Stefan Schramm Mirko Schäfer Editors New Horizons in Fundamental Physics FIAS Interdisciplinary Science Series

FIAS Interdisciplinary Science Series Series Editor: Walter Greiner

Editor-in-chief Walter Greiner, Frankfurt am Main, Germany

Editorial Board Ernst Bamberg, Frankfurt am Main, Germany Marc Thilo Figge, Jena, Germany Thomas Haberer, Heidelberg, Germany Volker Lindenstruth, Frankfurt am Main, Germany Joachim Reinhardt, Frankfurt, Germany Klaus Schulten, Urbana, USA Wolf Singer, Frankfurt am Main, Germany Horst Stöcker, Darmstadt, Germany The Frankfurt Institute for Advanced Studies (FIAS) is an independent research institute pursuing cutting-edge theoretical research in the areas of physics, life-science and chemistry, neuroscience, and computer science. A central aim of FIAS is to foster interdisciplinary co-operation and to provide a common platform for the study of the structure and dynamics of complex systems, both animate and inanimate. FIAS closely cooperates with the science faculties of Goethe University (Frankfurt) and with various experimentally oriented research centers in the vicinity. The series is meant to highlight the work of researchers at FIAS and its partner institutions, illustrating current progress and also reﬂecting on the historical development of science. The series comprises monographs on specialized current research topics, reviews summarizing the state of research in more broadly-framed areas, and volumes of conferences organized by FIAS.

More information about this series at http://www.springer.com/series/10781 Stefan Schramm • Mirko Schäfer Editors

New Horizons in Fundamental Physics

123 Editors Stefan Schramm Mirko Schäfer Frankfurt Institute for Advanced Studies Frankfurt Institute for Advanced Studies (FIAS) (FIAS) Goethe University Frankfurt Frankfurt am Main Frankfurt am Main, Hessen Germany Germany

FIAS Interdisciplinary Science Series ISBN 978-3-319-44164-1 ISBN 978-3-319-44165-8 (eBook) DOI 10.1007/978-3-319-44165-8

Library of Congress Control Number: 2016947749

© Springer International Publishing Switzerland 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.

Printed on acid-free paper

This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland Preface

Modern nuclear physics has become a highly complex area of research covering many topics with close connections to a whole array of different fields of physics. Therefore, from time to time, scientists working in this field need to “escape” from their own special topic of research to get a better understanding of the whole field and their interconnections, therewith also to gain new insight and novel ideas to tackle their scientific projects. In this spirit, we organized the Symposium New Horizons in Fundamental Physics, which took place at Makutsi Safari Farm in South Africa from November 23 to 27, 2016. The event followed a previous very successful symposium at the same place in 2011. It successfully managed to bring together world-class scientists with reports on cutting-edge research and very valuable and insightful extensive discussions in a wonderful setting, surrounded by South African wilderness. The topics of the symposium included nuclear structure calculations of cluster states, exotic neutron-rich isotopes, and the search for long-lived new superheavy elements. Relativistic heavy-ion collisions with their wide spectrum of observables and in a vast range of bombarding energies were discussed in detail. The effect of extreme conditions of temperature and density and ultrahigh electric and magnetic fields on nuclear, atomic, and astrophysical systems was investigated. Among many other facets of the general field, the status of highly accurate calculations of quantum electrodynamics effects in atoms was addressed extensively. Demonstrating the relevance of the research for other fields, methods of describing complex systems were translated to modeling the extension of the European electricity grid. These and more highly timely research topics were presented at the symposium and can be found in this volume. Aside from the many highly valuable contributions by the participants, this symposium could not have succeeded without the tireless work by Ms. Laura Quist and Daniela Radulescu, who were heavily involved in the many tasks before, during, and after the event. We also want to acknowledge the excellent organization and care given to us by Dr. Gerhard Weber, his family, and team from Makutsi

v vi Preface

Safari Farm, who were always very helpful and readily available at every point of time during the meeting. The symposium was held in honor of Prof. Walter Greiners’ 80th birthday. Much of the program was inspired by him during the months of preparation of the event. His incredibly varied research in nuclear physics stretching over many decades is reflected by the large range of topics covered at the meeting. In many of these fields, he has contributed with important and seminal work, inspiring numerous follow-up research activities. Therefore, we believe that this symposium with its unique combination of scientific topics is a fitting tribute to Walter Greiners’ profound and lasting influence on nuclear physics. Just as this manuscript was about to go to press, we received very sad news. Walter Greiner has passed away. He was our friend, teacher and mentor over many years, and a source of inspiration for much of the work presented in this volume. He will be dearly missed by all of us. We hope that this book will serve as a small but heartfelt recognition of Walter’s lasting scientific contribution to physics.

Frankfurt am Main, Germany Stefan Schramm June 2016 Mirko Schäfer Contents

Part I Nuclear Structure and Superheavy Elements Intertwining of Greiner’s Theoretical Works and Our Experimental Studies ...... 3 J.H. Hamilton, A.V. Ramayya and E.H. Wang Eighty Years of Research on Super-Heavy Nuclei ...... 15 Sigurd Hofmann Perspectives of Heavy and Superheavy Nuclei Research ...... 31 A.V. Karpov, V.I. Zagrebaev and W. Greiner Superheavy Element Chemistry—New Experimental Results Challenge Theoretical Understanding ...... 41 R. Eichler 25 Years of FRS Experiments and New Horizons ...... 55 H. Geissel, G. Münzenberg and C. Scheidenberger SHE Research with Rare-Isotope Beams, Challenges and Perspectives, and the New Generation of SHE Factories ...... 81 G. Münzenberg, H.M. Devaraja, T. Dickel, H. Geissel, M. Gupta, S. Heinz, S. Hofmann, W.R. Plass, C. Scheidenberger, J.S. Winﬁeld and M. Winkler Multi-modal Collinear Ternary Fission ...... 91 W. von Oertzen and A.K. Nasirov From the Stable to the Exotic: Clustering in Light Nuclei...... 103 C. Beck Towards Laser Spectroscopy of Superheavy Elements...... 115 H. Backe

