and becomes increasingly accurate as $n$ and $l$ increase. Most properties of Rydberg states rapidly scale with $n$. For instance, their polarizability scales as $n^7$, their electric dipole moment scales as $n^2$, and the minimal electric field needed for their efficient ionization scales as $n^{-4}$ (see [1]).

Rydberg states form series that converge on the different electronic, and in the case of molecules also vibrational ($v^+$) and rotational ($N^+$), quantum states of the molecular ion core (see figure 1(a)). At high $n$ values, the Rydberg electron does not influence the ion core but maintains the charge neutrality of the molecular system. The use of Rydberg states to characterize positively charged ions relies on these properties. The measurement of Rydberg series and their extrapolation yield the energy-level structure of cations [2]. The energy-level structure of cations can also be obtained by the selective pulsed field ionization (PFI) of very high Rydberg states, as illustrated in figure 1(c). With their large dipole moments (beyond 1500 Debye at $n = 25$) Rydberg atoms and molecules can easily be accelerated in inhomogeneous electric fields, and numerous devices have been developed that enable the deceleration, the deflection and the reflection of beams of Rydberg atoms and molecules, and the storage of cold Rydberg atoms and molecules in electric traps [3]. These devices have considerable potential for studies of ion-molecule reactions at low temperatures.

## Current and future challenges

*Precision measurements of ionization energies and ionic level structures by Rydberg series extrapolation.* High-resolution spectra of high-*n* Rydberg states can be used to determine the series limits, and thus the ionization energies of atoms and molecules with high precision. In atomic systems with a closed-shell ion core (Li, Na, K), the extrapolation can be performed

with equation (1). Using ultracold atomic samples to suppress Doppler and transit-time broadening in combination with photoexcitation with frequency-comb-stabilized single-mode continuous-wave lasers, the ionization energy of Cs [5] was determined to be $E_l(hc) = 31\ 406.467\ 7325(14)\ \text{cm}^{-1}$. To reach this level of accuracy, it is necessary to measure and compensate stray electric and magnetic fields to better than 1 mV cm$^{-1}$ and 1 mG, respectively. Pressure shifts and shifts arising from dipole-dipole interactions with neighboring Rydberg atoms must also be quantified. The extrapolation of Rydberg series in atoms with open-shell ion cores and in molecules necessitates the consideration of interactions between series converging on different ionic states. The most reliable extrapolations are not carried out with equation (1) but using multichannel quantum defect theory (MQDT) [6, 7], which can even be used to determine the hyperfine structure of the cations [8].

Molecular hydrogen has been the test system for the application of MQDT to molecules [7]. The MQDT analysis of recent measurements of the Rydberg spectrum of $H_2$ has allowed its ionization and dissociation energies, and rotational and hyperfine intervals in $H_2^+$ [8, 9], to be determined with high accuracy. The most accurate measurements of Rydberg series in $H_2$ reach an accuracy of 65 kHz [10] and are precise enough to be sensitive to the finite size of the proton [11].

Future steps in precision Rydberg spectroscopy for the determination of accurate ionization energies include (i) the development of methods and light sources to record high-resolution Rydberg spectra of a broader range of molecules, (ii) the generation of corresponding cold-molecule samples, and (iii) a rigorous establishment of the uncertainties of the Rydberg-series limits extrapolated by MQDT. In future, MQDT-assisted Rydberg spectroscopy of cations is expected to contribute not only to solve problems of molecular structure and dynamics. When applied to few-electron systems, precision Rydberg spectroscopy may also contribute to test theory at its most fundamental level, improve fundamental constants or discover new effects.

*Ion-neutral reactions within the orbit of a Rydberg electron.* At sufficiently high $n$ values, the ion-core can undergo chemical reactions with neutral molecules located within the Rydberg-electron orbit. The Rydberg electron does not affect the reaction but provides charge neutrality to the reaction system and shields it from stray electric fields. Heating of the ions by uncontrolled acceleration through stray fields is thus avoided.

This opens up the prospect of studying ion-neutral reactions at very low temperatures. Instead of observing the reaction $A^+ + B \rightarrow C^+$ (or $C^+ + D$), one observes the reaction $A^* + B \rightarrow C^*$ (or $C^* + D$), where * symbolizes a high Rydberg state. In the limit where the Rydberg electron acts as a spectator, both reactions take place at the same rate [12]. This idea has recently been used to study the $H_2^+ + H_2 \rightarrow H_3^+ + H$ reaction [13] and the radiative association reaction $H^+ + H \rightarrow H_2^+ + h\nu$ [14] at temperatures where quantum-mechanical effects strongly affect the reaction rates (figure 2).
# RYDBERG ATOMS AND COLD COLLISIONS

## 1. High Rydberg states and ion chemistry

Frédéric Merkt

ETH Zurich, Switzerland; Free University of Amsterdam, The Netherlands

Status. This contribution focuses on the use of high Rydberg states of neutral molecular systems to characterize the structure, dynamics and reactivity of molecular cations. Rydberg states can be defined as the states of atoms and molecules having spectral positions $v_n$ that can be approximated by Rydberg's formula

$$v_n = E_1(\alpha^+) / h - cR_M / (n - d_l)^2. \quad (1)$$

In equation (1), $n$ is the principal quantum number, $\delta_l$ is the quantum defect of the series with electron orbital-angular-momentum quantum number $l$, $R_M$ is the mass-dependent Rydberg constant, $E_l(\alpha^+)$ represents the series limit as $n$ approaches infinity and thus the onset of the ionization continuum associated with the production of a singly charged ion in the quantum state $\alpha^+$ (see figure 1(a)). Equation (1) implies independent, separable motions of the Rydberg electron and the ion core and becomes increasingly accurate as $n$ and $l$ increase. Most properties of Rydberg states rapidly scale with $n$. For instance, their polarizability scales as $n^7$, their electric dipole moment scales as $n^2$, and the minimal electric field needed for their efficient ionization scales as $n^{-4}$ (see [1]).

Rydberg states form series that converge on the different electronic, and in the case of molecules also vibrational ($v^+$) and rotational ($N^+$), quantum states of the molecular ion core (see figure 1(a)). At high $n$ values, the Rydberg electron does not influence the ion core but maintains the charge neutrality of the molecular system. The use of Rydberg states to characterize positively charged ions relies on these properties. The measurement of Rydberg series and their extrapolation yield the energy-level structure of cations [2]. The energy-level structure of cations can also be obtained by the selective pulsed field ionization (PFI) of very high Rydberg states, as illustrated in figure 1(c). With their large dipole moments (beyond 1500 Debye at $n = 25$) Rydberg atoms and molecules can easily be accelerated in inhomogeneous electric fields, and numerous devices have been developed that enable the deceleration, the deflection and the reflection of beams of Rydberg atoms and molecules, and the storage of cold Rydberg atoms and molecules in electric traps [3]. These devices have considerable potential for studies of ion-molecule reactions at low temperatures.

### Current and future challenges

Precision measurements of ionization energies and ionic level structures by Rydberg series extrapolation. High-resolution spectra of high-$n$ Rydberg states can be used to determine the series limits, and thus the ionization energies of atoms and molecules with high precision. In atomic systems with a closed-shell ion core (Li, Na, K), the extrapolation can be performed

with equation (1). Using ultracold atomic samples to suppress Doppler and transit-time broadening in combination with photoexcitation with frequency-comb-stabilized single-mode continuous-wave lasers, the ionization energy of Cs [5] was determined to be $E_l(hc) = 31\ 406.467\ 7325(14)\ \text{cm}^{-1}$. To reach this level of accuracy, it is necessary to measure and compensate stray electric and magnetic fields to better than 1 mV cm$^{-1}$ and 1 mG, respectively. Pressure shifts and shifts arising from dipole-dipole interactions with neighboring Rydberg atoms must also be quantified. The extrapolation of Rydberg series in atoms with open-shell ion cores and in molecules necessitates the consideration of interactions between series converging on different ionic states. The most reliable extrapolations are not carried out with equation (1) but using multichannel quantum defect theory (MQDT) [6, 7], which can even be used to determine the hyperfine structure of the cations [8].

Molecular hydrogen has been the test system for the application of MQDT to molecules [7]. The MQDT analysis of recent measurements of the Rydberg spectrum of $H_2$ has allowed its ionization and dissociation energies, and rotational and hyperfine intervals in $H_2^+$ [8, 9], to be determined with high accuracy. The most accurate measurements of Rydberg series in $H_2$ reach an accuracy of 65 kHz [10] and are precise enough to be sensitive to the finite size of the proton [11].

Future steps in precision Rydberg spectroscopy for the determination of accurate ionization energies include (i) the development of methods and light sources to record high-resolution Rydberg spectra of a broader range of molecules, (ii) the generation of corresponding cold-molecule samples, and (iii) a rigorous establishment of the uncertainties of the Rydberg-series limits extrapolated by MQDT. In future, MQDT-assisted Rydberg spectroscopy of cations is expected to contribute not only to solve problems of molecular structure and dynamics. When applied to few-electron systems, precision Rydberg spectroscopy may also contribute to test theory at its most fundamental level, improve fundamental constants or discover new effects.

Ion-neutral reactions within the orbit of a Rydberg electron. At sufficiently high $n$ values, the ion-core can undergo chemical reactions with neutral molecules located within the Rydberg-electron orbit. The Rydberg electron does not affect the reaction but provides charge neutrality to the reaction system and shields it from stray electric fields. Heating of the ions by uncontrolled acceleration through stray fields is thus avoided.

This opens up the prospect of studying ion-neutral reactions at very low temperatures. Instead of observing the reaction $A^+ + B \rightarrow C^+$ (or $C^+ + D$), one observes the reaction $A^* + B \rightarrow C^*$ (or $C^* + D$), where * symbolizes a high Rydberg state. In the limit where the Rydberg electron acts as a spectator, both reactions take place at the same rate [12]. This idea has recently been used to study the $H_2^+ + H_2 \rightarrow H_3^+ + H$ reaction [13] and the radiative association reaction $H^+ + H \rightarrow H_2^+ + h\nu$ [14] at temperatures where quantum-mechanical effects strongly affect the reaction rates (figure 2).
<figure><img src="image_4.png" /><figcaption>Figure 1. (a) Rydberg series converging on the different rovibrational levels (red) of a molecular ion. (b) Rydberg spectrum and (c) PFI spectrum of Ar near the $^2P_{3/2}$ ionization threshold (red bar) (from [4]). (d) Schematic representation of a molecular Rydberg state consisting of an ion core $M^+$ surrounded by the orbit of a distant Rydberg electron.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 2. (a) Cross sections of the $H^+$ + H (green) and $D^+$ + D (red and blue) radiative association reactions for approach on potentials of the ground ($X^+$) and first excited ($A^+$) states (from [13]). (b) Cross section and relative rate coefficient of the $H_2^+ + H_2 \rightarrow H_3^+ + H$ reaction. Black dots [15]; green dashed line [16]; black dashed line (Langevin behavior). Colored dots: merged-beam results from [14].</figcaption></figure>

In the study of the $H_2^+ + H_2 \rightarrow H_3^+ + H$ reaction, a chip-based Rydberg-Stark deflector and decelerator [13] was used to merge a beam of cold, velocity- and state-selected Rydberg $H_2$ molecules with a supersonic beam of cold ground-state $H_2$ molecules and to vary their relative velocity. In this way, the energy dependence of the reaction cross section could be measured at collision energies as low as $k_B \times 300$ mK, where deviations from classical Langevin behavior were observed [13] (Inset of figure 2(b)).

The $H^+ + H \rightarrow H_2^+ + h\nu$ reaction was studied following excitation of $H_2$ to high ($n \ ? \ 200$) Rydberg states near the dissociative ionization threshold of $H_2$ in a half-collision approach [14]. By observing the shape resonances of $H_2^+$ and analyzing their role in the dissociation of the $H_2^+$ ion core, the radiative association cross section and rate coefficient could be determined in the collision-energy range between 10 mK and $10^5$ K [14] (figure 2(a)).

**Concluding remark.** Progress in the development of tunable narrow-band light sources, of frequency-calibration methods, of cold-molecule preparation techniques and of new devices to manipulate the translational motion of Rydberg atoms and molecules are currently opening new perspectives for investigations of ions, with applications ranging from metrology to cold ion-neutral chemistry.

## Acknowledgments

Our research is supported by the Swiss National Science Foundation (Project 200020-172620) and the European Research Council (ERC) (Advanced Grant 743121). FM thanks the Free University of Amsterdam for a van der Waals visiting professorship.
<figure><img src="image_5.png" /><figcaption>Figure 1. (a) Rydberg series converging on the different rovibrational levels (red) of a molecular ion. (b) Rydberg spectrum and (c) PFI spectrum of Ar near the $^2P_{3/2}$ ionization threshold (red bar) (from [4]). (d) Schematic representation of a molecular Rydberg state consisting of an ion core $M^+$ surrounded by the orbit of a distant Rydberg electron.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 2. (a) Cross sections of the $H^+$ + H (green) and $D^+$ + D (red and blue) radiative association reactions for approach on potentials of the ground ($X^+$) and first excited ($A^+$) states (from [13]). (b) Cross section and relative rate coefficient of the $H_2^+ + H_2 \rightarrow H_3^+ + H$ reaction. Black dots [15]; green dashed line</figcaption></figure>

[16]; black dashed line (Langevin behavior). Colored dots: merged-beam results from [14].

In the study of the $H_2^+ + H_2 \rightarrow H_3^+ + H$ reaction, a chip-based Rydberg-Stark deflector and decelerator [13] was used to merge a beam of cold, velocity- and state-selected Rydberg $H_2$ molecules with a supersonic beam of cold ground-state $H_2$ molecules and to vary their relative velocity. In this way, the energy dependence of the reaction cross section could be measured at collision energies as low as $k_B \times 300$ mK, where deviations from classical Langevin behavior were observed [13] (Inset of figure 2(b)).

The $H^+ + H \rightarrow H_2^+ + h\nu$ reaction was studied following excitation of $H_2$ to high ($n \ ? \ 200$) Rydberg states near the dissociative ionization threshold of $H_2$ in a half-collision approach [14]. By observing the shape resonances of $H_2^+$ and analyzing their role in the dissociation of the $H_2^+$ ion core, the radiative association cross section and rate coefficient could be determined in the collision-energy range between 10 mK and $10^5$ K [14] (figure 2(a)).

**Concluding remark.** Progress in the development of tunable narrow-band light sources, of frequency-calibration methods, of cold-molecule preparation techniques and of new devices to manipulate the translational motion of Rydberg atoms and molecules are currently opening new perspectives for investigations of ions, with applications ranging from metrology to cold ion-neutral chemistry.

## Acknowledgments

Our research is supported by the Swiss National Science Foundation (Project 200020-172620) and the European Research Council (ERC) (Advanced Grant 743121). FM thanks the Free University of Amsterdam for a van der Waals visiting professorship.
## 2. Resonant energy transfer with Rydberg atoms

T F Gallagher

University of Virginia, United States of America

**Status.** The study of dipole-dipole interactions of Rydberg atoms began as an effort to explore systematically resonant energy transfer. A classic example of resonant energy transfer is the HeNe laser, which is based on resonant collisional energy transfer from the metastable 2s states of He to the ground state of Ne, resulting in the selective population of the upper laser levels of the HeNe laser [17]. While the HeNe laser works, it does not tell us much about the sharpness of the resonance, only that the match between the He and Ne energy levels is close enough.

One approach to probing resonance in collisional energy transfer is examining fine structure changing collisions of Br with different molecular collision particles. The different frequencies of the molecular vibrational transitions straddle the Br $5p_{1/2} \rightarrow 5p_{3/2}$ interval and provide a measure of tunability [18]. Rydberg atoms, with their $1/n^3$ scaling of energy levels, provide a more systematic approach. Here n is the principal quantum number of Rydberg atom. A series of experiments with Xe Rydberg atoms and polar molecules, such as $NH_3$, showed sharp collisional resonances in which the changes in the binding energy of the Rydberg electron matched the frequencies of rotational transitions of the molecule [19]. In these collisions the impact parameters are approximately equal to the diameter of the Rydberg atom or smaller, so the interaction responsible is not simply the dipole-dipole interaction; several multipoles are involved.

