Progress of Time-Dependent Nuclear Reaction Theory

Book Series: Frontiers in Nuclear and Particle Physics

Volume 2

by

Yoritaka Iwata

DOI: 10.2174/97816810876411190201
eISBN: 978-1-68108-764-1, 2019
ISBN: 978-1-68108-765-8
ISSN: 2589-7551 (Print)
ISSN: 2589-756X (Online)



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Table of Contents

Foreword

- Pp. i-iii (3)
Yoritaka Iwata
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Preface

- Pp. iv
Yoritaka Iwata
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List of Contributors

- Pp. v-vi (2)
Yoritaka Iwata
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A short introduction to the equations of motion

- Pp. vii-ix (3)
Yoritaka Iwata
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Numerical Calculations of TDHF

- Pp. 1-18 (18)
P. D. Stevenson

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Density constrained TDHF

- Pp. 19-39 (21)
V.E. Oberacker and A.S. Umar

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Multinucleon transfer reaction in time-dependent Hartree-Fock theory

- Pp. 40-56 (17)
Kazuyuki Sekizawa and Kazuhiro Yabana

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Nuclear Reactions and Superfluid Time Dependent Density Functional Theory

- Pp. 57-71 (15)
Piotr Magierski

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Counting particles in microscopic systems

- Pp. 72-92 (21)
Cédric Simenel

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Large amplitude collective dynamic beyond the independent particle/quasiparticle picture

- Pp. 93-113 (21)
Denis Lacroix

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AMD approach to go beyond the mean field

- Pp. 114-131 (18)
Akira Ono

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Reaction Dynamics of Complex Nuclei at Low Energy within a Molecular Picture

- Pp. 132-149 (18)
Alexis Diaz-Torres

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Kadanoff-Baym dynamics for strongly coupled relativistic quantum systems

- Pp. 150-173 (24)
W. Cassing

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Linear chain structure in light nuclei

- Pp. 174-209 (36)
N. Itagaki, T. Ichikawa, Y. Iwata and P. W. Zhao

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Cluster states in stable and unstable nuclei

- Pp. 210-232 (23)
M. Kimura

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Molecular dynamics approach to nuclear manybody systems

- Pp. 233-254 (22)
M. Kimura

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Dynamical Study on the Synthesis of Superheavy Elements

- Pp. 255-282 (28)
Y. Aritomo

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Subject Index

- Pp. 283-293 (11)
Yoritaka Iwata
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Foreword

It is a great pleasure for me that I am in charge to write the preface to this book in honor of my highly estimated colleague Prof. Dr. J. A. Maruhn to celebrate his retirement. The broad span of contributions collected here demonstrates the versatility and the great public visibility of Joachim Maruhn. One can read off from the collection that he has worked in many areas of theoretical physics: structure of exotic nuclei, large-amplitude nuclear dynamics, and plasmas with high energy density. The entrance to each one of these fields was novel and pioneering computational development. To see this in more detail, we have to go back to the beginnings of his career. I happened to be grown up in the same institute as Joachim Maruhn, namely in the institute for Theoretical Physics of the Johann-Wolfgang- Goethe university Frankfurt under Prof. Dr. W. Greiner. At this time around 1970, Joachim Maruhn was the first to dig deep into the architecture of those days mainframe computers. He had the patience to scrutinize all their bulky manuals, did even understand them, and was able to squeeze the most out of these cumbersome monsters. I remember standing at the controller room of the “huge” Univac 1108 of this time while his codes were running. All of a sudden the tapes moved miraculously forth and back something which never happened with our other codes. Joachim Maruhn was the one to grasp the obnoxious instructions to speak to these devices and so he managed to write code for problems which were considered extraordinarily bulky at this time when the RAM covered as much as 64 Kwords. At a later occasion, I watched him installing one of the first affordable local computers by typing in machine instructions in hexadecimal code, again very close to the hardware architecture. These examples should not mislead the reader to the false impression that Joachim Maruhn were a computer freak having lost contact to the real world. Yes, it is true that he has a sixth sense for computing. But he keeps that in the proper balance and considers it as useful tool to reach physics goals. Many of his developments started indeed as computational progress, but all of them ended up in long standing and fruitful physics projects as can be read off from his list of publications and from the articles in this book.