vii viii Contents

Part II Physics of Heavy-Ion Collisions Chemical Freeze-Out Conditions in Hadron Resonance Gas ...... 127 V. Vovchenko, M.I. Gorenstein, L.M. Satarov and H. Stöcker The QCD Phase Diagram and Hadron Formation in Relativistic Nuclear Collisions ...... 139 Francesco Becattini, Marcus Bleicher, Jan Steinheimer and Reinhard Stock Degrees of Freedom of the Quark Gluon Plasma, Tested by Heavy Mesons ...... 151 H. Berrehrah, M. Nahrgang, T. Song, V. Ozvenchuck, P.B. Gossiaux, K. Werner, E. Bratkovskaya and J. Aichelin Electromagnetic Emissivity of Hot and Dense Matter ...... 167 E.L. Bratkovskaya, O. Linnyk and W. Cassing Heavy-Ion Collisions: Status of Chemical Equilibrium ...... 181 J. Cleymans Novel Developments of HYDJET++ Model for Ultra-relativistic Heavy-Ion Collisions ...... 187 L. Bravina, B.H. Brusheim Johansson, J. Crkovská, G. Eyyubova, V. Korotkikh, I. Lokhtin, L. Malinina, E. Nazarova, S. Petrushanko, A. Snigirev and E. Zabrodin Jet Tomography in Heavy-Ion Collisions—Challenges, Results, and Open Problems ...... 199 Barbara Betz

Part III QED—Strong Fields and High Precision Probing QED Vacuum with Heavy Ions ...... 211 Johann Rafelski, Johannes Kirsch, Berndt Müller, Joachim Reinhardt and Walter Greiner Laser Assisted Breit-Wheeler and Schwinger Processes...... 253 T. Nousch, A. Otto, D. Seipt, B. Kämpfer, A.I. Titov, D. Blaschke, A.D. Panferov and S.A. Smolyansky A Method to Measure Vacuum Birefringence at FCC-ee...... 263 Ulrik I. Uggerhøj and Tobias N. Wistisen Unifying Quantum Electro-Dynamics and Many-Body Perturbation Theory ...... 271 Ingvar Lindgren, Sten Salomonson and Johan Holmberg Contents ix

Part IV Astrophysics Simulations of Accretion Disks Around Massive stars ...... 285 M.B. Algalán, P.O. Hess and W. Greiner Neutron Stars—Possibilities and Limits for Exotic Phases ...... 297 S. Schramm, V. Dexheimer and R. Mallick The Case for an Underground Neutrino Facility in South Africa ...... 307 Z.Z. Vilakazi, S.M. Wyngaardt, R.T. Newman, R. Lindsay, A. Bufﬂer, R. de Meijer, P. Maleka, J. Bezuidenhout, R. Nchodu, M. van Rooyen and Z. Ndlovu

Part V Special Topics Covariant Hamiltonian Representation of Noether’s Theorem and Its Application to SU(N) Gauge Theories...... 317 Jürgen Struckmeier, Horst Stöcker and David Vasak Infrastructure Estimates for a Highly Renewable Global Electricity Grid ...... 333 Magnus Dahl, Rolando A. Rodriguez, Anders A. Søndergaard, Timo Zeyer, Gorm B. Andresen and Martin “Walterson” Greiner Power Flow Tracing in Complex Networks...... 357 Mirko Schäfer, Sabrina Hempel, Jonas Hörsch, Bo Tranberg, Stefan Schramm and Martin Greiner Patent Protection of High-Level Research Results ...... 375 Thomas J. Bürvenich Appendix A: Conference Photographs...... 385 Part I Nuclear Structure and Superheavy Elements Intertwining of Greiner’s Theoretical Works and Our Experimental Studies

J.H. Hamilton, A.V. Ramayya and E.H. Wang

Abstract The one phonon γ -vibrational bands in 154Gd are compared with the theories existing at the time (1960) showing the best agreement with the rotation vibration model of Faessler and Greiner. In recent years experimental evidences have been found for both one, two, and possibly three phonon γ bands in the A=103–110 region including the ﬁrst such bands in odd N-even Z and even N-odd Z nuclei. Nuclear shape coexistence was discovered in both 72Se and 184−188Hg with the Frankfurt Generalized Collective Model reproducing the two different shapes. Clus- ter radioactivity predicted by Sandulescu, Poenaru and Greiner has been observed. Maximum cluster radioactivity is seen in the zero neutron emission in cold binary and ternary ﬁssion of 252Cf. Finally, recent super heavy discoveries of the new elements 115, 117 and 118 are described. The half lives in 117 which is closest in N to N=184 on the Island of Stability support the theoretical predictions of the long-lived island.

1 Introduction

This paper will describe the intertwining of Professor Greiner’s theoretical work and our experimental studies from the past through the present in several different areas from γ -vibrational bands in deformed nuclei, through nuclear shape coexistence and the generalized collective model onto superheavy nuclei.

2 Gamma Vibrational Bands

Professor Faessler and Greiner [1] ﬁrst introduced the rotation vibrational model to explain the deviations of the β and γ band properties from those of the Bohr- Mottelson model of deformed nuclei [2]. Better agreement with the Faessler-Greiner

J.H. Hamilton (B) · A.V. Ramayya · E.H. Wang Vanderbilt University, Nashville 37235, USA e-mail: [email protected]

© Springer International Publishing Switzerland 2017 3 S. Schramm and M. Schäfer (eds.), New Horizons in Fundamental Physics, FIAS Interdisciplinary Science Series, DOI 10.1007/978-3-319-44165-8_1 4 J.H. Hamilton et al.