An ideal way to probe a collisional resonance is to tune continuously the energy of the collision partners through resonance, and the enormous Stark shifts of Rydberg atoms provide a simple way to do so. Perhaps the most well studied example is the resonant energy transfer between two Rydberg atoms, for example the process [20]

$$Na \ 16s + Na \ 16s \square Na \ 16p + Na \ 15p, \quad (2)$$

which is tuned into resonance in fields of $E \sim 600$ V cm$^{-1}$. In most cases static fields have been used, but the AC Stark shifts from a near resonant microwave field provide a way to alter only a few states with the field [21]. The process of equation (2), observed with a thermal atomic beam, yields sharp collisional resonances with widths of $\sim 1$ GHz and cross sections of $\sigma \sim 10^9$ A$^2$. The resonance widths imply that the duration, or time, of the collisions is $\tau = 1$ ns, and the cross sections imply impact parameters one hundred times larger than the size of the atoms. The energy transfer is due to the dipole-dipole interaction, and it is straightforward to show that for the process

$$Na \ ns + Na \ ns \square Na \ np + Na \ (n-1)p \quad (3)$$

the cross section $\sigma$ and duration $\tau$ are given, in atomic units, by

$$s = n^4/v \quad (4)$$

and

$$t = n^2/v^{3/2}, \quad (5)$$

where $v$ is the collision velocity. Compared to gas kinetic collision times of one picosecond, one nanosecond collision times are extremely long, allowing systematic study of radiative collisions, those in which photons are absorbed or emitted during the collisions [22]. Collisions in which multiple microwave photons are emitted and absorbed have been observed and characterized [23].

The experiments described above were conducted with thermal beams in which the collision velocity is determined by the velocity spread of the beam. Velocity selection has been used to produce beams with internal temperatures of 1 K, leading to collisional resonances as narrow as 1 MHz [24], and shortening the time during which the atoms can collide to less than one microsecond produces transform limited collisions, with known beginning and ending times [24].

The first cold atom experiments, conducted in magneto optical traps (MOTs), were also resonant energy transfer experiments, often termed Forster resonances [25, 26]. The properties of a MOT, temperature $T = 300$ µK and density $\rho = 10^9$ cm$^{-3}$, combined with the 3 µs lifetime of an $n = 20$ Rydberg atom bring the experiments into a new regime. In a MOT the typical atomic spacings and velocities are $10^{-3}$ cm and $10$ cm s$^{-1}$, so in the one microsecond duration of a typical experiment the atoms move $\sim 1\%$ of their typical spacing. In short, they are frozen in place. The atoms do not collide; instead, the interactions are between static atoms, as in an amorphous solid. In the initial experiments energy transfer resonances many MHz wide were observed. For example, the process [26]

$$Cs \ 23p + Cs \ 23p \square Cs \ 24s + Cs \ 23s \quad (6)$$

has a width of 80 MHz. The dominant interaction is still the dipole-dipole interaction, and the observed widths of the energy transfer resonances, such as equation (6), are primarily due to pairs of atoms which are close together. However, unlike collisions, other atoms play a role. For example, the diffusive processes

$$Cs \ 23p + Cs \ 23s \square Cs \ 23s + Cs \ 23p \quad (7)$$

and

$$Cs \ 23p + Cs \ 24s \square Cs \ 24s + Cs \ 23p \quad (8)$$

also contribute to the widths. In addition to changing energy transfer from a binary to a many body problem, the use of cold atoms allows the Forster resonances to be examined by coherent laser spectroscopy, specifically, Ramsey interferometry [27].

The enormous range of the dipole-dipole interaction between Rydberg atoms has led to proposals for their use in a broad spectrum of applications, from quantum gates and simulators to the construction of ultralong range molecules [29, 30]. One of the gate notions, the dipole blockade, has proven to be widely applicable [28]. In the blockade the strong dipole-dipole or van der Waals (off resonant dipole-dipole) interaction prevents the excitation of more than one
## 2. Resonant energy transfer with Rydberg atoms

T F Gallagher

University of Virginia, United States of America

**Status.** The study of dipole-dipole interactions of Rydberg atoms began as an effort to explore systematically resonant energy transfer. A classic example of resonant energy transfer is the HeNe laser, which is based on resonant collisional energy transfer from the metastable 2s states of He to the ground state of Ne, resulting in the selective population of the upper laser levels of the HeNe laser [17]. While the HeNe laser works, it does not tell us much about the sharpness of the resonance, only that the match between the He and Ne energy levels is close enough.

One approach to probing resonance in collisional energy transfer is examining fine structure changing collisions of Br with different molecular collision particles. The different frequencies of the molecular vibrational transitions straddle the $Br\ 5p_{1/2} \rightarrow 5p_{3/2}$ interval and provide a measure of tunability [18]. Rydberg atoms, with their $1/n^3$ scaling of energy levels, provide a more systematic approach. Here n is the principal quantum number of Rydberg atom. A series of experiments with Xe Rydberg atoms and polar molecules, such as $NH_3$, showed sharp collisional resonances in which the changes in the binding energy of the Rydberg electron matched the frequencies of rotational transitions of the molecule [19]. In these collisions the impact parameters are approximately equal to the diameter of the Rydberg atom or smaller, so the interaction responsible is not simply the dipole-dipole interaction; several multipoles are involved.

An ideal way to probe a collisional resonance is to tune continuously the energy of the collision partners through resonance, and the enormous Stark shifts of Rydberg atoms provide a simple way to do so. Perhaps the most well studied example is the resonant energy transfer between two Rydberg atoms, for example the process [20]

$$Na\ 16s + Na\ 16s \Box Na\ 16p + Na\ 15p, \quad (2)$$

which is tuned into resonance in fields of $E \sim 600$ V cm$^{-1}$. In most cases static fields have been used, but the AC Stark shifts from a near resonant microwave field provide a way to alter only a few states with the field [21]. The process of equation (2), observed with a thermal atomic beam, yields sharp collisional resonances with widths of $\sim 1$ GHz and cross sections of $\sigma \sim 10^9$ A$^2$. The resonance widths imply that the duration, or time, of the collisions is $\tau = 1$ ns, and the cross sections imply impact parameters one hundred times larger than the size of the atoms. The energy transfer is due to the dipole-dipole interaction, and it is straightforward to show that for the process

$$Na\ ns + Na\ ns \Box Na\ np + Na\ (n-1)p \quad (3)$$

the cross section $\sigma$ and duration $\tau$ are given, in atomic units, by

$$s = n^4/v \quad (4)$$

and

$$t = n^2/v^{3/2}, \quad (5)$$

where $v$ is the collision velocity. Compared to gas kinetic collision times of one picosecond, one nanosecond collision times are extremely long, allowing systematic study of radiative collisions, those in which photons are absorbed or emitted during the collisions [22]. Collisions in which multiple microwave photons are emitted and absorbed have been observed and characterized [23].

The experiments described above were conducted with thermal beams in which the collision velocity is determined by the velocity spread of the beam. Velocity selection has been used to produce beams with internal temperatures of 1 K, leading to collisional resonances as narrow as 1 MHz [24], and shortening the time during which the atoms can collide to less than one microsecond produces transform limited collisions, with known beginning and ending times [24].

The first cold atom experiments, conducted in magneto optical traps (MOTs), were also resonant energy transfer experiments, often termed Forster resonances [25, 26]. The properties of a MOT, temperature $T = 300$ µK and density $\rho = 10^9$ cm$^{-3}$, combined with the 3 µs lifetime of an $n = 20$ Rydberg atom bring the experiments into a new regime. In a MOT the typical atomic spacings and velocities are $10^{-3}$ cm and $10$ cm s$^{-1}$, so in the one microsecond duration of a typical experiment the atoms move $\sim 1\%$ of their typical spacing. In short, they are frozen in place. The atoms do not collide; instead, the interactions are between static atoms, as in an amorphous solid. In the initial experiments energy transfer resonances many MHz wide were observed. For example, the process [26]

$$Cs\ 23p + Cs\ 23p \Box Cs\ 24s + Cs\ 23s \quad (6)$$

has a width of 80 MHz. The dominant interaction is still the dipole-dipole interaction, and the observed widths of the energy transfer resonances, such as equation (6), are primarily due to pairs of atoms which are close together. However, unlike collisions, other atoms play a role. For example, the diffusive processes

$$Cs\ 23p + Cs\ 23s \Box Cs\ 23s + Cs\ 23p \quad (7)$$

and

$$Cs\ 23p + Cs\ 24s \Box Cs\ 24s + Cs\ 23p \quad (8)$$

also contribute to the widths. In addition to changing energy transfer from a binary to a many body problem, the use of cold atoms allows the Forster resonances to be examined by coherent laser spectroscopy, specifically, Ramsey interferometry [27].

The enormous range of the dipole-dipole interaction between Rydberg atoms has led to proposals for their use in a broad spectrum of applications, from quantum gates and simulators to the construction of ultralong range molecules [29, 30]. One of the gate notions, the dipole blockade, has proven to be widely applicable [28]. In the blockade the strong dipole-dipole or van der Waals (off resonant dipole-dipole) interaction prevents the excitation of more than one
Rydberg atom in a blockade radius, forming a superatom in each blockade zone in which one of the many atoms is in the Rydberg state, the rest remaining in the ground state. Superatoms behave like two level systems and multiple superatoms in a sample can be observed to self organize into regular patterns [30].

While the first cold Rydberg atom experiments resembled an amorphous solid, it is possible to put Rydberg atoms into well defined arrays. The first such arrays were linear chains of three atoms, in which the excitation was observed to travel back and forth along the chain [31]. Much longer linear chains have been constructed and used to simulate many body phenomena under controllable conditions [32, 33].

**Concluding remarks.** Finally, methods of placing atoms in well defined positions in two dimensional arrays have been developed, and these arrays have been used to compare thermalization in striaght (linear) and zig zag chains [34]. In the latter each atom has four, not two, nearest neighbors. The combination of the rapid advance in the ability to manipulate atoms combined with the enormous dipole-dipole interactions of Rydberg atoms suggest that there will be a continuing stream of fascinating discoveries.

Acknowledgment

This work has been supported by the Air Force Office of
Scientific Research under grant FA9550-14-1-0288.
Rydberg atom in a blockade radius, forming a superatom in each blockade zone in which one of the many atoms is in the Rydberg state, the rest remaining in the ground state. Superatoms behave like two level systems and multiple superatoms in a sample can be observed to self organize into regular patterns [30].

While the first cold Rydberg atom experiments resembled an amorphous solid, it is possible to put Rydberg atoms into well defined arrays. The first such arrays were linear chains of three atoms, in which the excitation was observed to travel back and forth along the chain [31]. Much longer linear chains have been constructed and used to simulate many body phenomena under controllable conditions [32, 33].

*Concluding remarks.* Finally, methods of placing atoms in well defined positions in two dimensional arrays have been developed, and these arrays have been used to compare thermalization in striaght (linear) and zig zag chains [34]. In the latter each atom has four, not two, nearest neighbors. The combination of the rapid advance in the ability to manipulate atoms combined with the enormous dipole-dipole interactions of Rydberg atoms suggest that there will be a continuing stream of fascinating discoveries.

Acknowledgment

This work has been supported by the Air Force Office of
Scientific Research under grant FA9550-14-1-0288.
### 3. Studies involving high-n Rydberg atoms

F Barry Dunning

Rice University, United States of America

**Status.** High-*n* Rydberg atoms possess physical characteristics quite unlike those associated with atoms in ground or low-lying excited states. They are physically very large allowing many of their properties to be discussed using the classical Bohr model of the atom. At high *n* the excited electron orbits far from the nucleus and its motion can be strongly perturbed by application of even modest external electric fields. In addition, as *n* increases the classical electron orbital period, *T*<sub>p</sub>, (~4 ns at *n* ~ 300) increases rapidly allowing high-*n* states to be manipulated (and probed) using conventional fast pulse electronics and carefully-tailored series of electric field pulses whose characteristic times (duration and/or rise/fall times) are less than *T*<sub>p</sub> [35]. Such pulse series have been used to engineer quasi-one- and two-dimensional Rydberg states and, with periodic driving, to create non-dispersive wave packets whose behavior mimics that of classical particles [36, 37]. This work has enabled ongoing studies of strongly-interacting Rydberg systems and of the production of so-called planetary atoms.

Scattering of the Rydberg electron from neighboring ground-state atoms can lead to formation of ultralong-range Rydberg molecules [38]. Such scattering can be described using a Fermi pseudopotential and results in a molecular potential that can (see inset in figure 3) support multiple vibrational levels with binding energies (typically) of a few to a few tenths of a megahertz. At sufficiently high atom densities multiple ground-state atoms can be bound to a single Rydberg atom allowing formation of not only dimers but also trimers, tetramers, (see figure 3). In a dense Bose-Einstein condensate (BEC) the Rydberg orbit can, for *n* ? 50, enclose tens to hundreds of ground-state atoms [39]. Rydberg excitation introduces an 'impurity' into the BEC and elicits a collective response resulting in the formation of polaron-like quasiparticles comprising the impurity dressed by excitations of the background BEC [40]. Rydberg molecule production provides new opportunities for the study of particle correlations and the effects of quantum statistics.

#### Future directions and challenges

**Dynamics of strongly-coupled Rydberg systems.** Long-range interactions in many-body systems give rise to a rich variety of phenomena of fundamental importance to many areas of physics. Rydberg atoms offer advantages for the study of strongly-coupled systems because their extreme dipole moments result in strong long-range interactions whose strength can be simply controlled by manipulating the atomic states. Recent experiments show that single very-high-*n*, *n* ~ 300, Rydberg atoms can be prepared in well-defined locally-blockaded regions [41] which provides a convenient starting point for future detailed study of strongly-interacting Rydberg systems. If two atoms are prepared in reasonably-well-separated blockaded regions, a tailored series

<figure><img src="image_6.png" /><figcaption>Figure 3. Rydberg excitation spectrum in the vicinity of the 5s38s $^3$S$_1$ strontium Rydberg state. Inset—calculated molecular potential for 5s38s $^3$S$_1$–5s$^2$ $^1$S$_0$ atom pair. Wavefunctions $R_c(R)$ for the $v=0, j=1$, and 2 molecular vibrational states are included.</figcaption></figure>

of short electric field pulses may be used to increase their mutual interactions by exciting them to states of much higher *n*, the degree of coupling being tuned by varying the final target state (and initial interatomic spacing). Given that the two atoms are excited simultaneously by the same electric field pulses, the initial conditions are particularly well-defined. Questions of interest relate to the dynamics of energy interchange and its dependence on the degree of coupling, which might be further controlled by varying the relative orientations of the states involved. For example, pairs of quasi-one-dimensional states may be formed that are oriented parallel or perpendicular to their line of centers. Excitation to Rydberg orbits whose size is comparable to the interatomic spacing leads to formation of transient Rydberg 'molecules' whose stability against autoionization through electron-electron scattering can be examined. Since the excited electron motions can be locked to an external periodic drive field [37, 38], long-lived configurations might exist where, due to their correlated motions, the electrons remain far apart. Initial experiments have been undertaken in an atomic beam but relative motions associated with the distribution of atomic velocities in the beam limit the time over which measurements of Rydberg-Rydberg interactions can be undertaken. Use of cold atomic gases can overcome this limitation but the optical access required for cold atom trapping presents a challenge in reducing the stray fields present in the trapping volume to the levels required, ?50 µV cm⁻¹, for study of very-high-*n* states. To date, Rydberg studies in cold atom traps have been limited to atoms with values of *n* ? 200 [39]. Nonetheless, if stray fields can be controlled successfully, use of a 'pancake-shaped' trap and multiple blockaded regions would make possible detailed studies of interactions involving two, three, or more Rydberg atoms and their dependence on the geometrical arrangement of the atoms.
### 3. Studies involving high-*n* Rydberg atoms

F Barry Dunning

Rice University, United States of America

**Status.** High-*n* Rydberg atoms possess physical characteristics quite unlike those associated with atoms in ground or low-lying excited states. They are physically very large allowing many of their properties to be discussed using the classical Bohr model of the atom. At high *n* the excited electron orbits far from the nucleus and its motion can be strongly perturbed by application of even modest external electric fields. In addition, as *n* increases the classical electron orbital period, $T_p$, (~4 ns at *n* ~ 300) increases rapidly allowing high-*n* states to be manipulated (and probed) using conventional fast pulse electronics and carefully-tailored series of electric field pulses whose characteristic times (duration and/or rise/fall times) are less than $T_p$ [35]. Such pulse series have been used to engineer quasi-one- and two-dimensional Rydberg states and, with periodic driving, to create non-dispersive wave packets whose behavior mimics that of classical particles [36, 37]. This work has enabled ongoing studies of strongly-interacting Rydberg systems and of the production of so-called planetary atoms.