As his first master-piece, Joachim Maruhn delivered in the early 1970ies the Fortran code for the Two-Center Shell-Model, a code which was used since for decades by many colleagues all over the world for theoretical research on nuclear fusion, fission, and multi- fragmentation. Not much later, he was one of the first to enter the field of simulating nuclear dynamics fully microscopically on the basis of the time-dependent Hartree-Fock (TDHF) method. This was a rather daring enterprise at that time where computer capacities were comparatively poor. I remember wise colleagues shaking their head and recommending rather to do something useful, because they could not believe that numerical capacities will evolve so rapidly as they did. Today, we see that realistic TDHF simulations under varied conditions are feasible and widely used. Thanks to the foreseeing, pioneering work of Joachim Maruhn and similarly brave colleagues, we dispose now of long standing coding experience and a variety of useful tools for these (still) demanding TDHF simulations. Besides that, this experience has been successfully transferred to related areas in nuclear physics, particularly the adiabatic description of nuclear collective motion and fission in a fully self-consistent fashion. Also in the 1970ies, Joachim Maruhn entered the field of dynamical simulations in plasma physics. And again, he managed to start novel developments which were at this time at the edge of feasibility, if not beyond. In the meantime, the codes have been employed successfully for many research projects up to now, particularly for the numerically demanding plasma state under the extreme conditions of inertial fusion. Within these long standing great development lines, there appeared often remarkable details. For example, Joachim Maruhn composed a time- and memory-saving generator for FFT routines which managed to generate automatically code for each grid size separately, so taking advantage of trivial numbers (e.g. multiplication by 1) occurring for many cases, but always at different places. To the best of my knowledge, this was the fastest FFT routine around for long time until the modern libraries appeared, as e.g. FFTW, which, in fact, use similar strategies of dedicated coding for given grid size. There are many others example for such fine details. Quite generally, the itching limitations of former computers called for careful coding to use resources as efficient as possible. Up to these days, Joachim Maruhn’s codes are exemplary for excellent coding, readable, efficient and reliable. But again, coding was never considered as an end in itself. It provided “merely” a sound basis for far reaching physics projects. These project lines can be grouped in four main branches which will be briefly outlined below.

The earliest achievement was the Two-Center Shell-Model (TCSM) which belongs to the class of microscopic-macroscopic models. This kind of modeling was the method of choice in the 1960ies and 70ies. At that time one could not dream of the later progress of fully self-consistent models. Thus one tailored effective single-particle potentials (shell models) following the physical intuition associated with nuclear collective motion and fis- sion. Combining the quantum effects from the shell model with the well understood bulk properties from the liquid-drop model provides a remarkably reliable description which is still competitive today. The TCSM was a big step forward within this successful family of microscopic-macroscopic models because it was the first one to work in a basis of single- particle wavefunctions which cover the fragmentation of nuclear centers. This was achieved by putting two harmonic oscillator potentials side by side and cutting them at the crossing point. This gives the model the freedom to handle any fragment shapes, however at the price of making the numerical handling of the basis functions more involved which was a challenge in the 1970ies. Since then, the TCSM with its great versatility has found widespread appli- cations and remains even today a useful tool for first explorations of exotic fragmentation channels.

Purely macroscopic modeling is used in the hydrodynamical code which Joachim Maruhn developed since the mid 1970ies. Motivated was this by the upcoming heavy-ion facilities. There was a need for an affordable simulation of the dynamics of violent heavy-ion collisions up to including a pertinent description of nuclear shock waves. But later on, the hydro- dynamical code found its major applications in a different field, namely plasma physics. This was still related to heavy-ion facilities, here, however, related to a totally different use of heavy-ion beams, namely for the generation of extremely hot and dense plasma states. The fact that the university Frankfurt close to GSI Darmstadt allowed an extremely fruitful collaboration between Joachim Maruhn’s plasma group and experimentalists at GSI up to these days. The theoretical simulations are here deeply connected with application. They serve as crucial instruments to understand and design experiments.