Fig. 1 Example of one and two and possibly a third γ -vibrational band [5]

Fig. 2 Systematic comparison of the one and two phonon γ vibrational bands in 103−108Mo. Such bands in 103,107Mo were newly identiﬁed in 2015

Model was found in our early work on these B(E2) branching ratios from these bands in 154Gd [3]. Gamma vibrational bands have continued through the present to be important both experimentally and theoretically. We found the first evidence for a one and two Intertwining of Greiner’s Theoretical Works and Our … 5 phonon γ -vibrational band in an odd-A nucleus in 105Mo [4] and in odd-Z nucleus in 103,105Nd [5]. We have experimentally identified for the first time the one and two phonon γ -vibrational bands in odd-N even-Z and even-N, odd-Z nuclei 103,105,107Mo, 103,105Nb and 107,109Tc. An example of these results for 105Nb is shown in Fig.1.In 103Nb one and two phonon γ bands and a third band candidate for a three phonon γ band are found which are essentially identical to 105Nb with their band heads within 50-85 keV of each other. Note a band with all the properties of a three phonon band are seen in 103,105Nb for the first time. Figure 2 shows a comparison of the odd-A and even-A Mo nuclei where γ -vibrational bands are seen. The energies of the one and two phonon γ bands in the odd-A and even-A are remarkably consistent in 103−108Mo to provide significant tests of microscopic theories.

3 Shape Coexistence in Complex Nuclei

Nuclear shape coexistence, the coexistence of energy levels built on two different nuclear shapes in the same nucleus, was ﬁrst predicted by Hill and Wheeler [6]. Then Morinaga [7] observed high energy excited states in 16O built on two quite different

Fig. 3 First example of shape coexistence in a complex nucleus with calculations by the Frankfurt group [11, 13] 6 J.H. Hamilton et al.

Fig. 4 First evidence for shape coexistence in heavy elements, Vanderbilt-UNISOR [12, 13] shapes. Greiner [8] introduced nuclear shape coexistence to explain the excited bands in 110Cd. Then Soloviev [9] and Kumar [10] called for searches to be made for shape coexisting energy levels. In 1974 we discovered overlapping energy levels in 72Se [11] and 184Hg [12] built on near spherical and well deformed shapes. While some theoretically opposed the suggestion of shape coexistence in such complex nuclei, these nuclei are now textbook examples of shape coexistence as seen in Eisenberg and Greiner [13], Figs. 3 and 4. The theoretical potential energy calculations in Fig. 3 for 72Se [11] were carried out by two of Greiners former students in the Generalized Collective Model introduced by Gneuss et al. [14]. The overlapping near spherical and well deformed band seen in A=182–188 for mercury nuclei far off stability are shown in Fig. 4. Nuclear shape coexistence is now seen throughout the Periodic Table. Intertwining of Greiner’s Theoretical Works and Our … 7

4 Cluster Radioactivity and Cold Binary and Ternary Fission

Sandulescu et al. [15] predicted in 1980 the new phenomena of cluster radioactivity where clusters like 14C are emitted in decays to lead nuclei. The wide variety of such clusters are described in their review of the experimental and theoretical work on cluster radioactivity [16]. Together we published a paper entitled “Exotic Nuclear Decay of 223Ra by Emission of 14C Nuclei” [17] to point out the theoretical predictions came out before the experimental observation. Then we discovered zero neutron emissions of binary spontaneous ﬁssion into 148Ba + 104Mo, 146Ba + 106Mo, 144Ba + 108Mo, 148Ce + 104Zr, (Fig. 5) the ultimate (largest) cluster radioactivity co-authored with Prof. Greiner [18]. We followed this with a theoretical paper including Greiner on such cluster radioactivity [19]. We also discovered zero neutron emission cold ternary spontaneous ﬁssion with the third particle being an particle another form of cluster radioactivity, co-authored with Greiner. Then came several cooperative studies [20].

5 Super Heavy Elements

In 1960, macroscopic nuclear theory predicted that elements with Z > 100 should not exist since they would have spontaneous ﬁssion lifetimes of ≤10−14 s. The introduction of microscopic shell corrections to explain the ﬁssion barriers of the actinides led to the prediction of new deformed and spherical shell gaps for Z > 100 and N > 150 as shown in Fig. 6. Several groups, including Prof. Greiner, [21–24],

Fig. 5 Zero neutron emission in spontaneous ﬁssion of 252Cf: a form of cluster radioactivity 8 J.H. Hamilton et al.