Scattering of the Rydberg electron from neighboring ground-state atoms can lead to formation of ultralong-range Rydberg molecules [38]. Such scattering can be described using a Fermi pseudopotential and results in a molecular potential that can (see inset in figure 3) support multiple vibrational levels with binding energies (typically) of a few to a few tenths of a megahertz. At sufficiently high atom densities multiple ground-state atoms can be bound to a single Rydberg atom allowing formation of not only dimers but also trimers, tetramers, (see figure 3). In a dense Bose-Einstein condensate (BEC) the Rydberg orbit can, for *n* ? 50, enclose tens to hundreds of ground-state atoms [39]. Rydberg excitation introduces an 'impurity' into the BEC and elicits a collective response resulting in the formation of polaron-like quasiparticles comprising the impurity dressed by excitations of the background BEC [40]. Rydberg molecule production provides new opportunities for the study of particle correlations and the effects of quantum statistics.

#### Future directions and challenges

**Dynamics of strongly-coupled Rydberg systems.** Long-range interactions in many-body systems give rise to a rich variety of phenomena of fundamental importance to many areas of physics. Rydberg atoms offer advantages for the study of strongly-coupled systems because their extreme dipole moments result in strong long-range interactions whose strength can be simply controlled by manipulating the atomic states. Recent experiments show that single very-high-*n*, *n* ~ 300, Rydberg atoms can be prepared in well-defined locally-blockaded regions [41] which provides a convenient starting point for future detailed study of strongly-interacting Rydberg systems. If two atoms are prepared in reasonably-well-separated blockaded regions, a tailored series

<figure><img src="image_7.png" /><figcaption>Figure 3. Rydberg excitation spectrum in the vicinity of the 5s38s $^3$S$_1$ strontium Rydberg state. Inset—calculated molecular potential for 5s38s $^3$S$_1$–5s$^2$ $^1$S$_0$ atom pair. Wavefunctions $R_c(R)$ for the $v=0, j=1$, and 2 molecular vibrational states are included.</figcaption></figure>

of short electric field pulses may be used to increase their mutual interactions by exciting them to states of much higher *n*, the degree of coupling being tuned by varying the final target state (and initial interatomic spacing). Given that the two atoms are excited simultaneously by the same electric field pulses, the initial conditions are particularly well-defined. Questions of interest relate to the dynamics of energy interchange and its dependence on the degree of coupling, which might be further controlled by varying the relative orientations of the states involved. For example, pairs of quasi-one-dimensional states may be formed that are oriented parallel or perpendicular to their line of centers. Excitation to Rydberg orbits whose size is comparable to the interatomic spacing leads to formation of transient Rydberg 'molecules' whose stability against autoionization through electron-electron scattering can be examined. Since the excited electron motions can be locked to an external periodic drive field [37, 38], long-lived configurations might exist where, due to their correlated motions, the electrons remain far apart. Initial experiments have been undertaken in an atomic beam but relative motions associated with the distribution of atomic velocities in the beam limit the time over which measurements of Rydberg-Rydberg interactions can be undertaken. Use of cold atomic gases can overcome this limitation but the optical access required for cold atom trapping presents a challenge in reducing the stray fields present in the trapping volume to the levels required, ?50 µV cm⁻¹, for study of very-high-*n* states. To date, Rydberg studies in cold atom traps have been limited to atoms with values of *n* ? 200 [39]. Nonetheless, if stray fields can be controlled successfully, use of a 'pancake-shaped' trap and multiple blockaded regions would make possible detailed studies of interactions involving two, three, or more Rydberg atoms and their dependence on the geometrical arrangement of the atoms.
**Two-electron excited states.** Interest in two-electron excited states stems from early attempts to quantize many-electron systems using the Bohr-Sommerfeld quantization rules which met with little success due to the dynamical instability of the proposed structures. Early studies of two-electron-excited states focused on Group II elements and were limited by the dipole selection rules to states of low *L* which undergo rapid autoionization. However, it is now possible to engineer very-high-*n*, *n* ~ *ℓ*, near-circular states for which the overlap between the excited Rydberg electron and inner core electrons is negligible, even if one of the inner core electrons is itself in a (lower-lying) excited state. The production of two-electron excited states in which both electrons remain far from the core ion and from each other in near classical orbits reduces the autoionization rate and admits the possibility of creating long-lived so-called 'planetary atoms' [42]. One possible strategy for the production of such atoms involves creation of a localized very-high-*n*, *n* ~ 600, wavepacket traveling in a near-circular Bohr-like orbit followed by excitation of a second 'inner' electron to a state of lower *n*, *n* ~ 200. The 'outer' electron as it rotates polarizes the orbit of the 'inner' electron creating a dipole that rotates in step with the 'outer' electron and whose field preserves the localization of the 'outer' electron. Classical trajectory calculations suggest that such correlated motion can result in long-term stability against autoionization. Initial experiments show that autoionization rates are dramatically reduced when the 'outer' electron is in a high-*ℓ* state to the point that the lifetime of the two-electron-excited state is governed by radiative decay of the 'inner' electron [43]. However, in these experiments, undertaken in strontium, the 'inner' electron was only excited to the 5p state and multiple additional lasers will be required to excite it to high-*n* states. Simulations suggest the existence of a second long-lived two-electron-excited state, termed the frozen planet configuration, which embodies very different electron dynamics and which should also be amenable to study using carefully-engineered high-*n* Rydberg atoms [42].

**Ultralong-range Rydberg molecules.** Correlations in atomic gases become difficult to observe when their characteristic length scales fall below the wavelength of light. However, ultralong-range Rydberg molecules promise a means to investigate such correlations in this previously inaccessible regime. The wavefunction for the molecular ground vibrational state is strongly localized near the outermost well in the molecular potential (see figure 3). The probability of creating a ground-state dimer molecule therefore depends strongly on the likelihood of finding a pair of atoms with the appropriate separation. Thus measurements of dimer formation as a function of *n*, i.e. the position of the outermost potential well, can provide information on finding

<figure><img src="image_7.png" /><figcaption>Figure 4. Pair correlation functions $g^{(2)}(R)$ versus interparticle separation normalized to the deBroglie wavelength $\lambda_{dB}$.</figcaption></figure>

atom pairs with different separations and hence on the pair correlation function, $g^{(2)}(R)$. Values of $g^{(2)}(R)$ for thermal gases of non-interacting identical bosons, fermions, and non-identical (or classical) particles are presented in figure 4 and diverge markedly for interparticle separations, $R$, less than the thermal de Broglie wavelength, $\lambda_{dB}$. For $T \sim 900$ nK, $\lambda_{dB} \sim 200$ nm which corresponds to the radius of an *n* ~ 45 s state suggesting that measurements of dimer formation over the interval 30 ? *n* ? 45 can be used to probe the effects of quantum statistics on $g^{(2)}(R)$ for $R < \lambda_{dB}$. $^{87}$Sr which has a nuclear spin *I* = 9/2 is attractive for such studies and can be conveniently optically pumped to the $m_F = 9/2$ state to obtain a gas of identical fermions. Since the dimer formation rate depends not only on the number of ground-state atoms present but also their spatial distribution, i.e. density, a major challenge will be to account for such factors in analysis of the data. Dimer formation might also be used to examine two-atom correlations that arise in a quantum gas from resonant atom-atom scattering.

**Concluding remarks.** Although Rydberg atoms have been studied for many years, new applications continue to emerge that address important physical questions related to few- and many-body interactions.

## Acknowledgments

Research by the author and his colleagues discussed here was supported by the AFOSR, the NSF, and the Robert A Welch Foundation (Grant # C-0734).
**Two-electron excited states.** Interest in two-electron excited states stems from early attempts to quantize many-electron systems using the Bohr-Sommerfeld quantization rules which met with little success due to the dynamical instability of the proposed structures. Early studies of two-electron-excited states focused on Group II elements and were limited by the dipole selection rules to states of low *L* which undergo rapid autoionization. However, it is now possible to engineer very-high-*n*, *n* ~ *ℓ*, near-circular states for which the overlap between the excited Rydberg electron and inner core electrons is negligible, even if one of the inner core electrons is itself in a (lower-lying) excited state. The production of two-electron excited states in which both electrons remain far from the core ion and from each other in near classical orbits reduces the autoionization rate and admits the possibility of creating long-lived so-called 'planetary atoms' [42]. One possible strategy for the production of such atoms involves creation of a localized very-high-*n*, *n* ~ 600, wavepacket traveling in a near-circular Bohr-like orbit followed by excitation of a second 'inner' electron to a state of lower *n*, *n* ~ 200. The 'outer' electron as it rotates polarizes the orbit of the 'inner' electron creating a dipole that rotates in step with the 'outer' electron and whose field preserves the localization of the 'outer' electron. Classical trajectory calculations suggest that such correlated motion can result in long-term stability against autoionization. Initial experiments show that autoionization rates are dramatically reduced when the 'outer' electron is in a high-*ℓ* state to the point that the lifetime of the two-electron-excited state is governed by radiative decay of the 'inner' electron [43]. However, in these experiments, undertaken in strontium, the 'inner' electron was only excited to the 5p state and multiple additional lasers will be required to excite it to high-*n* states. Simulations suggest the existence of a second long-lived two-electron-excited state, termed the frozen planet configuration, which embodies very different electron dynamics and which should also be amenable to study using carefully-engineered high-*n* Rydberg atoms [42].

**Ultralong-range Rydberg molecules.** Correlations in atomic gases become difficult to observe when their characteristic length scales fall below the wavelength of light. However, ultralong-range Rydberg molecules promise a means to investigate such correlations in this previously inaccessible regime. The wavefunction for the molecular ground vibrational state is strongly localized near the outermost well in the molecular potential (see figure 3). The probability of creating a ground-state dimer molecule therefore depends strongly on the likelihood of finding a pair of atoms with the appropriate separation. Thus measurements of dimer formation as a function of *n*, i.e. the position of the outermost potential well, can provide information on finding

<figure><img src="image_8.png" /><figcaption>Figure 4. Pair correlation functions $g^{(2)}(R)$ versus interparticle separation normalized to the deBroglie wavelength $\lambda_{dB}$.</figcaption></figure>

atom pairs with different separations and hence on the pair correlation function, $g^{(2)}(R)$. Values of $g^{(2)}(R)$ for thermal gases of non-interacting identical bosons, fermions, and non-identical (or classical) particles are presented in figure 4 and diverge markedly for interparticle separations, $R$, less than the thermal de Broglie wavelength, $\lambda_{dB}$. For $T \sim 900$ nK, $\lambda_{dB} \sim 200$ nm which corresponds to the radius of an *n* ~ 45 s state suggesting that measurements of dimer formation over the interval 30 ? *n* ? 45 can be used to probe the effects of quantum statistics on $g^{(2)}(R)$ for $R < \lambda_{dB}$. $^{87}$Sr which has a nuclear spin *I* = 9/2 is attractive for such studies and can be conveniently optically pumped to the $m_F = 9/2$ state to obtain a gas of identical fermions. Since the dimer formation rate depends not only on the number of ground-state atoms present but also their spatial distribution, i.e. density, a major challenge will be to account for such factors in analysis of the data. Dimer formation might also be used to examine two-atom correlations that arise in a quantum gas from resonant atom-atom scattering.

**Concluding remarks.** Although Rydberg atoms have been studied for many years, new applications continue to emerge that address important physical questions related to few- and many-body interactions.

## Acknowledgments

Research by the author and his colleagues discussed here was supported by the AFOSR, the NSF, and the Robert A Welch Foundation (Grant # C-0734).
# 4. Chemistry close to 0 K

Paul Scheier, Olof Echt

Universität Innsbruck, Austria

**Status.** Helium nanodroplets (HNDs) are readily formed by expanding helium through a nozzle into vacuum. The average droplet size can be varied by varying helium pressure and nozzle temperature. In vacuum HNDs rapidly cool by evaporation to about 0.37 K. They are superfluid and can be doped efficiently by passing the droplet beam through a pick-up cell containing a low-density vapor of atoms or molecules. The technique has led to an entirely new approach to synthesize and characterize complex systems [44, 45]. Multiple collisions with dopant species lead to the formation of clusters; their size can be controlled by varying the droplet size or the vapor pressure in the pick-up cell. Uniquely shaped species such as ultrathin metallic nanowires or nanofoam form in very large HNDs [45, 46]. Two successive pick-up cells may be used to form binary aggregates with distinct core–shell structure [47], or to study reactions.

Equally impressive are the novel ways by which doped droplets can be investigated. HNDs form an ideal matrix for spectroscopy because of the weak interaction with the dopant, optical transparency, and low temperature. Problems inherent to bulk (liquid) helium, namely agglomeration and accumulation of dopants at walls, are avoided because most dopants will preferentially reside near the center of HNDs; low dopant concentration (=1 per droplet) will avoid agglomeration. Furthermore, the weak binding of helium (bulk cohesive energy 0.62 meV) opens a path for highly sensitive action spectroscopy because absorption of a photon will cause ejection of one or more helium atoms [48]. Reaction dynamics have been followed by pump-probe spectroscopy, ion imaging and other techniques [49]. Other new venues have been explored. For example, the superfluid environment makes it possible to orient polar dopants in an external electric field, providing a molecular goniometer for electron diffraction of single molecules [50].

**Current and future challenges.** Research involving HNDs offers many tracks. Some use HNDs as vehicles to synthesize, manipulate or characterize the species of interest; others explore quantum phenomena in superfluid systems of finite dimensions or ultrafast dynamics in helium [51]. Still others seek to generate ever larger HNDs, or more intense beams of HNDs [52]. All these tracks are meritorious and actively being pursued. In this short contribution we outline the prospects of yet another, new track, namely forming intense beams of large, size-selected HNDs. Novel structures are formed upon doping very large HNDs, including nanowires, nanofoam, and granular, multi-center clusters [45, 46]. However, as discussed further below, well-defined nanostructures cannot be formed by doping unless the HNDs are large and monodisperse.

<figure><img src="image_8.png" /><figcaption>Figure 5. Mass spectrum of HNDs measured at different electron emission currents. The size-to-charge ratio *n/z* decreases with increasing current as *z* increases.</figcaption></figure>

In the early years of HND research, few experimental groups had the technical means of generating HNDs containing more than a few hundred or thousand atoms. Improved designs, pumps with larger capacity, and the use of pulsed supersonic nozzles by some groups have now pushed the limit beyond $n \approx 10^{11}$, corresponding to droplet diameters of $\approx 2 \ \mu\text{m}$ [44, 52]. At this size, new forms of matter such as core–shell clusters, nanowires or nanofoam may form inside helium doped droplets [45–47]. Moreover, these objects can be deposited on surfaces and imaged by STM or TEM; the HND provides for a disposable cushion that prevents break-up of the object upon landing.

We have recently formed and detected very large, multiply charged HNDs. Figure 5 displays the yield of HNDs cations obtained by electron ionization at 40 eV and ion deflection in an electrostatic sector field. The approach uses the fact that the velocity distribution of neutral droplets is narrow and independent of the droplet size. The deflection voltage has been converted to a mass-to-charge ratio *n/z*; the ion yield has been corrected for an $n^{2/3}$ dependence of the ionization cross section. The distributions are markedly dependent on the emission current because large droplets may collide with multiple electrons, leading to charge states $z > 1$. The charge state *z* of these ions can be explored by post-ionization or electron attachment. Values up to *z* = 19 have been identified; the size of the charged droplets extends to *n* = $10^{12}$.

