Nuclear Particle Correlations and Cluster Physics

Schröder Wolf-Udo

• Publisher: WSPC
• Year: 2017
• ISBN:
  9789813209367
• Topic: Scienze fisiche
• Subtopic: Teoria quantistica

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A timely presentation of new results, challenges, and opportunities in the quickly developing field of nuclear cluster physics, presented by an international group of eminent theoretical and experimental scientists active in the field. Their work reveals how correlations of nucleons can appear spontaneously, propagate, and survive in nuclear matter at both low and high densities. Characteristic nuclear substructures, beyond those predicted by mean-field or collective scenarios, appear on microscopic and cosmic length scales. They can influence the dynamics of fusion of light nuclei and the decay of heavy, fissioning nuclei or of systems produced transiently in heavy-ion reactions. A must-read for young scientists entering the field and a valuable resource for more seasoned nuclear researchers!

--> Contents:

• General Cluster Properties:
  • Similarities and Differences Between Nuclear and Metal Clusters (P M Dinh, P-G Reinhard and E Suraud)
• Particle Correlations in Dilute and Dense Matter:
  • Correlations and Clustering in Dilute Matter (G Röpke)
  • Nuclear Clustering in Fermionic Molecular Dynamics (H Feldmeier and T Neff)
  • Comparison of Equation of State Models with Different Cluster Dissolution Mechanisms (H Pais and S Typel)
  • Clustering and Pasta Phases in Nuclear Density Functional Theory (B Schuetrumpf, C Zhang and W Nazarewicz)
  • Fragmentation of Neutron Star Matter (P N Alcain and C O Dorso)
• General Cluster Properties:
  • Clustering in Stable and Exotic Light Nuclei (C Beck)
  • Clusters in Astrophysics (M Wiescher and T Ahn)
  • Persistence of Clustering at High Excitation Energy: Clues from 24 Mg (F Gulminelli, L Morelli, M Bruno, M D'Agostino and G Baiocco)
  • Particle-Particle Correlations: A Tool for Investigating Excited States and Clustering Effects in the Decay of Excited Nuclei (L Morelli, M Bruno, M D'Agostino, G Baiocco, F Gulminelli, T Marchi and S Barlini)
• Cluster Radioactivity/Fission and SHE:
  • Nuclear Size Isomers: The Excited States of Light Nuclei with Cluster Structure and Nonstandard Sizes (A A Ogloblin, A N Danilov, A S Demyanova, S A Goncharov, T L Belyaeva and W Trzaska)
  • Manifestations of Clustering in Binary and Ternary Fission of Low Excited Heavy Nuclei (Yu V Pyatkov and D V Kamanin)
  • Spontaneous Fission, Cluster Radioactivity and Alpha Decay of Superheavy Nuclei 282,284 Cn and 286 Lv (D N Poenaru and R A Gherghescu)
  • Predictions on the Feasible Alpha and Cluster Decays from 298–336 126 Superheavy Nuclei (K P Santhosh and B Priyanka)
• Cluster Effects in Nuclear Reactions:
  • Mean-Field Instabilities and Cluster Formation in Nuclear Reactions (M Colonna, P Napolitano and V Baran)
  • Clusters in Heavy-Ion Collision Dynamics (A Ono)
  • Molecular Structures in Slow Nuclear Collisions (A Diaz-Torres)
  • Dynamical Collective Clusterization in Hot and Rotating or Non-Rotating Compound Nuclei Including Spontaneous Cluster Radioactivity (R K Gupta)
  • Multifragmentation in the Perspectives of Various Clusterization Algorithms (R Kumar, A Sharma, S Sood and R K Puri)
  • Using Fast Processes to Investigate Cluster States and Nuclear Correlations in Medium-Heavy Nuclei: Specific Tools and New Opportunities with Radioactive Ion Beams (T Marchi, F Gramegna, L Morelli, S Barlini, D Fabris, V L Kravchuk and O V Fotina)
  • "Necklace" Cluster Fragmentation of the Dinuclear System in Dissipative Reactions (S O Nyibule, M J Quinlan, E Henry, H Singh, I Pawelczak, J Tõke, W U Schröder, L Auditore, G Cardella, M B Chatterjee, E De Filippo, G Lanzalone, C Maiolino, A Pagano, M Papa, S Pirrone, G Politi, F Rizzo, P Russotto, A Trifiro and G Verde)

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--> Readership: Researchers and graduate students in nuclear, high energy and particle physics. -->