Fig. 6 Chart of nuclides showing deformed and spherical shell gaps in the second half of the 1960s predicted that elements beyond Z > 100 should be observed leading up to an Island of Stability around a spherical shell gap at N =184 with different theories predicting a spherical shell gap for Z at 114 or 120 or 126. The isotopes in and around the Island of Stability were predicted to have lifetimes possibly even as long as the age of the earth. These 1960s predictions led to various laboratories seeking to push the discoveries of new elements with Z > 102 by different techniques. A review of all approaches can be found in Ref. [25]. The GSI laboratory used what is called cold fusion that involves bombarding stable targets of 208Pb and 209Bi with projectiles of 48Ca to 64Ni. The reactions are called cold fusion because after fusion the nucleus of the new element had only enough internal energy to boil off one neutron. By using cold fusion, the new elements with Z=107–112 were discovered at GSI and an isotope of 113 was found in RIKEN in Japan. The Flerov Laboratory for Nuclear Reactions pioneered hot fusion reactions to discover new elements with Z=113–118. In hot fusion, the internal energy is suffi- cient to boil off 3–5 neutrons. New elements 114 and 116 were first identified and certified. They were given the names Flerovium for 114 and Livermorium for 116. In 2005 Oganessian, who had been cooperating in nuclear structure research with Vanderbilt for over 10 years, asked Vanderbilts help to obtain 249Bk target material from the High Flux Reactor in Oak Ridge National Laboratory in order to discover the unknown element 117. Oganessian and Hamilton met with the reactor scientists. The Intertwining of Greiner’s Theoretical Works and Our … 9 cost of making just a 249Bk target was prohibitive but were told that from time to time commercial companies pay for a campaign to make 252Cf. The 249Bk is a by-product of making 252Cf and for $600,000 they could chemically separate out the 249Bk. However, they had no such campaign planned. So for the next 3 years, Hamilton called the reactor scientist every 3 months to see if a campaign was under way. Three years later, in August 2008, the answer was yes. In September 2008, Vanderbilt held a small symposium in honor of Hamiltons 50 Years of Teaching and Research at Vanderbilt. At the meeting, Hamilton arranged a luncheon with Oganessian and J. Roberto, Deputy Director of ORNL, to have Oganessian explain the importance of the 249Bk target. Roberto was excited by the presentation and subsequently asked K. Rykaczewski (ORNL) and Hamilton to write him a proposal for $500,000 which they did and it was funded. Then Hamilton called his collaborator in structure research, M. Stoyer at Lawrence Livermore National Laboratory, to see if LLNL would like to join the experiment and provide the additional $100,000 for the cost of the chemical separation to which they agreed. The target material came out of the reactor in December 2008 and was allowed to cool for 3 months to allow the short lived radioactivities to decay. In March 2009 Oganessian and Hamilton went to ORNL to see the start of the chemical separation which took 3 months (Fig. 7). The 249Bk is in the long aluminum tube inside the first hot cell (Fig. 7). The target material was sent to Dubna in June and the experiment began in late July with the Vanderbilt group there for the starting week. The experiment was successful and was published in Physical Review Letters in April 2010 with only three days between submission and acceptance. The data presented were featured on the cover (Fig. 8)[26]. This was the first new element to be reported in over 5 years and was reported in over 250 news reports in newspapers and TV world-wide. The results were presented at the International Nuclear Physics Conference in Vancouver on June 20, 2010 [27] and also highlighted in another talk there as an example of the US Department of Energy’s response to the Presidents request to carry out important basic research. To provide definitive evidence for the new elements 113 and 115, the FLNR, ORNL, VU, LLNL collaboration carried out two sets of experiments from 11/2010– 2/2012 of the reaction 243Am + 48Ca at five beam energies [28, 29]. The results were first reported at the Nucleus-Nucleus Collisions Conference in May 2012 [29]. We obtained 28 new events of 289115 and very important four events of 289115 for the first time in this reaction. These α-289115 events provided cross bombardment checks to give definitive evidence for the discoveries of 113, 115, 117 as shown in Fig.9 [28, 29]. With new 249Bk target material divided between FLNR and TASCA at GSI, eleven new events of 293117 and 3 new events of 294117 were found at FLNR along with one new 249Cf + 48Cf → 294118 + 3n reaction toward the end of the run where 249Bk had beta decayed to 249Cf which was then 30 % of the target [30]. At TASCA at GSI, the reaction 249Bk + 48Ca was studied and our discovery [26] of the new element 117 was confirmed [31]. In 2010, while serving on a Review Committee for the High Flux Reactor, Hamil- ton found out that there were old 252Cf sources which had been returned with mixed 10 J.H. Hamilton et al.

Fig. 7 Hamilton and Oganessian observing the irradiated target with Berkelium as it came out the ORNL reactor

249,250,251Cf isotopes that included tens of milligrams of 251Cf. On discussing this discovery with ORNL and FLNR, it was decided to seek to make a mixed target to study the 251Cf + 48Ca → 295,296118 + 4,3n reactions. With two neutrons closer to the center of the Island of Stability at N =184, 296118 should have a factor of 100 or more longer lifetime and its decay products too. These longer lifetimes should open up studies of the chemistry of elements with Z ≥ 113 to test theoretical predictions that these nuclei should have different chemical properties than elements above them in the Periodic Table. Oak Ridge successfully made a target wheel of this very radioactive material and this experiment is now in progress in Dubna.

6 Our Collaborations

In our collaborations, Professor Greiner and Vanderbilt scientists co-authored 20 regular journal articles plus 8 letter articles, 36 conference proceedings, 1 book article and 5 articles in books edited by Professor Greiner. In addition, 6 articles were co-authored with his former Ph.D. students. From 1979–93, Greiner gave a full course very spring in theoretical physics at Vanderbilt for graduate students and brought 2 of his young graduate students with him. Hamilton received a Humboldt Intertwining of Greiner’s Theoretical Works and Our … 11

Fig. 8 Evidence for the discovery of the new element 117

Prize in 1979–80 to work in Frankfurt and GSI and later spent 2 months in the summer on 3 occasions. Ramayya received a Humboldt Award for a years research at Frankfurt and GSI. Thus it gave us great pleasure to participate in this conference honoring Professor Walter Greiner for his enormous contributions in so many areas of physics on the 12 J.H. Hamilton et al.

Fig. 9 Cross bombardment checks give deﬁnitive evidence for 113, 115, 117 occasion of his 80th birthday. We have especially enjoyed our close friendship and collaboration with him for over 45 years.

Acknowledgments The work at Vanderbilt University was supported by the US Department of Energy through grant DE-FG-05-88ER40407.