Large, monodisperse HNDs will also enable the investigation of so-called Coulomb crystals which may form at low temperatures when several free ions, or quasi-free ions in superfluid helium, are spatially confined. In ion traps these crystals enable measurements of state-selective reaction rates in a diverse range of systems [53]. At least $n_c = 2 \times 10^5$ atoms are needed to support two charges in a HND. The appearance of ordered charge arrangements might be detected by electron scattering. Alternatively, one may dope the HND by collisions with several charged atomic or molecular ions,
# 4. Chemistry close to 0 K

Paul Scheier, Olof Echt

Universität Innsbruck, Austria

**Status.** Helium nanodroplets (HNDs) are readily formed by expanding helium through a nozzle into vacuum. The average droplet size can be varied by varying helium pressure and nozzle temperature. In vacuum HNDs rapidly cool by evaporation to about 0.37 K. They are superfluid and can be doped efficiently by passing the droplet beam through a pick-up cell containing a low-density vapor of atoms or molecules. The technique has led to an entirely new approach to synthesize and characterize complex systems [44, 45]. Multiple collisions with dopant species lead to the formation of clusters; their size can be controlled by varying the droplet size or the vapor pressure in the pick-up cell. Uniquely shaped species such as ultrathin metallic nanowires or nanofoam form in very large HNDs [45, 46]. Two successive pick-up cells may be used to form binary aggregates with distinct core–shell structure [47], or to study reactions.

Equally impressive are the novel ways by which doped droplets can be investigated. HNDs form an ideal matrix for spectroscopy because of the weak interaction with the dopant, optical transparency, and low temperature. Problems inherent to bulk (liquid) helium, namely agglomeration and accumulation of dopants at walls, are avoided because most dopants will preferentially reside near the center of HNDs; low dopant concentration (=1 per droplet) will avoid agglomeration. Furthermore, the weak binding of helium (bulk cohesive energy 0.62 meV) opens a path for highly sensitive action spectroscopy because absorption of a photon will cause ejection of one or more helium atoms [48]. Reaction dynamics have been followed by pump-probe spectroscopy, ion imaging and other techniques [49]. Other new venues have been explored. For example, the superfluid environment makes it possible to orient polar dopants in an external electric field, providing a molecular goniometer for electron diffraction of single molecules [50].

**Current and future challenges.** Research involving HNDs offers many tracks. Some use HNDs as vehicles to synthesize, manipulate or characterize the species of interest; others explore quantum phenomena in superfluid systems of finite dimensions or ultrafast dynamics in helium [51]. Still others seek to generate ever larger HNDs, or more intense beams of HNDs [52]. All these tracks are meritorious and actively being pursued. In this short contribution we outline the prospects of yet another, new track, namely forming intense beams of large, size-selected HNDs. Novel structures are formed upon doping very large HNDs, including nanowires, nanofoam, and granular, multi-center clusters [45, 46]. However, as discussed further below, well-defined nanostructures cannot be formed by doping unless the HNDs are large and monodisperse.

<figure><img src="image_9.png" /><figcaption>Figure 5. Mass spectrum of HNDs measured at different electron emission currents. The size-to-charge ratio *n/z* decreases with increasing current as *z* increases.</figcaption></figure>

In the early years of HND research, few experimental groups had the technical means of generating HNDs containing more than a few hundred or thousand atoms. Improved designs, pumps with larger capacity, and the use of pulsed supersonic nozzles by some groups have now pushed the limit beyond $n \approx 10^{11}$, corresponding to droplet diameters of $\approx 2 \ \mu\text{m}$ [44, 52]. At this size, new forms of matter such as core–shell clusters, nanowires or nanofoam may form inside helium doped droplets [45–47]. Moreover, these objects can be deposited on surfaces and imaged by STM or TEM; the HND provides for a disposable cushion that prevents break-up of the object upon landing.

We have recently formed and detected very large, multiply charged HNDs. Figure 5 displays the yield of HNDs cations obtained by electron ionization at 40 eV and ion deflection in an electrostatic sector field. The approach uses the fact that the velocity distribution of neutral droplets is narrow and independent of the droplet size. The deflection voltage has been converted to a mass-to-charge ratio *n/z*; the ion yield has been corrected for an $n^{2/3}$ dependence of the ionization cross section. The distributions are markedly dependent on the emission current because large droplets may collide with multiple electrons, leading to charge states $z > 1$. The charge state *z* of these ions can be explored by post-ionization or electron attachment. Values up to *z* = 19 have been identified; the size of the charged droplets extends to *n* = $10^{12}$.

Large, monodisperse HNDs will also enable the investigation of so-called Coulomb crystals which may form at low temperatures when several free ions, or quasi-free ions in superfluid helium, are spatially confined. In ion traps these crystals enable measurements of state-selective reaction rates in a diverse range of systems [53]. At least $n_c = 2 \times 10^5$ atoms are needed to support two charges in a HND. The appearance of ordered charge arrangements might be detected by electron scattering. Alternatively, one may dope the HND by collisions with several charged atomic or molecular ions,
or multiply ionize droplets that have been doped with neutral multicenter clusters [45]. The charges would thus be localized at the impurities which, for sufficiently large separation, would mainly interact via Coulombic forces. Their spatial arrangement could be measured indirectly by soft-landing on a surface followed by TEM or STM imaging.

*Advances in science and technology to meet challenges.* Controlling the growth of nanostructures requires large, monodisperse HNDs. Doping is a statistical process; for fixed *n* the size distribution of aggregates grown in the HND would follow Poisson statistics whose relative width decreases with average size $\langle n_d \rangle$ as $1/\sqrt{\langle n_d \rangle}$. The dopant distribution would have a width of only 3% if $\langle n_d \rangle = 10^5$. In practice, two factors ruin narrow distributions: First, HNDs shrink upon doping. For example, a release of 2 eV, a typical cohesive energy per atom for metallic clusters, would cause the evaporation of some 3000 He. Second, the size distributions of HNDs are broad. Depending on expansion conditions they are either log-normal or bimodal [44]. The first problem is avoided if large HNDs are being doped (loss of $3 \times 10^6$ atoms from a droplet containing $10^8$ or more atoms would be acceptable), but the second problem necessitates the use of monodisperse HND beams. We foresee three possible ways for doing this.

1. HNDs can be efficiently ionized by electron impact. We have realized situations where droplets carry up to 19 charges due to successive collisions with electrons, and the size-to-charge ratio exceeds $n/z = 10^8$. Their size distributions are broad. Narrow slices of the distribution have been selected with an electric sector field but the presence of different charge states implies multimodal size distributions.

2. The production of size selected clusters has always been the holy grail of cluster science. Size selection of charged clusters by mass spectrometry wastes a large fraction of all clusters in the beam. A much less wasteful approach would be to select the singly

charged, nearly monodisperse HNDs that are ejected from highly charged droplets as a result of electrostatic combination with Coulomb repulsion. Although not in the $n \approx 10^8$ regime that is needed to grow large, strongly bound structures, they could be used to synthesize smaller, less strongly bound systems.

3. Toennies et al have formed HNDs containing $n = 10^{10}-10^{12}$ atoms by expanding pressurized liquid helium through a nozzle below 4.2 K [44]. Rayleigh oscillation-induced breakup of the liquid jet produces droplets with an exceedingly narrow angular and velocity distribution but the width of the size distribution, said to be mono-disperse, was not characterized. Also, the generation of droplets much larger than needed may have undesirable side effects, namely large gas loads even if the flux of droplets is modest.

*Concluding remarks.* Research involving or merely using HNDs is a burgeoning field. New opportunities such as messenger spectroscopy of He-tagged complex ions or electron diffraction of single aligned molecules are just some of many new research directions. In this contribution we have outlined another one, namely the prospects and use of large, monodisperse droplets. With sizes between 100 nm to 1 µm they would cover the mesoscopic regime; they could serve as vessels to synthesize and characterize, in situ or after deposition on surfaces, novel structures such as nanowires, Coulomb crystals, or ligand-free catalysts. Preliminary experiments by several groups have already shown the viability of this approach.

## Acknowledgments

This work was supported by the FWF (project number P31149) and the European Regional Development Fund (EFRE, project FAENOMENAL).
or multiply ionize droplets that have been doped with neutral multicenter clusters [45]. The charges would thus be localized at the impurities which, for sufficiently large separation, would mainly interact via Coulombic forces. Their spatial arrangement could be measured indirectly by soft-landing on a surface followed by TEM or STM imaging.

*Advances in science and technology to meet challenges.* Controlling the growth of nanostructures requires large, monodisperse HNDs. Doping is a statistical process; for fixed *n* the size distribution of aggregates grown in the HND would follow Poisson statistics whose relative width decreases with average size $\langle n_d \rangle$ as $1/\sqrt{\langle n_d \rangle}$. The dopant distribution would have a width of only 3% if $\langle n_d \rangle = 10^5$. In practice, two factors ruin narrow distributions: First, HNDs shrink upon doping. For example, a release of 2 eV, a typical cohesive energy per atom for metallic clusters, would cause the evaporation of some 3000 He. Second, the size distributions of HNDs are broad. Depending on expansion conditions they are either log-normal or bimodal [44]. The first problem is avoided if large HNDs are being doped (loss of $3 \times 10^6$ atoms from a droplet containing $10^8$ or more atoms would be acceptable), but the second problem necessitates the use of monodisperse HND beams. We foresee three possible ways for doing this.

1. HNDs can be efficiently ionized by electron impact. We have realized situations where droplets carry up to 19 charges due to successive collisions with electrons, and the size-to-charge ratio exceeds $n/z = 10^8$. Their size distributions are broad. Narrow slices of the distribution have been selected with an electric sector field but the presence of different charge states implies multimodal size distributions.

2. The production of size selected clusters has always been the holy grail of cluster science. Size selection of charged clusters by mass spectrometry wastes a large fraction of all clusters in the beam. A much less wasteful approach would be to select the singly

charged, nearly monodisperse HNDs that are ejected from highly charged droplets as a result of electrostatic combination with Coulomb repulsion. Although not in the $n \approx 10^8$ regime that is needed to grow large, strongly bound structures, they could be used to synthesize smaller, less strongly bound systems.

3. Toennies et al have formed HNDs containing $n = 10^{10}-10^{12}$ atoms by expanding pressurized liquid helium through a nozzle below 4.2 K [44]. Rayleigh oscillation-induced breakup of the liquid jet produces droplets with an exceedingly narrow angular and velocity distribution but the width of the size distribution, said to be mono-disperse, was not characterized. Also, the generation of droplets much larger than needed may have undesirable side effects, namely large gas loads even if the flux of droplets is modest.

*Concluding remarks.* Research involving or merely using HNDs is a burgeoning field. New opportunities such as messenger spectroscopy of He-tagged complex ions or electron diffraction of single aligned molecules are just some of many new research directions. In this contribution we have outlined another one, namely the prospects and use of large, monodisperse droplets. With sizes between 100 nm to 1 µm they would cover the mesoscopic regime; they could serve as vessels to synthesize and characterize, *in situ* or after deposition on surfaces, novel structures such as nanowires, Coulomb crystals, or ligand-free catalysts. Preliminary experiments by several groups have already shown the viability of this approach.

## Acknowledgments

This work was supported by the FWF (project number P31149) and the European Regional Development Fund (EFRE, project FAENOMENAL).
COLLISIONS INVOLVING HEAVY PROJECTILES

5. Non-relativistic ion–atom collision theory

Tom Kirchner

York University, Canada

*Status.* One may say that the ultimate goal of non-relativistic ion-atom collision theory is the development of approaches that provide a complete and accurate description of a given collision system. Complete means that all reaction channels are taken into account simultaneously, and accurate that the numerical results explain existing experimental data and make trustworthy predictions in regions where there are none. This is difficult to achieve since in many situations of interest a number of channels, direct and rearrangement, are open and contribute at the same time. Methods for the description of *individual* channels, such as excitation, ionization, or electron transfer are usually perturbative in nature [54]. These methods have enjoyed many successes, in particular when based on distorted-wave approaches, but they are somewhat limited in scope. A full account of all, potentially competing, processes calls for a fully non-perturbative treatment implemented via advanced numerical techniques.

Despite significant progress over a long period of time [55] it is perhaps fair to say that the feat of a truly complete calculation has only recently been achieved for the prototypical one-electron proton-hydrogen collision system. A fully quant- um-mechanical converged close-coupling (QM-CCC) approach has been developed and applied to this fundamental three-body problem of two Coulomb-interacting protons and one electron [56]. As an example figure 6 shows the total ionization cross section obtained from the QM-CCC method in comparison with a selection of previous non-perturbative calculations and the available experimental data. Interestingly, the overall agreement is not satisfactory in the 30–100 keV impact energy region in which the cross section maximum occurs. One may conclude that further investigation, both theoretical and experimental, is warranted before this case can be considered understood and closed [56]. This is all the more true for the study of differential cross sections, which in the past has been the domain of perturbative and classical trajectory methods, but for which fully non-perturbative calculations have started to emerge as well (see [57] and references therein).

A large body of theoretical ion-atom work, including all but the QM-CCC calculations of figure 6, makes use of the semiclassical approximation (SCA) according to which the nuclei are assumed to move classically (most often on straight-line trajectories) and only the electronic motion is treated quantum mechanically [55]. Over a wide range of impact energies the SCA is essentially exact, at least as far as cross sections that are integrated over the projectile deflection are concerned. For the case of projectile-angular differential cross sections there is a well-established procedure, called eikonal approximation [55], which re-introduces quantum mechanics into the heavy-particle scattering and often gives very accurate

<figure><img src="image_9.png" /><figcaption>Figure 6. Total ionization cross section for proton-hydrogen collisions as a function of projectile energy. References to indicated previous works are given in [56]. Reproduced with permission from [56]. © IOP Publishing Ltd. All rights reserved.</figcaption></figure>

results. In the framework of the SCA the scattering problem has similarities with the problem of laser-field induced excitation and ionization in that a time-dependent Schrödinger equation has to be solved to find the electronic wave function. Indeed some cross-fertilization between both areas in terms of method and code development has happened (see, e.g. [58]).

Most ion-atom collision problems involve few- or many-electron atoms. It has long been known that the independent-particle model (IPM) is often not sufficient to understand experimental observations in these systems. Explicit methods to deal with beyond-IPM situations are mostly restricted to two-electron systems, i.e. collisions involving helium atoms whose double ionization famously cannot be properly described without taking electron correlation effects into account (see, e.g. [58]). Recent work has shown that also three-electron problems can be studied with non-perturbative methods that are based on correlated many-electron wave functions [59]. Figure 7 shows an example: the angular-differential cross section for electron transfer from the target ground state to the projectile ground state in He⁺-He collisions at 60 keV amu⁻¹ impact energy [59]. While a correlated, fully non-perturbative three-electron calculation (that uses the eikonal approximation to extract the differential cross section) is in excellent agreement with the experimental data, results from previous perturbative efforts are not.

*Current and future challenges.* The above discussion suggests that there is still work to be done to reach a quantitative understanding of one-electron problems. But the bigger challenge lies in the treatment of many-electron systems given that the majority of them will remain beyond the reach of explicit methods for some time to come. Perhaps the most promising alternative approach is time-dependent density functional theory (TDDFT). The time-dependent (so-called Kohn–Sham) equations in TDDFT calculations look like IPM
COLLISIONS INVOLVING HEAVY PROJECTILES

5. Non-relativistic ion–atom collision theory

Tom Kirchner

York University, Canada

*Status.* One may say that the ultimate goal of non-relativistic ion–atom collision theory is the development of approaches that provide a complete and accurate description of a given collision system. Complete means that all reaction channels are taken into account simultaneously, and accurate that the numerical results explain existing experimental data and make trustworthy predictions in regions where there are none. This is difficult to achieve since in many situations of interest a number of channels, direct and rearrangement, are open and contribute at the same time. Methods for the description of *individual* channels, such as excitation, ionization, or electron transfer are usually perturbative in nature [54]. These methods have enjoyed many successes, in particular when based on distorted-wave approaches, but they are somewhat limited in scope. A full account of all, potentially competing, processes calls for a fully non-perturbative treatment implemented via advanced numerical techniques.

Despite significant progress over a long period of time [55] it is perhaps fair to say that the feat of a truly complete calculation has only recently been achieved for the prototypical one-electron proton-hydrogen collision system. A fully quant- um-mechanical converged close-coupling (QM-CCC) approach has been developed and applied to this fundamental three-body problem of two Coulomb-interacting protons and one electron [56]. As an example figure 6 shows the total ionization cross section obtained from the QM-CCC method in comparison with a selection of previous non-perturbative calculations and the available experimental data. Interestingly, the overall agreement is not satisfactory in the 30–100 keV impact energy region in which the cross section maximum occurs. One may conclude that further investigation, both theoretical and experimental, is warranted before this case can be considered understood and closed [56]. This is all the more true for the study of differential cross sections, which in the past has been the domain of perturbative and classical trajectory methods, but for which fully non-perturbative calculations have started to emerge as well (see [57] and references therein).