Also in the mid 1970ies appeared on the horizon first fully self-consistent microscopic nuclear mean-field models which allowed a reliable description of nuclear properties. This triggered a storm of new developments in modeling nuclear structure and dynamics. Time- dependent Hartree-Fock (TDHF) is the most far fetched application in this scenario. Joachim Maruhn was one of the forerunners in this first wave of TDHF development. The early TDHF studies allowed to gain insight into the basic mechanisms of nuclear collisions as flow pattern or the threshold between fusion and inelastic scattering.

The limitations of former days computers hindered to proceed with TDHF to realis- tic simulations. However, the elaborate griding techniques developed for TDHF could be recycled for many useful applications in nuclear structure physics and adiabatic nuclear dy- namics. Joachim Maruhn exploited that extensively which led to a rich series of publications on exotic nuclei, particularly super-heavy elements. A crucial issue was here the prediction of stability which is related to a reliable estimate of fission barriers. Mind that these stud- ies deal with far extrapolations. This raises questions about the reliability of the effective density functionals used in self-consistent nuclear models. Careful as he is, Joachim thus focused very much on studying critically the parametrizations of nuclear density functionals, the relativistic mean-field model as well as the non-relativistic Skyrme-Hartree-Fock func- tional. These extensive investigations have eventually pointed out quite clearly the regimes of nuclei and observables which can be predicted reliably well and those which have to be taken with care. These results have, furthermore, served to improve the self-consistent models and its parametrization.

Meanwhile, computing capacities have evolved so rapidly that one can actually perform those realistic TDHF simulations which we were dreaming in the 1970ies. This led to a remarkable revival of TDHF studies and, of course, Joachim Maruhn is heavily involved in this second round TDHF. It is now possible to do away with all symmetry restrictions which hampered early TDHF codes and to run unbiased simulations. This allows, e.g., to run collisions of truly heavy ions (as Pb or U) and to spend sizable computing effort or detailed analysis of the results which, in turn, inspired a couple of novel investigations. One example is the detailed microscopic computation of cross sections for over-barrier fusion of heavy nuclei. Another example is the tracking of collisional dynamics in a phase space picture with the help of the six-dimensional Wigner transformation which gives insight, e.g., into dynamical transfer processes or into dissipation mechanisms at work in TDHF. Really huge systems were attacked in the realm of astro-physics when simulating hot nuclear matter under the typical conditions in a super-nova explosion. The various phases of nuclear matter which had been previously assessed in symmetry-restricted stationary models can now be probed in a truly dynamical situation which yields additional information on their structure, stability and prevalence. One of the exciting results is that nuclear matter can form under certain conditions a gyroid structure which is a curved, interwoven network of matter and voids. This is surely not the end of the TDHF revival. There are still many promising investigations in the queue as, e.g., an improved description of fission and a better understanding (or modeling) of dissipation. I am confident that Joachim Maruhn continues to contribute to these studies.

Thus far, I have reviewed Joachim Maruhn from a purely scientific perspective. But that leaves an incomplete picture. Joachim Maruhn was not only digging deep into computers and publishing good papers all day. He was for long time appointed as Professor at the Johann-Wolfgang-Goethe university Frankfurt and as such predominantly a teacher. He took it very serious and delivered excellent lectures. His list of publications shows a couple of textbooks and looking at them gives an impression of his clear and crisp explanations. Students appreciated that very much and honored him with the price for good teaching, probably that achievement of which Joachim Maruhn is most proud of. And this pride in itself demonstrated how much he focused on teaching students. More than that, he cared for them, listening to their concerns and often inventing creative solutions for sticky administrative blockades with examinations and certificates. Not surprising that he was asked to serve the faculty as Dean of Students, a time-consuming burden which he fulfilled with patience and equanimity. He did it fully hearted and right with the same commitment as his scientific enterprises.

I close with a personal remark. We started common projects in the late 1970ies, at the time when he came back to Frankfurt as Professor for Theoretical Physics. Since then we continue close collaboration in nuclear structure physics and TDHF. I am very thankful for all we could work out together, for his advice and for is inspiration. I wish Joachim Maruhn that he can stay in science for many further years, supplying more of his interesting findings, and, somewhat egoistically, that we can enjoy further common projects.


Preface

This book focuses on the time-dependent theory for sub-atomic reactions. There are two important theoretical ingredients for sub-atomic reactions such as heavy-ion reactions. One arises from the quantum theoretical aspects, and the other from the many-body theoretical aspects. At this point, for heavy-ion reactions, there is no theoretical calculations fully taking into account both of the two aspects. This simply tell us the difficulty of calculating and understanding many-nucleon systems.