References

1. A. Faessler, W. Greiner. Z. Phys. 177, 190 (1964); A. Faessler, W. Greiner, R.K. Sheline. Nucl. Phys. 70, 33 (1965) 2. A. Bohr and B.R. Mottleson, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 27, N016 (1953) 3. L.L. Riedinger, Ph.D. Thesis (Vanderbilt University, 1969); L.L. Riedinger, N.R. Johnson, J.H. Hamilton, Phys. Rev. Lett. 19, 1243 (1967) 4. H.B. Ding et al., Phys. Rev. C 74, 054301 (2006) 5. J.G. Wang, S.J. Zhu, J.H. Hamilton et al. Phys. Lett. B 675, 430 (2009); H.J. Li et al. Phys. Rev. C 88, 054311 (2013) 6. D.L. Hill, J.A. Wheeler, Phys. Rev. 89, 1102 (1953) 7. H. Morinaga, Phys. Rev. 101, 254 (1956) 8. W. Greiner, in Proceedings of the International Conference on Neutron Capture (Jülich, Ger- many, 1965) 9. V.G. Soloviev, Phys. Lett. 21, 311 (1966) 10. K. Kumar, in Electromagnetic Interaction in Nuclear Spectroscopy, ed. by W.D. Hamilton (North-Holland, Amsterdam, 1975), p. 119 Intertwining of Greiner’s Theoretical Works and Our … 13

11. J.H. Hamilton et al., Phys. Rev. Lett. 32, 239 (1974) 12. J.H. Hamilton et al., Phys. Rev. Lett. 35, 562 (1975) 13. J.M. Eisenberg, W. Greiner, Nuclear Models (North-Holland, Amsterdam, 1987), pp. 278–285 14. G. Gneuss, U. Mosel, W. Greiner, Phys. Lett. B 30, 397 (1969) 15. A. Sandulescu, D.N. Poenaru, W. Greiner, Sov. J. Part. Nucl. 11, 528 (1980) 16. A. Sandulescu, W. Greiner, Rep. Prog. Phys. 55, 1423 (1992) 17. A. Sandulescu, D.N. Poenaru, W. Greiner, J.H. Hamilton, Phys. Rev. Lett. 54, 490 (1985) 18. J.H. Hamilton et al., J. Phys. G: Nucl. Part. Lett. 20, L85 (1994) 19. A. Sandulescu et al., Int. J. Mod. Phys. E 7, 625 (1998) 20. A.V. Ramayya et al., Phys. Rev. C 57, 2370 (1998) 21. A. Sobiczewski et al., Phys. Lett. 22, 500 (1966) 22. H. Meldner, Ark. Fys. 36, 593 (1967) 23. S.G. Nilsson et al., Nucl. Phys. A 115, 545 (1968) 24. U.Mosel,W.Greiner,Z.Phys.228, 371 (1969) 25. J.H. Hamilton, S. Hofmann, Y.T. Oganessian, Annu. Rev. Nucl. Part. Sci. 63, 383–405 (2013) 26. Yu. Ts. Oganessian et al., Phys. Rev. Lett. 104, 142502 (2010) 27. J.H. Hamilton et al., J. Phys. Conf. Ser. 312, 082026 (2011) 28. Yu. Ts. Oganessian et al., Phys. Rev. Lett. 108, 022502 (2012) 29. J.H. Hamilton et al., in 11th International Conference on NN Collisions.J.Phys.Conf.Series, 420, 012011 (2013) 30. Yu. Ts. Oganessian et al., Phys. Rev. C 87, 054621 (2013) 31. J. Khayagbaatar et al., Phys. Rev. Lett. 112, 172501 (2014) Eighty Years of Research on Super-Heavy Nuclei

Sigurd Hofmann

Abstract Extending borders is a strategy of evolution. So it is not astonishing that researchers wanted to know about the existence and properties of nuclei and elements beyond the known uranium. A short history is presented from early searches for trans- uraniums up to the production and safe identification of shell-stabilized super-heavy nuclei. The path is not only governed by noble and unambiguous scientific research, but also accompanied by errors and other human mistakes. However, obviously, evolution found the correct destination eventually. What can we expect for the future? Research using heavy ions will continue, accelerators and detectors will be improved, and theory will profit from inventive concepts and faster computers. Efforts will reveal the change of shell strength as function of proton and neutron number, the location of the most stable nuclei and how long their lifetime will be, the optimum method of their production, and, possibly, the existence of nucleonic formations and shapes, which are objects of speculation presently.

1 Review and Status of Experiments

Scientiﬁc attempts to synthesize new elements beyond uranium started in the 1930s, when the atomic model was established and the constituents of the atomic nucleus, protons and neutrons, were known. E. Fermi in Rome [1] and O. Hahn, L. Meitner, and F.W. Straßmann in Berlin [2] tried to use the nuclear reaction of neutron capture by uranium target nuclei and subsequent β− decay for production of transuranium elements. Although ﬁrst results were misinterpreted, the experiments opened a new area of research in nuclear physics. A chart of nuclei existing in 1935, the relevant year of this conference, is plotted on top of Fig.1.