A large body of theoretical ion–atom work, including all but the QM-CCC calculations of figure 6, makes use of the semiclassical approximation (SCA) according to which the nuclei are assumed to move classically (most often on straight- line trajectories) and only the electronic motion is treated quantum mechanically [55]. Over a wide range of impact energies the SCA is essentially exact, at least as far as cross sections that are integrated over the projectile deflection are concerned. For the case of projectile-angular differential cross sections there is a well-established procedure, called eikonal approximation [55], which re-introduces quantum mechanics into the heavy-particle scattering and often gives very accurate

<figure><img src="image_10.png" /><figcaption>Figure 6. Total ionization cross section for proton-hydrogen collisions as a function of projectile energy. References to indicated previous works are given in [56]. Reproduced with permission from [56]. © IOP Publishing Ltd. All rights reserved.</figcaption></figure>

results. In the framework of the SCA the scattering problem has similarities with the problem of laser-field induced excitation and ionization in that a time-dependent Schrödinger equation has to be solved to find the electronic wave function. Indeed some cross-fertilization between both areas in terms of method and code development has happened (see, e.g. [58]).

Most ion–atom collision problems involve few- or many- electron atoms. It has long been known that the independent- particle model (IPM) is often not sufficient to understand experimental observations in these systems. Explicit methods to deal with beyond-IPM situations are mostly restricted to two- electron systems, i.e. collisions involving helium atoms whose double ionization famously cannot be properly described without taking electron correlation effects into account (see, e.g. [58]). Recent work has shown that also three-electron problems can be studied with non-perturbative methods that are based on correlated many-electron wave functions [59]. Figure 7 shows an example: the angular-differential cross section for electron transfer from the target ground state to the projectile ground state in He⁺–He collisions at 60 keV amu⁻¹ impact energy [59]. While a correlated, fully non-perturbative three-electron calcul- ation (that uses the eikonal approximation to extract the differential cross section) is in excellent agreement with the experimental data, results from previous perturbative efforts are not.

*Current and future challenges.* The above discussion suggests that there is still work to be done to reach a quantitative understanding of one-electron problems. But the bigger challenge lies in the treatment of many-electron systems given that the majority of them will remain beyond the reach of explicit methods for some time to come. Perhaps the most promising alternative approach is time-dependent density functional theory (TDDFT). The time-dependent (so-called Kohn–Sham) equations in TDDFT calculations look like IPM
<figure><img src="image_10.png" /><figcaption>Figure 7. Angular differential cross section for ground-state transfer in He⁺–He collisions at 60 keV amu⁻¹ impact energy as a function of scattering angle. References to indicated previous works are given in [59]. Reprinted figure with permission from [59], Copyright 2018 by the American Physical Society.</figcaption></figure>

equations, but they involve a potential that, in its exact form, includes electron correlation effects. Similarly, the exact outcome analysis of the Kohn–Sham calculations involves a correlation integral. Both issues, correlation in the potential and correlation in the method to extract observables from the Kohn–Sham solutions, are areas of active research. Despite recent advances there is room for improvement of the current models (see, e.g. [60] and references therein).

TDDFT methods are also promising tools to deal with ion–molecule collision systems which are of relevance in the context of radiation biology [61] (see section 9 for an experimental perspective). Beyond conducting proof-of-principle studies it will be important for work in this area and in other, e.g. plasma-related applications to quantify the uncertainties of calculated cross sections. This is more challenging than it may sound given that it is straightforward (albeit perhaps tedious) to determine the numerical accuracy of a calculation. However, quantifying the uncertainties associated with the use of a particular many-body model is only poorly understood [62].

Experimental advances, most notably the development of recoil-ion momentum spectroscopy and the reaction microscope, have led to a wealth of highly-differential ion–atom and ion–molecule measurements (see section 7). They often show rich structure and probe theory and our fundamental understanding of the few-body problem on deeper levels than integrated cross section data. They may also point to aspects of the collision problem that are less well understood than assumed. A recent

example is the observation of effects that appear to be related to the coherence properties of the projectile beam [63]. This observation challenges a basic tenet of atomic collision theory in that it suggests that one can choose the set-up of an experiment such that the projectile beam is not fully coherent and the standard way of calculating a cross section does not apply.

*Advances in science and technology to meet challenges.* A large fraction of ion–atom collision theory research has been motivated by experimental studies, and this is not expected to change. Accordingly, active experimental research programs which generate accurate differential and integrated (see figure 6) data will be indispensable for progress on the theoretical side. It will be particularly useful to maintain or even expand on the breadth of the collision systems studied in the laboratory; the use of magneto-optical traps to allow for reaction-microscope studies of alkalis and the use of antiproton beams to initiate electron dynamics in a variety of atoms and molecules are important examples. Together with the ongoing advances in numerical method and code development plus the ever-increasing available computer power they will allow theorists to move forward in the areas outlined above. A few good ideas, e.g. on how to incorporate correlation effects in TDDFT models or on how to account for incomplete projectile coherence in such a way that it can be distinguished from other effects, will be required as well.

*Concluding remarks.* Ion–atom collision theory may be a mature field, but it remains highly relevant given the deep science questions it addresses and the data it produces. One can perhaps say that thanks to advances in computational methods and resources we have just started to answer some long-standing questions in a quantitative fashion, e.g. on the role of electron correlation effects in the few-particle dynamics, and can now produce (semi-) accurate data for more complex collision systems. This will continue. Moreover, similar questions are being addressed in neighboring research fields and knowledge and insights obtained from collisional studies may help answer them as well—as will progress in those areas benefit the advancement of atomic collision theory.

## Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. RGPIN-2014-03611. Thanks are due to the authors of [59] for providing figure 7.
<figure><img src="image_11.png" /><figcaption>Figure 7. Angular differential cross section for ground-state transfer in He⁺–He collisions at 60 keV amu⁻¹ impact energy as a function of scattering angle. References to indicated previous works are given in [59]. Reprinted figure with permission from [59], Copyright 2018 by the American Physical Society.</figcaption></figure>

equations, but they involve a potential that, in its exact form, includes electron correlation effects. Similarly, the exact outcome analysis of the Kohn–Sham calculations involves a correlation integral. Both issues, correlation in the potential and correlation in the method to extract observables from the Kohn–Sham solutions, are areas of active research. Despite recent advances there is room for improvement of the current models (see, e.g. [60] and references therein).

TDDFT methods are also promising tools to deal with ion–molecule collision systems which are of relevance in the context of radiation biology [61] (see section 9 for an experimental perspective). Beyond conducting proof-of-principle studies it will be important for work in this area and in other, e.g. plasma-related applications to quantify the uncertainties of calculated cross sections. This is more challenging than it may sound given that it is straightforward (albeit perhaps tedious) to determine the numerical accuracy of a calculation. However, quantifying the uncertainties associated with the use of a particular many-body model is only poorly understood [62].

Experimental advances, most notably the development of recoil-ion momentum spectroscopy and the reaction microscope, have led to a wealth of highly-differential ion–atom and ion–molecule measurements (see section 7). They often show rich structure and probe theory and our fundamental understanding of the few-body problem on deeper levels than integrated cross section data. They may also point to aspects of the collision problem that are less well understood than assumed. A recent

example is the observation of effects that appear to be related to the coherence properties of the projectile beam [63]. This observation challenges a basic tenet of atomic collision theory in that it suggests that one can choose the set-up of an experiment such that the projectile beam is not fully coherent and the standard way of calculating a cross section does not apply.

*Advances in science and technology to meet challenges.* A large fraction of ion–atom collision theory research has been motivated by experimental studies, and this is not expected to change. Accordingly, active experimental research programs which generate accurate differential and integrated (see figure 6) data will be indispensable for progress on the theoretical side. It will be particularly useful to maintain or even expand on the breadth of the collision systems studied in the laboratory; the use of magneto-optical traps to allow for reaction-microscope studies of alkalis and the use of antiproton beams to initiate electron dynamics in a variety of atoms and molecules are important examples. Together with the ongoing advances in numerical method and code development plus the ever-increasing available computer power they will allow theorists to move forward in the areas outlined above. A few good ideas, e.g. on how to incorporate correlation effects in TDDFT models or on how to account for incomplete projectile coherence in such a way that it can be distinguished from other effects, will be required as well.

*Concluding remarks.* Ion–atom collision theory may be a mature field, but it remains highly relevant given the deep science questions it addresses and the data it produces. One can perhaps say that thanks to advances in computational methods and resources we have just started to answer some long-standing questions in a quantitative fashion, e.g. on the role of electron correlation effects in the few-particle dynamics, and can now produce (semi-) accurate data for more complex collision systems. This will continue. Moreover, similar questions are being addressed in neighboring research fields and knowledge and insights obtained from collisional studies may help answer them as well—as will progress in those areas benefit the advancement of atomic collision theory.

## Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. RGPIN-2014-03611. Thanks are due to the authors of [59] for providing figure 7.
# 6. Correlation and polarization phenomena in relativistic ion-atom collisions

Stephan Fritzsche¹ and Andrey Surzhykov²

¹Helmholtz Institute Jena and Friedrich-Schiller-Universität Jena, Germany

²Technische Universität Braunschweig and Physikalisch-Technische Bundesanstalt, Germany

**Status.** Collisions of highly-charged heavy ions with atoms and electrons are central for much of our present day's knowledge about matter in strong (Coulomb) fields. Recent advances in heavy-ion accelerator and detection techniques have paved the way towards new (collision) experiments which help explore the angular distribution and polarization of energetic electrons and (x-ray) photons, emitted in such ion-atom and ion-electron collisions. Unlike measurements of total cross sections, these angle-resolved and polarization experiments provide valuable information about the dynamics of high-Z, few-electron systems in strong fields.

In collisions of fast bare ions with atoms, for example, initially quasi-free target electrons often recombine radiatively with ions under the emission of a photon; the time-reversed process to Einstein's well-known photoionization [64, 65]. If the electron is captured into the $2p_{3/2}$ level of a hydrogen-like ion, it will subsequently decay by a (second) Lyman-$\alpha_1$ ($2p_{3/2} \rightarrow 1s_{1/2}$) photon. This Lyman-$\alpha_1$ radiation of heavy ions appears very sensitive to both, the population of magnetic sublevels $|2p_{3/2} \mu>$, produced in the capture process, and to the E1-M2 *multipole mixing*, i.e. the coupling of the bound electron density to the different (multipole) components of the radiation field. Indeed, combined measurements of the angular distribution and linear polarization of the characteristic Lyman-$\alpha_1$ photons help *disentangle* here the formation of the excited ionic state from the subsequent decay and to determine the M2/E1 amplitude ratio without further assumptions about the population mechanism for the $2p_{3/2}$ state [66]. The M2/E1 amplitude ratio can be tested against quantum electrodynamics (QED) which is the fundamental theory for describing the electron dynamics of atom and ions in the presence of strong (Coulomb) fields.

Bremsstrahlung, the emission of photons due to the inelastic scattering of (quasi-) free electrons at ions and atoms, is a similarly fundamental process in relativistic collisions but with the 'capture' of the electron into the Dirac continuum. Detailed calculations of the bremsstrahlung spectra, angular distribution and polarization Stokes parameters of emitted photons, are however still a challenge to atomic theory, as they require a reliable representation of the (positive-energy) continuum for both, the initial and final electronic states as well as an accurate evaluation of 'free-free' transition amplitudes, especially at high electron and photon energies [67]. Measurements of the linear polarization of bremsstrahlung radiation with electrons of variable polarization for neutral gold atoms confirmed the need for accurate computations.

<figure><img src="image_11.png" /><figcaption>Figure 8. Degree of polarization of the $1s\ 2s^2\ 2p_{1/2}\ J = 1 \rightarrow 1s^2\ 2s^2\ J = 0$ emission perpendicular to the incident ion beam.</figcaption></figure>

Calculations with only the Coulomb repulsion (blue dashed lines) are compared with a full account of the electron-electron interaction (Coulomb+Breit; black solid line). Experimental data for the DR into beryllium-like Xe is from [68]. Reprinted figure with permission from [68], Copyright 2009 by the American Physical Society.

Distinct peaks in the observed x-ray spectra from high-Z ion-electron collisions arise especially due to the dielectronic recombination (DR) of the ions as competitive but resonant process to the radiative electron capture (EC). This resonant capture of electrons leads to the excitation of the bound electron density and often to a subsequent photon emission. Indeed, the DR in fast ion-electron collisions provides an important tool for studying the relativistic, i.e. magnetic and retardation contributions to the electron-electron interaction, known also as Breit interaction in atomic physics. To reveal details about the relativistic interactions between the electrons in the presence of strong Coulomb fields, measurements were proposed on the angular distribution and linear polarization of the $1s\ 2s^2\ 2p_{1/2}\ J = 1 \rightarrow 1s^2\ 2s^2\ J = 0$ (electric-dipole) photon emission, following the resonant EC into initially lithium-like ions. Multi-configuration Dirac-Fock (MCDF) calculations for this particular DR process demonstrated that the Breit interaction can dominate over the pairwise Coulomb repulsion among the electrons and may even cause a *qualitative* change of the characteristic photon emission [68]. For the DR of high-Z ions, for instance, the Breit term leads to a significant reduction of the (absolute value of) linear polarization of $1s\ 2s^2\ 2p_{1/2}\ J = 1 \rightarrow 1s^2\ 2s^2$ line; a behavior that has meanwhile been confirmed experimentally [69], see figure 8.

**Current and future challenges.** Any detailed interpretation of fast ion-atom collision experiments requires of course a deep understanding of the underlying mechanisms and their quantum (-field) theoretical formulation. Therefore, various theoretical methods have been developed during the past two decades in order to explain such polarization and correlation phenomena in heavy-ion collisions. In particular, the density matrix theory, combined with the calculus of spherical tensors, has been found a very versatile tool to incorporate all major relativistic and
# 6. Correlation and polarization phenomena in relativistic ion-atom collisions

Stephan Fritzsche¹ and Andrey Surzhykov²

¹Helmholtz Institute Jena and Friedrich-Schiller-Universität Jena, Germany

²Technische Universität Braunschweig and Physikalisch-Technische Bundesanstalt, Germany

**Status.** Collisions of highly-charged heavy ions with atoms and electrons are central for much of our present day's knowledge about matter in strong (Coulomb) fields. Recent advances in heavy-ion accelerator and detection techniques have paved the way towards new (collision) experiments which help explore the angular distribution and polarization of energetic electrons and (x-ray) photons, emitted in such ion-atom and ion-electron collisions. Unlike measurements of total cross sections, these angle-resolved and polarization experiments provide valuable information about the dynamics of high-Z, few-electron systems in strong fields.

In collisions of fast bare ions with atoms, for example, initially quasi-free target electrons often recombine radiatively with ions under the emission of a photon; the time-reversed process to Einstein's well-known photoionization [64, 65]. If the electron is captured into the $2p_{3/2}$ level of a hydrogen-like ion, it will subsequently decay by a (second) Lyman-$\alpha_1$ ($2p_{3/2} \rightarrow 1s_{1/2}$) photon. This Lyman-$\alpha_1$ radiation of heavy ions appears very sensitive to both, the population of magnetic sublevels $|2p_{3/2} \mu>$, produced in the capture process, and to the E1-M2 multipole mixing, i.e. the coupling of the bound electron density to the different (multipole) components of the radiation field. Indeed, combined measurements of the angular distribution and linear polarization of the characteristic Lyman-$\alpha_1$ photons help disentangle here the formation of the excited ionic state from the subsequent decay and to determine the M2/E1 amplitude ratio without further assumptions about the population mechanism for the $2p_{3/2}$ state [66]. The M2/E1 amplitude ratio can be tested against quantum electrodynamics (QED) which is the fundamental theory for describing the electron dynamics of atom and ions in the presence of strong (Coulomb) fields.