Much attention is paid to low-energy heavy-ion reactions. Several types of model equa- tions are investigated. Mean-field type theories with or without pairing correlation are included in Chap. 1 (P. Stevenson), Chap. 2 (V.E. Oberacker and A. S. Umar), Chap. 3 (K. Sekizawa and K. Yabana), and Chp. 4 (P. Magierski); beyond the mean-field type theories are included in Chap. 5 (C. Simenel), Chap. 6 (D. Lacroix), Chap. 7 (A. Ono), Chap. 8 (A. Diaz-Torres), Chap. 9 (W. Cassing), Chap. 10 (N. Itagaki, T. Ichikawa, Y. Iwata and P. W. Zhao), and Chap. 11 (M. Kimura); semi-classical and classical theories are included in Chap. 12 (T. Maruyama), and Chap. 13 (Y. Aritomo).

This book is published to celebrate 65 years old birthday of Prof. Maruhn. Fourteen modern and advanced topics in the field of time-dependent reaction theory are included in this book. Eventually I would like to thank all the authors. Shehzad Naqvi and Omer Shafi of Bentham Science Publishers are acknowledged for their efforts to realize this publication



Yoritaka Iwata
School of Science,
The University of Tokyo
Hongo, Tokyo, Japan

List of Contributors

Editor(s):
Yoritaka Iwata
School of Science
The University of Tokyo, Hongo 7-3-1, 113-0033 Tokyo,
Japan




Contributor(s):
A.S. Umar
Department of Physics and Astronomy
Vanderbilt University
Nashville
TN
USA


Akira Ono
Department of Physics
Tohoku Univesity
Sendai
Japan


Alexis Diaz-Torres
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT∗)
Strada delle Tabarelle 286, I-38123 Villazzano
Trento
Italy


C'edric Simenel
Department of Nuclear Physics
Research School of Physics and Engineering
The Australian, National University
Canberra
ACT
Australia
/
Center for Computational Sciences
University of Tsukuba
Tsukuba
Japan


Denis Lacroix
Institut de Physique Nucl'eaire
IN2P3-CNRS
Universit'e Paris-Sud
Orsay Cedex
France


Kazuhiro Yabana
Graduate School of Pure and Applied Sciences
University of Tsukuba
Tsukuba
Japan


Kazuyuki Sekizawa
Faculty of Physics
Warsaw University of Technology
ulica Koszykowa 75
Warsaw
Poland
/
Graduate School of Pure and Applied Sciences
University of Tsukuba
Tsukuba
Japan


M. Kimura
Department of Physics
Hokkaido University
Sapporo
Japan


N. Itagaki
Yukawa Institute for Theoretical Physics
Kyoto University
Kitashirakawa Oiwake-cho
Kyoto
Japan


P. D. Stevenson
Department of Physics
University of Surrey
Guildford
Surrey
UK


P. W. Zhao
Yukawa Institute for Theoretical Physics
Kyoto University
Kitashirakawa Oiwake-cho
Kyoto
Japan


Piotr Magierski
Faculty of Physics
Warsaw University of Technology
ulica Koszykowa 75
Warsaw
Poland
/
Faculty of Physics
University of Washington
Seattle
WA
USA


T. Ichikawa
Yukawa Institute for Theoretical Physics
Kyoto University
Kitashirakawa Oiwake-cho
Kyoto
Japan


Toshiki Maruyama
Advanced Science Research Center
Japan Atomic Energy Agency
Shirakata 2-4, Tokai
Ibaraki
Japan


V.E. Oberacker
Department of Physics and Astronomy
Vanderbilt University
Nashville
TN
USA


W. Cassing
Institute for Theoretical Physics
University of Giessen
Germany


Y. Aritomo
Faculty of Science and Engineering
Kindai University
Higashiosaka
Osaka
Japan


Y. Iwata
Center for Nuclear Study
The University of Tokyo
7-3-1 Hongo
Tokyo
Japan


Yoritaka Iwata
School of Science
The University of Tokyo
Hongo 7-3-1
Tokyo
Japan




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