S. Hofmann (B) GSI Helmholtzzentrum für Schwerionenforschung, Planckstrasse 1, 64291 Darmstadt, Germany e-mail: [email protected] S. Hofmann Institut für Physik, Goethe-Universität Frankfurt, 60438 Frankfurt, Germany

© Springer International Publishing Switzerland 2017 15 S. Schramm and M. Schäfer (eds.), New Horizons in Fundamental Physics, FIAS Interdisciplinary Science Series, DOI 10.1007/978-3-319-44165-8_2 16 S. Hofmann

Fig. 1 Three charts of nuclei from the years 1935, 1958, and 2015 demonstrating the advance in nuclear physics during 80 years of research. The nuclei known in 1935 were compiled by G. Fea working at the School of Nuclear Physics in Rome in collaboration with Rasetti and Segré [6]. The heaviest nucleus known at that time was 238U. Most of the stable isotopes have been iden- tiﬁed using mass spectrograph’s. Radioactive nuclei were known from the α-decay of uranium and thorium isotopes and at the lower end of the chart from nuclear reactions of those α particles with low Z target nuclei. The arrangement of the original chart was changed to an N over Z plot and the isotopes were colored according to the convention of the ‘Karlsruher Nuklidkarte’ shown in the lower part, which was compiled and published for the ﬁrst time in 1958 [7]

The discovery of Hahn and Straßmann [3] in 1938 was that uranium, more accurate the odd-mass isotope 235U, breaks into two approximately equal parts after neutron capture. This new phenomenon of nuclear fission was described by Meitner and O.R. Frisch in 1939 using the charged liquid-drop model [4]. One year later, Flerov and Petrjak [5] detected that uranium, 238U, decays spontaneously by fission from its ground-state. The first new elements beyond uranium were synthesized during the years of the Second World Warin laboratories in the US. These were the elements from neptunium Eighty Years of Research on Super-Heavy Nuclei 17

(Z=93) to curium (96). In the years 1949−55 the elements from berkelium (97) to mendelevium (101) were also produced in the US. The production processes were capture of fast neutrons from a reaction of 2H with 9Be by 238U and subsequent β− decay (239Np), β− decay of 238Np which was produced from 238U in irradiations with 2H(238Pu), slow neutron capture by 240Pu produced from 239Pu in a nuclear reactor and subsequent β− decay (241Am), fusion using a 4He beam from the 60-inch cyclotron in Berkeley (242Cm, 243Bk, 245Cf, 256Md), and rapid capture of 15 and 17 neutrons by 238U in a thermonuclear explosion and subsequent β− decays (253Es, 255Fm). Chemical separation of these new elements was essential for the identification, as it was already for the discovery of nuclear fission, which was identified by the observation of barium in a chemically separated sample. In the region of heavy elements, these studies resulted in the concept of a second series of chemically similar elements, the actinides, starting at element 89, actinium, besides the known lanthanides, both having unfilled f-electron shells. In 1951, G.T. Seaborg and E.M. McMillan received the Nobel Prize in Chemistry, “for their discoveries in the chemistry of the transuranium elements”. Limits of existence of nuclei were presented by J.A. Wheeler in a compilation of essays dedicated to Niels Bohr on the occasion of his 70th birthday [8] and at a conference ‘On the peaceful uses of atomic energy’ in Geneva in 1955 [9]. Solely based on the charged liquid-drop model, the results seemed reasonable, “to look for nuclei with a well defined existence with masses perhaps two or more times heavier than the heaviest nucleus now known, 256100”. Whereas in [8] these nuclei were still named ‘very heavy nuclei’, the term ‘superheavy nuclei’, now usually abbreviated SHN, was used in [9] for the first time. Two years later, F.G. Werner and Wheeler published a paper with the title ‘Superheavy Nuclei’, in which the properties of these nuclei were estimated in more detail but still disregarding shell effects. Also discussed at the Geneva conference was the problem of the binding of electrons in the strong electric field of such ‘superheavy nuclei’. This question was brought up by D.I. Blokhintsev in the discussion of Wheeler’s contribution [9]. Blokhintsev referred to the term −Z2α2 as radicand in the Dirac equation, which causes that calculation of the binding energy of K electrons fails for Z ≥ 137 for pointlike nuclei. However, Wheeler replied that they have found “that for a finite size of the nucleus even with a nuclear charge of 170, the K electron has a perfectly 2 reasonable wave function and has a binding energy of about 1.85 mec ”. This subject and related vacuum polarization and electron-positron pair creation in strong electric fields became later a major topic of theoretical studies at W. Greiner’s Institute at University Frankfurt [13, 14] and of experimental work at GSI (Gesellschaft für Schwerionenforschung) in Darmstadt [15]. In 1948, the magic numbers were successfully explained by the nuclear shell model [16, 17], and an extrapolation into the region of the next doubly magic nuclei beyond 208Pb was thus undertaken. The numbers 126 for the protons, later changed to 114, and 184 for the neutrons were predicted to be the next spherical shell closures. The perspectives offered by the nuclear shell model for production of SHN and the need for developing more powerful accelerators for their synthesis in heavy 18 S. Hofmann ion reactions was a main motivation for upgrading existing facilities or for found- ing new laboratories. In expectation of broad research fields the HILAC (Heavy Ion Linear Accelerator), later upgraded to the SuperHILAC, was built at LBNL (Lawrence Berkeley National Laboratory) in Berkeley in 1955, the U-300 and U- 400 cyclotrons at FLNR (Flerov Laboratory of Nuclear Reactions) at JINR (Joint Institute for Nuclear Research) in Dubna in 1957 and 1978, respectively, the UNILAC (Universal Linear Accelerator) at GSI in 1969, and the RILAC (RIKEN variable- frequency Linear Accelerator) at the RIKEN Nishina Center in Saitama near Tokio in 1980. Studies of the elements 100–106 were performed with the new cyclotron U-300 using fusion reactions with beams of 12Cto22Ne. In recognition of this early work in Dubna, element 105 is now officially named dubnium. At approximately the same time, the experiments at the HILAC in Berkeley cul- minated in the synthesis of the new element 106. After careful and deliberate deter- mination of well balanced discovery profiles by the International Unions of Pure and Applied Chemistry (IUPAC) and Physics (IUPAP), the names nobelium, lawren- cium, and rutherfordium are now officially accepted for the elements 102, 103, and 104, respectively, as well as seaborgium for element 106. In the middle of the 1960s, the concept of the macroscopic-microscopic (MM) model for calculating binding energies of nuclei also at large deformations was invented by V.M. Strutinsky [18]. Using this method a number of the measured phenomena could be naturally explained. In particular, it became possible to calculate the binding energy of a heavy fissioning nucleus as function of deformation and thus to determine the fission barrier. Partial fission half-lives were calculated using the so determined fission barrier. The calculations revealed the existence of so called ‘islands of stability’ far beyond the known nuclei [19–29]. Other important results which could be explained applying the Strutinsky method for calculation of the structure of the fission barrier are the fission isomers discovered by S.M. Polikanov et al. [30], which gain their stability from a second minimum in the fission barrier at large deformation, and the detection of the break of systematically long half-lives of N=152 isotones at element 104 by Yu.Ts. Oganessian et al. [31] due to the disappearance of a second hump in the fission barrier. The calculation of ground-state shell correction energies (SCE) of the MM model revealed a minimum (maximum in terms of stability) not only for spherical SHN at Z=114 and N =184, but also for deformed nuclei at Z=108 and N =162 [24]. The two minima, both having SCE values of −7 MeV, are clearly visible in Fig.2a. The figure shows SCE values taken from a calculation of A. Sobiczewski et al. [11]for a wide range of heavy and super-heavy nuclei. The shift of SHN with lowest SCE values to the region slightly above the shell closure at Z =114 and slightly below the shell closure at N=184 is due to the low level density for the protons between 114 and 126 and for the neutrons between 164 and 184, see graphs 53 and 54 in [12]. The nuclei at Z=108 and N =162 gain their stability from relatively high level densities below gaps of single particle levels for these nucleon numbers at deformations characterized by the deformation parameters Eighty Years of Research on Super-Heavy Nuclei 19