Bremsstrahlung, the emission of photons due to the inelastic scattering of (quasi-) free electrons at ions and atoms, is a similarly fundamental process in relativistic collisions but with the 'capture' of the electron into the Dirac continuum. Detailed calculations of the bremsstrahlung spectra, angular distribution and polarization Stokes parameters of emitted photons, are however still a challenge to atomic theory, as they require a reliable representation of the (positive-energy) continuum for both, the initial and final electronic states as well as an accurate evaluation of 'free-free' transition amplitudes, especially at high electron and photon energies [67]. Measurements of the linear polarization of bremsstrahlung radiation with electrons of variable polarization for neutral gold atoms confirmed the need for accurate computations.

<figure><img src="image_12.png" /><figcaption>Figure 8. Degree of polarization of the $1s\ 2s^2\ 2p_{1/2}\ J = 1 \rightarrow 1s^2\ 2s^2\ J = 0$ emission perpendicular to the incident ion beam.</figcaption></figure>

Calculations with only the Coulomb repulsion (blue dashed lines) are compared with a full account of the electron-electron interaction (Coulomb+Breit; black solid line). Experimental data for the DR into beryllium-like Xe is from [68]. Reprinted figure with permission from [68], Copyright 2009 by the American Physical Society.

Distinct peaks in the observed x-ray spectra from high-Z ion-electron collisions arise especially due to the dielectronic recombination (DR) of the ions as competitive but resonant process to the radiative electron capture (EC). This resonant capture of electrons leads to the excitation of the bound electron density and often to a subsequent photon emission. Indeed, the DR in fast ion-electron collisions provides an important tool for studying the relativistic, i.e. magnetic and retardation contributions to the electron-electron interaction, known also as Breit interaction in atomic physics. To reveal details about the relativistic interactions between the electrons in the presence of strong Coulomb fields, measurements were proposed on the angular distribution and linear polarization of the $1s\ 2s^2\ 2p_{1/2}\ J = 1 \rightarrow 1s^2\ 2s^2\ J = 0$ (electric-dipole) photon emission, following the resonant EC into initially lithium-like ions. Multi-configuration Dirac-Fock (MCDF) calculations for this particular DR process demonstrated that the Breit interaction can dominate over the pairwise Coulomb repulsion among the electrons and may even cause a qualitative change of the characteristic photon emission [68]. For the DR of high-Z ions, for instance, the Breit term leads to a significant reduction of the (absolute value of) linear polarization of $1s\ 2s^2\ 2p_{1/2}\ J = 1 \rightarrow 1s^2\ 2s^2$ line; a behavior that has meanwhile been confirmed experimentally [69], see figure 8.

**Current and future challenges.** Any detailed interpretation of fast ion-atom collision experiments requires of course a deep understanding of the underlying mechanisms and their quantum (-field) theoretical formulation. Therefore, various theoretical methods have been developed during the past two decades in order to explain such polarization and correlation phenomena in heavy-ion collisions. In particular, the density matrix theory, combined with the calculus of spherical tensors, has been found a very versatile tool to incorporate all major relativistic and
<figure><img src="image_12.png" /><figcaption>Figure 9. Angle-differential cross sections for the radiative electron capture into the $1s^2 2s^2 1S_0$ state of (initially) lithium-like uranium ions $U^{89+}$ with projectile energies of 2.18 and 218 MeV/u. Results are presented within the independent particle model (-dashed line) and MCDF approach (solid line). See [69] for further details. Reprinted figure with permission from [69] Copyright 2015 by the American Physical Society.</figcaption></figure>

many-body contributions into the computational framework. The density matrix approach is naturally built upon many-electron amplitudes of the electron-electron interaction and the coupling of the electrons to the radiation field and, thus, allows quite easily to incorporate many-body and non-dipole contributions into the theoretical predictions of all *observables* of the emitted x-rays. When combined with MCDF wave functions, this approach has indeed been found versatile to explain the electronic correlations in high-Z ion-electron collisions. For example, figure 9 displays the calculated angle-differential cross sections for the radiative capture of electrons into the $1s^2 2s^2 1S_0$ state of (initially) lithium-like uranium $U^{89+}$ ions with projectile energies $T_p = 2.18$ and $T_p = 218$ MeV/u. While the correlated motion of the electrons appears to be negligible for 218 MeV/u, it alters the angular distribution at lower energies [69].

Closely related to the ion-electron collisions from above is the (so-called) radiative double electron capture (RDEC) in which two electrons are simultaneously captured under the emission of a single energetic photon. Such an EC can occur only due to the interelectronic interactions in the continuum. Few measurements have been carried out [70] but with rather large uncertainties and until now in disagreement with theory. Further detailed angle-resolved RDEC experiments will here provide a stringent test for theory due to demand to deal with two *correlated* electrons in the continuum.

**Advances in science and technology to meet challenges.**

Recent years have seen significant progress in detecting (hard) x-rays by microcalorimeters and position as well as energy sensitive solid-state detectors, designed for advanced photon spectroscopy [71]. These detectors nowadays achieve a sub-millimeter spatial resolution as well as excellent time and energy resolution in the hard x-ray energy regime above 15 keV, and they helped advance both, x-ray polarimetry and medical imaging. Beside of EC and transfer processes, these detector advances will facilitate further QED studies and even investigations on parity-violating interactions in forthcoming years. A number of ion-atom (ion-electron) collision experiments have been proposed recently to scrutinize these interactions. For example, the parity mixing between $1s2p_{1/2}$ $^3P_0$ and $1s^2 1S_0$ states of helium-like ions leads to a rotation of the linear polarization of x-rays emitted in the L-shell EC [72], an experiment proposal that will likely become feasible in the near future. At FAIR, the currently built Facility for Antiproton and Ion Research in Darmstadt (Germany), such polarization measurements will be possible also for the negative-continuum dielectronic recombination (NCDR), in which a free electron is captured into a bound state of a heavy high-Z ion, while the energy is released by an electron-positron pair [73]. The NCDR process provides indeed an important benchmark for theory, describing the electron and positron dynamics in quite critical fields. Special interest refers here to the formation and subsequent radiative decay of excited ionic states, and which requires a QED treatment right from the beginning.

Finally, excited ionic states are created also by Coulomb excitations of few-electron ions in collisions with target atoms and molecules. Again, the subsequent decay of these states typically results in an anisotropic angular distribution and non-vanishing polarization of the characteristic radiation. For high-Z ions, these distributions of the characteristic x-ray lines will help explore especially magnetic corrections to the Coulomb interaction, i.e. further details about the Lienard-Wiechert potential.

**Concluding remarks.** Angular and polarization studies in relativistic ion-atom collisions help reveal new insights into the quantum dynamics in strong Coulomb fields [74]. Especially the comparison of high-resolution experiments with advanced theoretical techniques will provide an efficient route to further enhance our knowledge about the interaction of matter in extreme fields.
<figure><img src="image_13.png" /><figcaption>Figure 9. Angle-differential cross sections for the radiative electron capture into the $1s^2 2s^2 1S_0$ state of (initially) lithium-like uranium ions $U^{89+}$ with projectile energies of 2.18 and 218 MeV/u. Results are presented within the independent particle model (-dashed line) and MCDF approach (solid line). See [69] for further details. Reprinted figure with permission from [69] Copyright 2015 by the American Physical Society.</figcaption></figure>

many-body contributions into the computational framework. The density matrix approach is naturally built upon many-electron amplitudes of the electron-electron interaction and the coupling of the electrons to the radiation field and, thus, allows quite easily to incorporate many-body and non-dipole contributions into the theoretical predictions of all *observables* of the emitted x-rays. When combined with MCDF wave functions, this approach has indeed been found versatile to explain the electronic correlations in high-Z ion-electron collisions. For example, figure 9 displays the calculated angle-differential cross sections for the radiative capture of electrons into the $1s^2 2s^2 1S_0$ state of (initially) lithium-like uranium $U^{89+}$ ions with projectile energies $T_p = 2.18$ and $T_p = 218$ MeV/u. While the correlated motion of the electrons appears to be negligible for 218 MeV/u, it alters the angular distribution at lower energies [69].

Closely related to the ion-electron collisions from above is the (so-called) radiative double electron capture (RDEC) in which two electrons are simultaneously captured under the emission of a single energetic photon. Such an EC can occur only due to the interelectronic interactions in the continuum. Few measurements have been carried out [70] but with rather large uncertainties and until now in disagreement with theory. Further detailed angle-resolved RDEC experiments will here provide a stringent test for theory due to demand to deal with two *correlated* electrons in the continuum.

**Advances in science and technology to meet challenges.**

Recent years have seen significant progress in detecting (hard) x-rays by microcalorimeters and position as well as energy sensitive solid-state detectors, designed for advanced photon spectroscopy [71]. These detectors nowadays achieve a sub-millimeter spatial resolution as well as excellent time and energy resolution in the hard x-ray energy regime above 15 keV, and they helped advance both, x-ray polarimetry and medical imaging. Beside of EC and transfer processes, these detector advances will facilitate further QED studies and even investigations on parity-violating interactions in forthcoming years. A number of ion-atom (ion-electron) collision experiments have been proposed recently to scrutinize these interactions. For example, the parity mixing between $1s2p_{1/2}$ $^3P_0$ and $1s^2 1S_0$ states of helium-like ions leads to a rotation of the linear polarization of x-rays emitted in the L-shell EC [72], an experiment proposal that will likely become feasible in the near future. At FAIR, the currently built Facility for Antiproton and Ion Research in Darmstadt (Germany), such polarization measurements will be possible also for the negative-continuum dielectronic recombination (NCDR), in which a free electron is captured into a bound state of a heavy high-Z ion, while the energy is released by an electron-positron pair [73]. The NCDR process provides indeed an important benchmark for theory, describing the electron and positron dynamics in quite critical fields. Special interest refers here to the formation and subsequent radiative decay of excited ionic states, and which requires a QED treatment right from the beginning.

Finally, excited ionic states are created also by Coulomb excitations of few-electron ions in collisions with target atoms and molecules. Again, the subsequent decay of these states typically results in an anisotropic angular distribution and non-vanishing polarization of the characteristic radiation. For high-Z ions, these distributions of the characteristic x-ray lines will help explore especially magnetic corrections to the Coulomb interaction, i.e. further details about the Lienard-Wiechert potential.

**Concluding remarks.** Angular and polarization studies in relativistic ion-atom collisions help reveal new insights into the quantum dynamics in strong Coulomb fields [74]. Especially the comparison of high-resolution experiments with advanced theoretical techniques will provide an efficient route to further enhance our knowledge about the interaction of matter in extreme fields.
# 7. Experimental investigations on ion-atom collisions

Xinwen Ma

Chinese Academy of Sciences, People's Republic of China

**Status.** Experimental cross sections of ion-atom collisions in a wide range of impact energies play important roles in testing many-body theories and in application of astrophysics, plasma modeling, radiation damage, and ion-matter interaction, etc. The products of a collision usually consist of emitted photons, emitted electrons, recoil ions, and charge (un)changed scattered ions, and the ions may be in excited states. By detecting part of the particles in final states, experimentalists can extract essential information on collision dynamics. However, it is not just as that easy. The energies of emitted photons and outgoing electrons vary greatly depending on the collision systems and the collision energies, therefore, it is difficult to find one universal technique to detect photons, electrons and ions with sufficient resolution in one experiment. And further, due to very limited photon collection efficiency (solid angle and quantum efficiency of a detector system) compared to charged particle detection, coincidence measurements are generally difficult to apply for photons and charged particles. There are usually two types of experimental approaches for collisions studies, photon detection with high resolution and charged particles coincidence measurement. Few measurements have been reported with photon and ion in coincidence. Here the focus will be on the charged particle measurements.

Before the invention of reaction microscope [75] or COLTRIMS [76], only total cross sections and partial cross sections were obtained. Due to the powerful multiple coincidence measurements of charged particles, reaction microscope/COLTRIMS opens the way to perform multi-fold and even fully differential cross section (FDCS) studies, with reasonably good energy/momentum resolutions. The cross sections differential in scattering angle provide rich information of the impact parameter dependent collision dynamics where electron emission mechanism in a broad range of collision velocities have been studied [77].

In low to intermediate energy EC collisions, it is now possible to perform studies on quantum state-resolved charge exchange processes with high resolution. Figure 10 shows single-EC in collisions of 63 keV $Ne^{7+}$ ions with He studied using COLTRIMS [78], where the state-resolved differential cross sections have been determined with respect to the principal quantum number, subshell levels and spin states of the captured electron. Furthermore, it is possible to explore the high resolution method to study the electron correlations in double and multiple EC processes, and give new insight into mechanisms, e.g. symmetric/asymmetric population, sequential/non-sequential processes.

At high impact energies, only few measurements of FDCSs have been done, where first Born approximation is assumed to be valid. Schulz *et al* [79] found unexpected discrepancies of electron angular distribution between theory and experiment in the perpendicular plane for single ionization

of He by 100 MeV/u $C^{6+}$. This 'C$^{6+}$ puzzle' frustrates the community and needs to be solved in future experiments.

When more electrons are involved in a charge exchange process, electron correlation plays an important role, which is essential to understand many-body dynamics. For instance, in double-electron transfer with one electron ionized collisions of 80 keV/u $Ne^{8+}$ on He, distinct features of the correlated processes can be well separated from the un-correlated ones [80]. With multiple coincidence technique, Gao *et al* [81] obtained fully differential data for transfer ionization process of one electron transfer with two electron ionized (five-body process). It is found that the sum electron momentum and the individual electron momenta are surprisingly strongly correlated with the total momentum transfer. Dedicated experiments for multiple ionization are expected to better understand these phenomena, and rigorous theoretical treatments are needed as well.

In the past decades, the targets used in ion collisions have been extended from simple atom to molecules and even to atomic/molecular dimers/trimers, etc. The structure information of these complex system serves as extra dimensions for the investigation of the structure involved collision dynamics. The molecular frame can be determined from the coincidence detection of charged particles produced in these processes. Consequently, the characteristic of matter wave of massive particles has also been observed at atomic scale: Fraunhofer diffraction in atomic collisions and interference in molecule involved collisions. In the works of Schmidt *et al* [82] and Zhang *et al* [83], they revealed that the interference pattern, which is in contrast to the optical double-slit experiment, resulted from the $\pi$-phase shift due to the parity change of molecular hydrogen ion in the collision. Later, the double-slit interference effects is used to extract the phase information in collisions with asymmetric diatomic molecules [84]. Figure 11 shows the asymmetry and shift of two-center interference patterns of $He^{2+}$ on CO. In two different colliding energies, the scattering phase differences of $He^{2+}$ on C compared to $He^{2+}$ on O can be extracted.

**Current and future challenges.** Despite many successes in ion-atom collision studies, there are still challenges. To the least extent, here are some possible perspectives that one can look forwards in the near future. First, photon measurements in coincidence with charged particles. In ion collisions, photon emission from residual ions (recoils and/or scattered ions in multiply excited states) can provide additional information about the collision dynamics. However, so far sophisticated techniques where photon and charged particles are recorded in coincidence are still quite challenging.

Second, the phase information of the collision processes. Scattering phase contains important information about collision dynamics. In atomic transitions induced by the laser field, it has been shown that phase measurements show great potential in deeper understanding of the few-body problem. However, the long-range property of the Coulomb field of the projectile in ion collisions makes it nearly impossible to define the start/end point of the interactions as those of the
# 7. Experimental investigations on ion-atom collisions

Xinwen Ma

Chinese Academy of Sciences, People's Republic of China

**Status.** Experimental cross sections of ion-atom collisions in a wide range of impact energies play important roles in testing many-body theories and in application of astrophysics, plasma modeling, radiation damage, and ion-matter interaction, etc. The products of a collision usually consist of emitted photons, emitted electrons, recoil ions, and charge (un)changed scattered ions, and the ions may be in excited states. By detecting part of the particles in final states, experimentalists can extract essential information on collision dynamics. However, it is not just as that easy. The energies of emitted photons and outgoing electrons vary greatly depending on the collision systems and the collision energies, therefore, it is difficult to find one universal technique to detect photons, electrons and ions with sufficient resolution in one experiment. And further, due to very limited photon collection efficiency (solid angle and quantum efficiency of a detector system) compared to charged particle detection, coincidence measurements are generally difficult to apply for photons and charged particles. There are usually two types of experimental approaches for collisions studies, photon detection with high resolution and charged particles coincidence measurement. Few measurements have been reported with photon and ion in coincidence. Here the focus will be on the charged particle measurements.

Before the invention of reaction microscope [75] or COLTRIMS [76], only total cross sections and partial cross sections were obtained. Due to the powerful multiple coincidence measurements of charged particles, reaction microscope/COLTRIMS opens the way to perform multi-fold and even fully differential cross section (FDCS) studies, with reasonably good energy/momentum resolutions. The cross sections differential in scattering angle provide rich information of the impact parameter dependent collision dynamics where electron emission mechanism in a broad range of collision velocities have been studied [77].

In low to intermediate energy EC collisions, it is now possible to perform studies on quantum state-resolved charge exchange processes with high resolution. Figure 10 shows single-EC in collisions of 63 keV $Ne^{7+}$ ions with He studied using COLTRIMS [78], where the state-resolved differential cross sections have been determined with respect to the principal quantum number, subshell levels and spin states of the captured electron. Furthermore, it is possible to explore the high resolution method to study the electron correlations in double and multiple EC processes, and give new insight into mechanisms, e.g. symmetric/asymmetric population, sequential/non-sequential processes.

At high impact energies, only few measurements of FDCSs have been done, where first Born approximation is assumed to be valid. Schulz *et al* [79] found unexpected discrepancies of electron angular distribution between theory and experiment in the perpendicular plane for single ionization

of He by 100 MeV/$u$ $C^{6+}$. This 'C$^{6+}$ puzzle' frustrates the community and needs to be solved in future experiments.

When more electrons are involved in a charge exchange process, electron correlation plays an important role, which is essential to understand many-body dynamics. For instance, in double-electron transfer with one electron ionized collisions of 80 keV/$u$ $Ne^{8+}$ on He, distinct features of the correlated processes can be well separated from the un-correlated ones [80]. With multiple coincidence technique, Gao *et al* [81] obtained fully differential data for transfer ionization process of one electron transfer with two electron ionized (five-body process). It is found that the sum electron momentum and the individual electron momenta are surprisingly strongly correlated with the total momentum transfer. Dedicated experiments for multiple ionization are expected to better understand these phenomena, and rigorous theoretical treatments are needed as well.

In the past decades, the targets used in ion collisions have been extended from simple atom to molecules and even to atomic/molecular dimers/trimers, etc. The structure information of these complex system serves as extra dimensions for the investigation of the structure involved collision dynamics. The molecular frame can be determined from the coincidence detection of charged particles produced in these processes. Consequently, the characteristic of matter wave of massive particles has also been observed at atomic scale: Fraunhofer diffraction in atomic collisions and interference in molecule involved collisions. In the works of Schmidt *et al* [82] and Zhang *et al* [83], they revealed that the interference pattern, which is in contrast to the optical double-slit experiment, resulted from the $\pi$-phase shift due to the parity change of molecular hydrogen ion in the collision. Later, the double-slit interference effects is used to extract the phase information in collisions with asymmetric diatomic molecules [84]. Figure 11 shows the asymmetry and shift of two-center interference patterns of $He^{2+}$ on CO. In two different colliding energies, the scattering phase differences of $He^{2+}$ on C compared to $He^{2+}$ on O can be extracted.

**Current and future challenges.** Despite many successes in ion-atom collision studies, there are still challenges. To the least extent, here are some possible perspectives that one can look forwards in the near future. First, photon measurements in coincidence with charged particles. In ion collisions, photon emission from residual ions (recoils and/or scattered ions in multiply excited states) can provide additional information about the collision dynamics. However, so far sophisticated techniques where photon and charged particles are recorded in coincidence are still quite challenging.

Second, the phase information of the collision processes. Scattering phase contains important information about collision dynamics. In atomic transitions induced by the laser field, it has been shown that phase measurements show great potential in deeper understanding of the few-body problem. However, the long-range property of the Coulomb field of the projectile in ion collisions makes it nearly impossible to define the start/end point of the interactions as those of the
<figure><img src="image_13.png" /><figcaption>Figure 10. (a) Q-value spectrum and energy levels of Ne<sup>6+</sup> following single-electron capture from He at 0.355 au velocity. (b) Decomposition of the 2s4l spectrum into different subshells and spin states. (c) Differential capture cross sections [78]. Reproduced from [78]. © IOP Publishing Ltd. All rights reserved.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 11. Relative scattering phases extraction of He<sup>2+</sup> on C and O from two-center interference patterns of He<sup>2+</sup> + CO double capture collisions. Reprinted figure with permission from [84]. Copyright 2018 by the American Physical Society.</figcaption></figure>

photon experiments. So far there is only one successful scattering phase measurement achieved via two-center interference effects in ion collision processes [84], and it still challenges the community in finding proper ways to extract dedicated phase information of ion-atom collision dynamics.

Last but not least, electron correlation still challenges the understanding of collision dynamics. HCIs have strong Coulomb potential and thus can capture many electrons simultaneously when interacting with atoms at low and intermediate impact energies. These electrons usually populate to highly excited states and will decay via autoionization or radiation, where electron correlation plays crucial roles. High precision measurements are needed to understand the dynamics and decay process. When a HCI with relativistic velocity interacts with atoms/molecules, the interacting time is in a sub-attosecond time scale, similar to an ultrafast and strong electro-magnetic pulse, and target electrons can be kicked out instantly. This may create the ideal Heisenberg condition for studying electron correlation in an atom. On the other hand, strong electromagnetic field and relativistic will provide unprecedented extreme conditions and will lead to new phenomena in collision processes. All these investigations will challenge the present experimental technologies.

Advances in science and technology to meet challenges.
Theoretical description of ion-atom collision dynamics is
making progresses (see section 5) thanks to more
experimental differential data and the rapid increase of
<figure><img src="image_14.png" /><figcaption>Figure 10. (a) Q-value spectrum and energy levels of Ne<sup>6+</sup> following single-electron capture from He at 0.355 au velocity. (b) Decomposition of the 2s4l spectrum into different subshells and spin states. (c) Differential capture cross sections [78]. Reproduced from [78]. © IOP Publishing Ltd. All rights reserved.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 11. Relative scattering phases extraction of He<sup>2+</sup> on C and O from two-center interference patterns of He<sup>2+</sup> + CO double capture collisions. Reprinted figure with permission from [84]. Copyright 2018 by the American Physical Society.</figcaption></figure>

photon experiments. So far there is only one successful scattering phase measurement achieved via two-center interference effects in ion collision processes [84], and it still challenges the community in finding proper ways to extract dedicated phase information of ion-atom collision dynamics.

Last but not least, electron correlation still challenges the understanding of collision dynamics. HCIs have strong Coulomb potential and thus can capture many electrons simultaneously when interacting with atoms at low and intermediate impact energies. These electrons usually populate to highly excited states and will decay via autoionization or radiation, where electron correlation plays crucial roles. High precision measurements are needed to understand the dynamics and decay process. When a HCl with relativistic velocity interacts with atoms/molecules, the interacting time is in a sub-attosecond time scale, similar to an ultrafast and strong electro-magnetic pulse, and target electrons can be kicked out instantly. This may create the ideal Heisenberg condition for studying electron correlation in an atom. On the other hand, strong electromagnetic field and relativistic will provide unprecedented extreme conditions and will lead to new phenomena in collision processes. All these investigations will challenge the present experimental technologies.

Advances in science and technology to meet challenges.
Theoretical description of ion-atom collision dynamics is
making progresses (see section 5) thanks to more
experimental differential data and the rapid increase of
computation power. On the experimental side, MOTRIMS will provide much higher resolution for collision studies although only applicable to several atomic species. Some attempts have been made to incorporate photon detection in reaction microscope to get more accurate electronic level information. We are developing new ideas of scattering phase measurement, which will help to study details of collision dynamics. We pointed out a novel very fast breakup mechanism of dicationic acetylene dimers resulting from intermolecular proton transfer induced by ions [85] and even expecting breakup resulted from heavy ion transfer process in other dimers. These are important and relevant to DNA double-strand breakup induced by radiation. Furthermore, the rapid development of laser technology in recent years may help to realize laser assisted collisions studies.

In the meantime, new storage ring facilities under construction now, which will be equipped with reaction microscope and high resolution electron spectrometer, will provide HCIs with relativistic velocity, and further create excellent opportunities for investigation of collision dynamics under extreme conditions.

**Concluding remarks.** Ion-atom collision processes are by far the best choice to explore the few-body problem. First, in atomic physics the underlying Coulomb force between charged particles is precisely known and structure properties can be obtained with high accuracies, it guarantees that all discrepancies between experimental observations and theoretical predictions result from the quantum models. Second, in ion-atom collisions the number of active interacting particles can be well controlled which is essential to examine few-body processes. Few-body problem is a long-standing fundamental topic in science, more dimensions of freedoms will be accessible in experiments with the new developing technologies, and it is definitely needed to investigate the few-body dynamics in atomic collisions.

## Acknowledgments

This work was supported by the national Key R&D program of China under Grant No.2017YFA0402300.
computation power. On the experimental side, MOTRIMS will provide much higher resolution for collision studies although only applicable to several atomic species. Some attempts have been made to incorporate photon detection in reaction microscope to get more accurate electronic level information. We are developing new ideas of scattering phase measurement, which will help to study details of collision dynamics. We pointed out a novel very fast breakup mechanism of dicationic acetylene dimers resulting from intermolecular proton transfer induced by ions [85] and even expecting breakup resulted from heavy ion transfer process in other dimers. These are important and relevant to DNA double-strand breakup induced by radiation. Furthermore, the rapid development of laser technology in recent years may help to realize laser assisted collisions studies.

In the meantime, new storage ring facilities under construction now, which will be equipped with reaction microscope and high resolution electron spectrometer, will provide HCIs with relativistic velocity, and further create excellent opportunities for investigation of collision dynamics under extreme conditions.

**Concluding remarks.** Ion-atom collision processes are by far the best choice to explore the few-body problem. First, in atomic physics the underlying Coulomb force between charged particles is precisely known and structure properties can be obtained with high accuracies, it guarantees that all discrepancies between experimental observations and theoretical predictions result from the quantum models. Second, in ion-atom collisions the number of active interacting particles can be well controlled which is essential to examine few-body processes. Few-body problem is a long-standing fundamental topic in science, more dimensions of freedoms will be accessible in experiments with the new developing technologies, and it is definitely needed to investigate the few-body dynamics in atomic collisions.

## Acknowledgments

This work was supported by the national Key R&D program of China under Grant No.2017YFA0402300.
# 8. Interference effects in ion-molecule collisions

Roberto D Rivarola and Omar A Fojón

Instituto de Física Rosario (CONICET—UNR), Argentina

**Status.** A controversy between the corpuscular or wave nature of electrons remained for centuries. Based on the oscillatory structure observed in measurements of photoabsorption cross sections of the diatomic $N_2$ and $O_2$ molecules, in 1966 Cohen and Fano [86] suggested that this behavior is obtained from the fact that an electron is coherently emitted from the proximities of the nuclei of the targets. This mechanism was associated with the two-slit scenario of the Thomas Young experiment [87], where the coherent superposition of electrons demonstrated the wave character of these quantum objects. The effect was measured 35 years later than the Cohen and Fano prediction but for impact of 60 MeV/u Kr$^{34+}$on $H_2$ molecules [88]. In order to give visibility to the effect, experimental double differential cross sections (DDCS) as a function of the final electron velocity, at fixed emission angles, where divided by the corresponding theoretical ones for two independent effective H atoms (see figure 12; see also [89] for a case where atomic H experimental measurements were employed for comparison). Fit straight lines were drawn to enhance the visibility of the spectral structure. As a result, interference patterns were observed and a simple theoretical interpretation was given. Encouraged by this seminal work, numerous experiments and theoretical models were developed in the following years

In particular, evidences on the existence of the effect were also given for the impact of photon and electron beams, showing that the essence of this coherent behavior resided in the two-center character of the target and only depends in a secondary aspect on the projectile type (for a general review see [90]).

Usually for ion beams, perturbative approximations were employed to describe the reaction within an independent electron approximation and assuming that the residual target (including the non-ionized electrons) remains as frozen until the projectile-target interaction ends. This assumption is supported by the fact that the collision time considered is of the order of the sub-femtoseconds while the vibrational and rotational ones are much larger. Consequently, the orientation of the molecule remains fixed in space.

In general, the molecular bound orbitals are described as linear combinations of different bound states of the atoms that compose the target, and the molecular continuum in the exit channel is described by means of effective continuum states. In order to obtain DDCS the matrix elements describing the collision are integrated on the momentum transfer and then averaged over all possible molecular orientations.

Further theoretical work for $H_2$ targets was focussed to describe the dependence of the angular distribution of emitted electrons with the molecular orientation, for impact of high energetic bare carbon ions. Thus, triple differential cross sections (TDCS) were calculated for a coplanar geometry, where the molecule, the emitted electron and the projectile velocity are all in the same plane. It was shown that the

<figure><img src="image_15.png" /><figcaption>Figure 12. DDCS as a function of the electron velocity at fixed electron emission angles. See text. Reprinted figure with permission from [88] Copyright 2001 by the American Physical Society.</figcaption></figure>

presence of interference patterns is favored for a molecular orientation coinciding with the one of the initial projectile velocity $v$. The contribution from different momentum transfers tends to shadow the corresponding oscillations as the molecule is aligned perpendicularly to $v$.

FDCSs were also calculated for proton beams in order to investigate the contribution of fixed values of the momentum transfer. They put in evidence that for certain kinematical conditions when the molecular orientation is perpendicular to the impact velocity, the so called recoil peak tends to disappear due to destructive interference contributions.

Concerning the influence of the molecular orientation, experimental and theoretical results of the electron spectra as a function of projectile scattering angle at fixed electron losses, suggest that for small scattering angles a transverse molecular orientation dominates whereas for large scattering ones a parallel orientation is preferred.

Further research for proton impact was extended to the case of multi-orbital targets like $N_2$ molecules in a coplanar geometry [91]. The theoretical studies show the presence of interference patterns separately for each one of the molecular orbitals on the angular distribution of emitted electrons (see figure 13). The number of lobes revealing the apparition of coherent emission tends to increase as the electron energies
## 8. Interference effects in ion-molecule collisions

Roberto D Rivarola and Omar A Fojón

Instituto de Física Rosario (CONICET—UNR), Argentina

**Status.** A controversy between the corpuscular or wave nature of electrons remained for centuries. Based on the oscillatory structure observed in measurements of photoabsorption cross sections of the diatomic $N_2$ and $O_2$ molecules, in 1966 Cohen and Fano [86] suggested that this behavior is obtained from the fact that an electron is coherently emitted from the proximities of the nuclei of the targets. This mechanism was associated with the two-slit scenario of the Thomas Young experiment [87], where the coherent superposition of electrons demonstrated the wave character of these quantum objects. The effect was measured 35 years later than the Cohen and Fano prediction but for impact of 60 MeV/u Kr$^{34+}$on $H_2$ molecules [88]. In order to give visibility to the effect, experimental double differential cross sections (DDCS) as a function of the final electron velocity, at fixed emission angles, where divided by the corresponding theoretical ones for two independent effective H atoms (see figure 12; see also [89] for a case where atomic H experimental measurements were employed for comparison). Fit straight lines were drawn to enhance the visibility of the spectral structure. As a result, interference patterns were observed and a simple theoretical interpretation was given. Encouraged by this seminal work, numerous experiments and theoretical models were developed in the following years

In particular, evidences on the existence of the effect were also given for the impact of photon and electron beams, showing that the essence of this coherent behavior resided in the two-center character of the target and only depends in a secondary aspect on the projectile type (for a general review see [90]).

Usually for ion beams, perturbative approximations were employed to describe the reaction within an independent electron approximation and assuming that the residual target (including the non-ionized electrons) remains as frozen until the projectile-target interaction ends. This assumption is supported by the fact that the collision time considered is of the order of the sub-femtoseconds while the vibrational and rotational ones are much larger. Consequently, the orientation of the molecule remains fixed in space.

In general, the molecular bound orbitals are described as linear combinations of different bound states of the atoms that compose the target, and the molecular continuum in the exit channel is described by means of effective continuum states. In order to obtain DDCS the matrix elements describing the collision are integrated on the momentum transfer and then averaged over all possible molecular orientations.