Fig. 2 Shell-correction energies in MeV taken from [10, 11](a) and dominating decay modes of even-even nuclei (b) and of even-odd nuclei (c). The dominating decay modes were determined from partial half-lives for α-decay (yellow), β+ decay or electron capture (red), β− decay (blue), and SF (green) calculated in [10–12]. Hindrance factors of 10 and 1000 were assumed for α-decay and SF of even-odd nuclei, respectively. Arrows mark measured decay chains starting at the even element isotopes 264Hs, 270Ds, 268Hs, 270Hs, 294118, and 292Lv in (b)andat263Hs, 269Ds, 271Ds, 277Cn, 271Hs, 285Fl, 291Lv, and 293Lv in (c). The α-decay chains of even-even nuclei and most of the chains of even-odd nuclei end by SF in agreement with predictions

β2 ≈ 0.22, β4 ≈−0.07 [11]. However, these gaps between single particle levels of deformed nuclei do not result from shell closures in terms of the classical shell model for spherical nuclei. The ridge of maximum SCE values between the two minima separates the region of heavy and super-heavy nuclei. Roughly, the borderline follows the line of constant mass number at A=280. This definition of SHN is in agreement with definitions given in early calculations of the stability of SHN. However, it differs from the definition used by nuclear chemists nowadays, who define as super-heavy elements (SHE) the elements beyond the actinide series beginning with rutherfordium, element 104. 20 S. Hofmann

The calculation of spontaneous fission (SF) half-lives of SHN was still problem- atic. It depends sensitively from the size of the fission barrier, the inertia and for odd and odd-odd nuclei from nuclear structure effects which generate an increase of the fission barrier by the so called specialization energy. Predicted half-lives based on the Strutinsky model using various parameter sets differed by many orders of magnitude. Some of the half-lives approached the age of the universe, and attempts have been made to discover naturally occurring SHN [34–37]. Although the corresponding discoveries were announced from time to time, none of them could be substantiated after more detailed inspection. Even the location of the closed shells for protons and neutrons turned out to be model dependent. Self-consistent Hartree-Fock-Bogoliubov calculations and relativistic mean field models [38–43] predict for spherical nuclei shells at Z =114, 120, or 126 (indicated as dashed lines in Fig. 2) and N =172 or 184. In terms of the shell model, the uncertainty in Z and N is due to the uncertain spin-orbit splitting of shells and subshells of high and low angular momentum, respectively, from 114 to 126 for the protons and from 164 to 184 for the neutrons. The shortest half-lives which determine the decay mode are plotted in Fig. 2bfor even-even nuclei and in Fig.2c for even-odd nuclei. For the odd nuclei partial α and SF half-lives calculated in [11] were multiplied by factors of 10 and 1000, respectively, thus making provisions for the odd particle hindrance factors. However, one has to keep in mind that, in particular, fission hindrance factors show a wide distribution from 101 to 105, which is mainly a result of the specific levels occupied by the odd nucleon [9, 44]. For even-even nuclei in Fig. 2b, the two regions of deformed heavy nuclei near N=162 and spherical SHN merge and form a region of α emitters surrounded by spontaneously fissioning nuclei. Alpha-decay becomes the dominant decay mode beyond Z =110 with continuously decreasing half-lives. For nuclei at N=184 and Z<110 half-lives are determined by β− decay. For even-odd nuclei, Fig. 2c, the island character of α emitters disappears and for nuclei with neutron numbers 150– 160 α-decay prevails down to element 104 and beyond. Longest total half-lives do not occur for nuclei having the most negative SCE values. Due to the short partial α half-lives there, the longest half-lives of SHN are predicted for nuclei near element 110 and neutron number 182. The set-ups used in physics experiments for the investigation of SHN are described in detail in review articles [45–51]. Cold and hot fusion reactions based on targets of lead or bismuth and isotopes of actinides, respectively, were used for the synthesis of heavy and super-heavy nuclei. These experiments resulted in the identification of the new elements 107–112 at the vacuum velocity filter SHIP (Separator for Heavy Ion reaction Products) at GSI [45, 46], in the confirmation of part of these data and in the production of a new isotope of element 113 at GARIS (Gas-filled Recoil Ion Separator) at RIKEN [51]. New neutron-rich isotopes of element 112 and the new elements from 113 to 118 were produced at DGFRS (Dubna Gas-Filled Recoil Separator) at FLNR [50]. Isotopes which are presently known in the region of heavy and super-heavy nuclei are shown in Fig.3. Eighty Years of Research on Super-Heavy Nuclei 21