Further theoretical work for $H_2$ targets was focussed to describe the dependence of the angular distribution of emitted electrons with the molecular orientation, for impact of high energetic bare carbon ions. Thus, triple differential cross sections (TDCS) were calculated for a coplanar geometry, where the molecule, the emitted electron and the projectile velocity are all in the same plane. It was shown that the

<figure><img src="image_16.png" /><figcaption>Figure 12. DDCS as a function of the electron velocity at fixed electron emission angles. See text. Reprinted figure with permission from [88] Copyright 2001 by the American Physical Society.</figcaption></figure>

presence of interference patterns is favored for a molecular orientation coinciding with the one of the initial projectile velocity $v$. The contribution from different momentum transfers tends to shadow the corresponding oscillations as the molecule is aligned perpendicularly to $v$.

FDCSs were also calculated for proton beams in order to investigate the contribution of fixed values of the momentum transfer. They put in evidence that for certain kinematical conditions when the molecular orientation is perpendicular to the impact velocity, the so called recoil peak tends to disappear due to destructive interference contributions.

Concerning the influence of the molecular orientation, experimental and theoretical results of the electron spectra as a function of projectile scattering angle at fixed electron losses, suggest that for small scattering angles a transverse molecular orientation dominates whereas for large scattering ones a parallel orientation is preferred.

Further research for proton impact was extended to the case of multi-orbital targets like $N_2$ molecules in a coplanar geometry [91]. The theoretical studies show the presence of interference patterns separately for each one of the molecular orbitals on the angular distribution of emitted electrons (see figure 13). The number of lobes revealing the apparition of coherent emission tends to increase as the electron energies
<figure><img src="image_16.png" /><figcaption>Figure 13. Angular distribution of emitted electrons for each N₂ orbital at a 100 eV electron energy. Molecular orientation parallel to v. See text. Reproduced from [91] © IOP Publishing Ltd. All rights reserved.</figcaption></figure>

increase and appear to be preferable for a molecular orientation parallel to v (directed to 0°), as it happens for H₂. The oscillations corresponding to the different orbitals are shifted the ones with respect to the others, so that DDCS resulting from summing all their contributions do not present any signature of interference effects, as observed in existing experiments [92].

**Current and future challenges.** An important number of improvements are necessary from both theoretical and experimental sides. A tentative short list of them is given in the following.

From the theoretical aspect, it appears as relevant to investigate the role played by electron correlation not only in the description of molecular orbitals but also in an appropriate description of the molecular continuum in the exit channel, moreover in the case of multi-electron orbitals. The inclusion of vibrational and rotational movements are also necessary in the future.

Furthermore, measurements of multiple differential cross sections that take into account simultaneously the ejected

electron coordinates and the orientation of the molecule, including or not the projectile scattering angle, appear as fundamental for a more complete understanding of the effect.

The signatures of constructive and destructive interference contributions on FDCS for different molecular orientations with respect to the momentum transfer vector, in coplanar and no-coplanar geometries, are relevant. For the case of electron impact ionization of H₂, for coplanar geometries, it is observed that under certain kinematical conditions the binary and recoil peaks may disappear, depending on the gerade or ungerade character of final residual states [93]. Recent predictions [94] for ions seem to show a similar behavior to the one obtained for electron beams. The sum over all molecular orientations allows an adequate description of the Physics involved in existing experimental TDCS and an increase of the binary peak is observed due to constructive interferences.

The influence of the symmetry character of the bound states is a main aspect to consider. For example, the inner gerade and ungerade orbitals of the N₂ target show emission spectra in phase opposition. This effect has been shown to come from the mentioned symmetry character. Experimental research distinguishing the initial and final orbitals is an ambitious but useful project.

The verification of the possible existence of double frequency interference effects associated with the scattering of the ejected electron on both molecular centers is a matter of further research [95].

**Advances in science and technology to meet challenges.** As it was before mentioned a lot of theoretical work is still necessary for a more complete understanding of the Physics present in interference effects due to coherent electron emission from molecular targets. From the experimental point of view, a complete mapping of all resulting particles appears as a challenge, including the orientation of the molecular target during the collision. It could be perhaps obtained combining cold target recoil ion momentum spectroscopy (COLTRIMS) and laser techniques.

**Concluding remarks.** A brief review on the state of the art on the physical interpretation of interference effects due to coherent electron emission from molecular targets impacted by fast ion beams was presented. Future challenges for theoretical and experimental research lines are proposed.

## Acknowledgments

The authors acknowledge financial support from the Agencia Nacional de Investigaciones Científicas y Técnicas of the República Argentina through the project PICT 2015-3392. Discussions with Guillaume Laurent are acknowledged.
<figure><img src="image_17.png" /><figcaption>Figure 13. Angular distribution of emitted electrons for each N₂ orbital at a 100 eV electron energy. Molecular orientation parallel to v. See text. Reproduced from [91] © IOP Publishing Ltd. All rights reserved.</figcaption></figure>

increase and appear to be preferable for a molecular orientation parallel to v (directed to 0°), as it happens for H₂. The oscillations corresponding to the different orbitals are shifted the ones with respect to the others, so that DDCS resulting from summing all their contributions do not present any signature of interference effects, as observed in existing experiments [92].

**Current and future challenges.** An important number of improvements are necessary from both theoretical and experimental sides. A tentative short list of them is given in the following.

From the theoretical aspect, it appears as relevant to investigate the role played by electron correlation not only in the description of molecular orbitals but also in an appropriate description of the molecular continuum in the exit channel, moreover in the case of multi-electron orbitals. The inclusion of vibrational and rotational movements are also necessary in the future.

Furthermore, measurements of multiple differential cross sections that take into account simultaneously the ejected

electron coordinates and the orientation of the molecule, including or not the projectile scattering angle, appear as fundamental for a more complete understanding of the effect.

The signatures of constructive and destructive interference contributions on FDCS for different molecular orientations with respect to the momentum transfer vector, in coplanar and no-coplanar geometries, are relevant. For the case of electron impact ionization of H₂, for coplanar geometries, it is observed that under certain kinematical conditions the binary and recoil peaks may disappear, depending on the gerade or ungerade character of final residual states [93]. Recent predictions [94] for ions seem to show a similar behavior to the one obtained for electron beams. The sum over all molecular orientations allows an adequate description of the Physics involved in existing experimental TDCS and an increase of the binary peak is observed due to constructive interferences.

The influence of the symmetry character of the bound states is a main aspect to consider. For example, the inner gerade and ungerade orbitals of the N₂ target show emission spectra in phase opposition. This effect has been shown to come from the mentioned symmetry character. Experimental research distinguishing the initial and final orbitals is an ambitious but useful project.

The verification of the possible existence of double frequency interference effects associated with the scattering of the ejected electron on both molecular centers is a matter of further research [95].

**Advances in science and technology to meet challenges.** As it was before mentioned a lot of theoretical work is still necessary for a more complete understanding of the Physics present in interference effects due to coherent electron emission from molecular targets. From the experimental point of view, a complete mapping of all resulting particles appears as a challenge, including the orientation of the molecular target during the collision. It could be perhaps obtained combining cold target recoil ion momentum spectroscopy (COLTRIMS) and laser techniques.

**Concluding remarks.** A brief review on the state of the art on the physical interpretation of interference effects due to coherent electron emission from molecular targets impacted by fast ion beams was presented. Future challenges for theoretical and experimental research lines are proposed.

## Acknowledgments

The authors acknowledge financial support from the Agencia Nacional de Investigaciones Científicas y Técnicas of the República Argentina through the project PICT 2015-3392. Discussions with Guillaume Laurent are acknowledged.
# 9. Ion-molecule collisions—large molecules

Lokesh C Tribedi

Tata Institute of Fundamental Research, India

**Status.** Research on heavy ion collisions with atoms, molecules, clusters and solids is a natural extension of the electron-atom collision studies. While electron induced atomic molecular collision offers an excellent tool to probe the basic structure, properties and collisional aspects of the atoms and molecules, the collisions with ions have a wider scope due to the possibility of the variation of perturbation strength on a wider scale. This allows one to deal with the collision mechanisms from weak to strong perturbation regime. With the gradual development of experimental tools, such as, accelerators, ion sources, fast-electronics and detection systems, many of the investigations are renewed due to its importance towards fundamental interest in molecular physics as well as for its application in interdisciplinary sciences: radiation-biology, plasma physics, astrophysics and astrochemistry. Besides the well-known mechanisms of molecular interactions, completely new decay process—interatomic and intermolecular Coulombic decay (ICD) has been discovered [96] in case of clusters. It is only recently that the Young-type electron interference due to spatial coherence has been observed in a molecular-double slit [97, 98] under heavy ion-collisions following the original prediction by Cohen and Fano (1966). The experimental study of electron emission from atomic H under heavy ion was crucial to identify, unambiguously, the interference oscillation. Besides this, a new approach of using forward–backward asymmetry parameter to identify the interference and the existence of a second order interference were some of the highlights. Synchrotron based photo-ionization studies by Uwe Becker et al [99] as well as fast e-beam induced e-emission (Tribedi et al PRA 2016) have revealed the spatial coherence induced oscillations for $N_2$ and $O_2$ molecules. The interference oscillation has been used to estimate the bond-length in case of simple hydrocarbon molecules.

The fragmentation dynamics of multiply charged smaller polyatomic molecular ions using high resolution recoil-ion momentum imaging is under study to identify under what condition a concerted or sequential processes are crucial [100].

A new dimension to this research is the wide spread experimental and theoretical investigation of ionization and fragmentation of biologically relevant large and complex molecules under the interaction of swift ions. A detailed and systematic investigation is likely to open new avenue towards the applications in related fields, such as, radiation biology, in particular, for hadron therapy. In heavy-ion radiation therapy, the energy loss of swift ions inside the body exhibits a maximum in the Bragg peak region. Therefore, the study of ionization or fragmentation of the nucleobases, DNA, RNA, sugar phosphate backbone or water molecule over a wide energy range, across this Bragg-peak region will be of great importance. It is now well known that the electrons of energy, even lower than the ionization threshold, are primarily responsible for the single and

<figure><img src="image_17.png" /><figcaption>Figure 14. (a) TCS for ionization of uracil by $C_4 + [101]$ and p [102]. (b) Same data [101] along with a scaling formulation (dashed-line) by Montenegro et al [103].</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure 15. (a) e-DDCS for 76 MeV $F^{9+}$ colliding with $C_{60}$ [104]. (b) Relative DDCS (forward backward ratio) for Coronene under 60 MeV $O^{8+}$ impact [105].</figcaption></figure>

double strand breaks. A detailed knowledge of the ion-induced electron emission mechanism [101, 102] is of importance for radiobiologists. One may refer to a series of experimental work by Mark et al; Itoh et al; Tribedi et al and Moretto-Capelle et al. There has been substantial progress in theoretical modeling too (e.g see Rivarola et al, Champion et al and Kirchner et al). One example is given in figure 14. Calculations based on the CDW-EIS model predict about twice the total ionization cross section (TCS) measured for Uracil by fast $C^{4+}$-ion impact at high energy (figure 14(a)), but it overestimates by a larger factor at the peak region. Montenegro et al showed that the inclusion of transfer-ionization, in a scaling formulation [103] (figure 14(b)) gives excellent qualitative agreement.

Another direction of this research involves the study of plasmon excitation by detecting the plasmon electron peak in the low energy part of the e-spectrum [104] for $C_{60}$ (figure 15(a) as well as PAH molecules [105] (e.g. for coronene as shown in figure 15(b)). Polycyclic aromatic hydrocarbon (PAH) molecules are quite abundant in the interstellar space and, hence, attract lot of interest in astrophysics and astrochemistry. Recently observed [103] plasmon excitation peak at ~17 eV for coronene helps to explore the UV photon absorption by the PAHs in the interstellar medium. Besides PAHs, the $C_{60}$ fullerene and its clusters are of importance in the study of many body physics and giant plasmon excitation. The clusters of PAH are also important for nano-electronics and UV plasmonic devices. The ion collisions with such clusters and the question of instability
# 9. Ion-molecule collisions—large molecules

Lokesh C Tribedi

Tata Institute of Fundamental Research, India

**Status.** Research on heavy ion collisions with atoms, molecules, clusters and solids is a natural extension of the electron-atom collision studies. While electron induced atomic molecular collision offers an excellent tool to probe the basic structure, properties and collisional aspects of the atoms and molecules, the collisions with ions have a wider scope due to the possibility of the variation of perturbation strength on a wider scale. This allows one to deal with the collision mechanisms from weak to strong perturbation regime. With the gradual development of experimental tools, such as, accelerators, ion sources, fast-electronics and detection systems, many of the investigations are renewed due to its importance towards fundamental interest in molecular physics as well as for its application in interdisciplinary sciences: radiation-biology, plasma physics, astrophysics and astrochemistry. Besides the well-known mechanisms of molecular interactions, completely new decay process—interatomic and intermolecular Coulombic decay (ICD) has been discovered [96] in case of clusters. It is only recently that the Young-type electron interference due to spatial coherence has been observed in a molecular-double slit [97, 98] under heavy ion-collisions following the original prediction by Cohen and Fano (1966). The experimental study of electron emission from atomic H under heavy ion was crucial to identify, unambiguously, the interference oscillation. Besides this, a new approach of using forward–backward asymmetry parameter to identify the interference and the existence of a second order interference were some of the highlights. Synchrotron based photo-ionization studies by Uwe Becker et al [99] as well as fast e-beam induced e-emission (Tribedi et al PRA 2016) have revealed the spatial coherence induced oscillations for $N_2$ and $O_2$ molecules. The interference oscillation has been used to estimate the bond-length in case of simple hydrocarbon molecules.

The fragmentation dynamics of multiply charged smaller polyatomic molecular ions using high resolution recoil-ion momentum imaging is under study to identify under what condition a concerted or sequential processes are crucial [100].

A new dimension to this research is the wide spread experimental and theoretical investigation of ionization and fragmentation of biologically relevant large and complex molecules under the interaction of swift ions. A detailed and systematic investigation is likely to open new avenue towards the applications in related fields, such as, radiation biology, in particular, for hadron therapy. In heavy-ion radiation therapy, the energy loss of swift ions inside the body exhibits a maximum in the Bragg peak region. Therefore, the study of ionization or fragmentation of the nucleobases, DNA, RNA, sugar phosphate backbone or water molecule over a wide energy range, across this Bragg-peak region will be of great importance. It is now well known that the electrons of energy, even lower than the ionization threshold, are primarily responsible for the single and

<figure><img src="image_18.png" /><figcaption>Figure 14. (a) TCS for ionization of uracil by $C_4 + [101]$ and p [102]. (b) Same data [101] along with a scaling formulation (dashed-line) by Montenegro et al [103].</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Figure 15. (a) e-DDCS for 76 MeV $F^{9+}$ colliding with $C_{60}$ [104]. (b) Relative DDCS (forward backward ratio) for Coronene under 60 MeV $O^{8+}$ impact [105].</figcaption></figure>

double strand breaks. A detailed knowledge of the ion-induced electron emission mechanism [101, 102] is of importance for radiobiologists. One may refer to a series of experimental work by Mark et al; Itoh et al; Tribedi et al and Moretto-Capelle et al. There has been substantial progress in theoretical modeling too (e.g see Rivarola et al, Champion et al and Kirchner et al). One example is given in figure 14. Calculations based on the CDW-EIS model predict about twice the total ionization cross section (TCS) measured for Uracil by fast $C^{4+}$-ion impact at high energy (figure 14(a)), but it overestimates by a larger factor at the peak region. Montenegro et al showed that the inclusion of transfer-ionization, in a scaling formulation [103] (figure 14(b)) gives excellent qualitative agreement.

Another direction of this research involves the study of plasmon excitation by detecting the plasmon electron peak in the low energy part of the e-spectrum [104] for $C_{60}$ (figure 15(a) as well as PAH molecules [105] (e.g. for coronene as shown in figure 15(b)). Polycyclic aromatic hydrocarbon (PAH) molecules are quite abundant in the interstellar space and, hence, attract lot of interest in astrophysics and astrochemistry. Recently observed [103] plasmon excitation peak at ~17 eV for coronene helps to explore the UV photon absorption by the PAHs in the interstellar medium. Besides PAHs, the $C_{60}$ fullerene and its clusters are of importance in the study of many body physics and giant plasmon excitation. The clusters of PAH are also important for nano-electronics and UV plasmonic devices. The ion collisions with such clusters and the question of instability