54 257 Cr Fm 86 51 254 Kr V Es 249 Cf 82 249 Se Bk 248 Cm 76 243 Ge Am 244 Pu 70 237 Zn Np 70 238 Zn U 64 Ni 64 Ni 58 Fe

54 Cr

Fig. 3 Upper end of the chart of nuclei showing the presently (2016) known nuclei. For each known isotope the element name, mass number, and half-life are given. Colours are attributed to their decay mode: α-decay (yellow), β+ or electron-capture decay (red), β− decay (blue), SF (green), and γ decaying isomers (white). The relatively neutron-deﬁcient isotopes of the elements up to proton number 113 were produced in cold fusion reactions based on 208Pb and 209Bi targets after evaporation of one or two neutrons from the compound nuclei (CN) (dark blue frames with isotope of the beam in white). Not yet studied or studied with negative results are the reactions using beams of 76Ge, 82Se, and 86Kr. The more neutron-rich isotopes from element 112–118 were produced in reactions using a 48Ca beam and targets of 238U, 237Np, 239Pu, 240Pu, 242Pu, 244Pu, 243Am, 245Cm, 248Cm, 249Bk, and 249Cf. Red frames with the isotope of the target in white mark the CN. Reactions with the extremely difﬁcult to produce targets of 257Fm and 254Es were not yet studied or studied with negative result, respectively. The corresponding CN are already in a region of decreasing shell-correction energy. Frames in orange mark the CN of reactions with a 248Cm target and beams of 51V (not yet studied) and 54Cr (studied in [32]). The expected residue of the latter reaction after evaporation of three neutrons is 299120 which is expected to α-decay into 295118 (yellow frames). An attempt to re-interpret an event chain originally assigned to an α-decay chain starting at 289Fl in [33] was made by assigning this chain to 290Fl which decays by electron capture to 290113, see [32]. The magic numbers for protons at element 114 and 120 are emphasized. The bold dashed lines mark proton number 108 and neutron numbers 152 and 162. Nuclei with that number of protons or neutrons have increased stability; however, they are deformed contrary to the spherical super-heavy nuclei. At Z =114 and N =162 it is uncertain whether nuclei in that region are deformed or spherical. The background structure shows the calculated shell correction energy according to the macroscopic-microscopic model [10, 11], see Fig.2a

A key role in answering open questions related to the location of the major shell closure in the region of SHN plays the synthesis of isotopes of element 120. However, recent attempts using fusion reactions with targets of 244Pu [52], 238U[53]were negative or, as in the case of 249Cf [54], the data are not yet completely analyzed. 22 S. Hofmann

In an attempt to produce an isotope of element 120, the reaction 54Cr + 248Cm → 302120* was investigated at SHIP [32], see Fig.3. This reaction is more asymmetric than the reactions 64Ni + 238U and 58Fe + 244Pu and thus less Coulomb repulsion exists in the entrance channel. Although the reaction 50Ti + 249Cf is even more asymmetric, the choice using a 248Cm target could profit from being three neutrons nearer to the N=184 shell closure. To date, the measured cross-sections were always higher when more neutron rich projectile and/or target isotopes were used. It was planned to reach a cross-section limit of 100 fb for which a beam time of 140 days was requested. Safe operation of SHIP under the experimental conditions was successfully tested in a preparatory experiment in 2010 [55]. In the reaction 48Ca + 248Cm → 296Lv* decay data of 293Lv and 292Lv previously obtained at FLNR were confirmed. During a first part of the 54Cr + 248Cm experiment lasting 38 days in 2011, three correlated signals were measured occurring within a period of 279 ms. The surprising properties of the signals were that the energies of the first two signals are in agreement with calculated values for the α energies of 299120 and its daughter isotope 295118 [12, 56, 57] and the third signal agrees with the previously measured α energy and lifetime of the granddaughter 291Lv [58]. And, secondly, a very low probability was calculated that the chain of signals was produced by chance. Nevertheless, an unambiguous assignment of the signals cannot be made. The implantation of the parent nucleus with a short lifetime corresponding to the high decay energy was not found. The time to the nearest implanted nucleus is unexpect- edly long, and it cannot be distinguished from an accidental event. An unexpected long lifetime was measured also for the relatively high decay energy of the daughter nucleus. An explanation of the first two signals as isomeric decays is possible. How- ever, without confirmation in further experiments such explanations remain specu- lative. Unfortunately, the experiment could not be continued. Beam time was not allocated or already allocated beam time was canceled in favor of other experiments.

2 Perspectives

Despite the synthesis of nuclei as heavy as 294118, the extension of the island in proton and neutron numbers and also the locations of the centers of highest stability resulting in highest production cross-sections and that of longest half-lives is not yet explored. The reasons are experimental constraints like availability of targets, limited beam intensities and consequently long measuring times at cross-section levels of picobarn and below. The progress towards the exploration of the island of SHN is difﬁcult to predict. Hot fusion based on actinide targets and 48Ca beams terminate at element 118, because targets beyond Cf can be produced only with tremendous costs and efforts. How heavier beams like 50Ti, 54Cr, etc. will affect the fusion cross-section is subject of experiments planned for the near future. However, these heavier beams are mandatory for exploration of the island of SHN into the north-east direction, the direction towards new elements. Strong shell effects, if they exist at Z =120 or 126,