Part 1

General Cluster Properties

CHAPTER 1

SIMILARITIES AND DIFFERENCES BETWEEN NUCLEI AND METAL CLUSTERS

P. M. Dinh

Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, France

P.-G. Reinhard

Institut für Theoretische Physik, Universität Erlangen, Staudtstraße 7, D-91058 Erlangen, Germany

E. Suraud^∗

Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, France

Besides the topic of this volume, namely clustering in nuclei, the keyword “cluster” addresses a special form of large molecules consisting out of the same building blocks (atoms or small molecules) piled up to a large compound, so to say a small piece of a solid. A particular species are metal clusters whose valence electrons can be viewed as Fermi liquid. This establishes the similarity to nuclei which also consist of the Fermi liquid of protons and neutrons. In this article, we discuss similarities and differences of nuclei and metal clusters with respect to structure, resonance excitations, and fission. The latter process is closely related, again, to clustering, the emergence of sub-units in a larger compound.

1.Introduction

Clustering in nuclei is associated with more or less identifiable substructures within a nucleus which consist themselves of small nuclei, particularly of α particles. Molecular or atomic clusters are, at first glance, totally different objects. These are large composites of molecules or atoms of the same sort piled up to a large molecule or, looking at it the other way round, small pieces of bulk material. ¹ According to the huge variety of chemical materials, there is a huge variety of cluster types with different bonding types. ² Unlike nuclei which consist out of one sort of material with one type of binding (“metallic”), all sorts of relations between the substructures (atoms or small molecules) and the total system can be found for atomic/molecular clusters. The task to discriminate substructures is thus also very relevant in molecular or cluster physics and several tools have been developed for this. A useful tool is, for example, the electron localization criterion which allows to identify areas where one electron wave function dominates. ³ In fact, this localization criterion can also be used to identify α clustering in light nuclei. ⁴ This is only one example out of many more tools which are common to nuclear and cluster physics. Already the basic theoretical description in terms of energy-density functionals proceeds very similar. ^{5, 6} But in addition to the similar tools, nuclei and molecules cover also systems with comparable properties. From the many conceivable bonding types in molecules, metallic binding comes closest to nuclear binding. In both cases, the system’s fermions (valence electrons, or nucleons respectively) have a long mean-free path and thus belong to the whole system. This suggests that metal clusters should have something in common with nuclei. This is indeed the case, particularly for simple metals (Li, Na, K, Cs, Rb) where the valence shell is well decoupled from ionic cores (that is the nucleus and the core electrons). Thus a comparison between structural and dynamical properties of nuclei and metal clusters has been a much discussed issue, for examples see Refs. 7 – 9. Many similarities have been worked out concerning spatial profiles, shell structure (magic numbers, deformation) and resonance excitations (giant resonances in nuclei, plasmons in clusters). We will address them in sections 2 and 3. In section 2, we show that, by introducing appropriate natural units, even a similarity at quantitative level can be found for density distributions and potentials. Section 3 takes a look at spectral properties in the stationary state as well as in excitations.

Clustering phenomena as they are discussed in nuclear physics can appear for metal clusters in decay channels. The dominant decay channels for excited clusters are electron or monomer (atom) emission. At sufficient excitation energy, multiple electron emission can lift the cluster charge above the stability limit. The strong repulsive Coulomb force thus generated drives dissociation of the system, Coulomb expansion with subsequent fission as moderate process near threshold ^{10– 12} and Coulomb explosion producing several smaller fragments for higher charging. ^{13, 14} We will address cluster fission in section 4 taking numerical simulations for Coulomb induced fission of Na₁₄ as an example.

Before carrying on with the detailed comparison of structural and (low-energy) dynamical properties at the level of a mean-field description, we summarize here briefly a couple of differences and similarities which are not addressed later on. At the experimental side, the dramatically different dimensions of nuclei and clusters require, of course, much different machines. It requires much higher efforts and patience to elicit information from the awfully small nuclei. Nonetheless, nuclei are probably the best studied objects, both what concerns structural and dynamical properties. In particular the long developments of detailed experimental investigations have allowed to reach a remarkable degree of detail, both in terms of spectroscopic properties (for structure and low energy dynamics) and in terms of analysis of (possibly violent) dynamical scenarios with the highly sophisticated 4π multi-detectors even able to work on an event-by-event basis. Metal clusters have not yet been scrutinized at that level of resolution and details. Development is here still going on, e.g., in detailed measurement of angular distributions and kinetic energies of electrons emitted in connection with laser excitation. On the other hand, clusters are better to handle and have time scale in reach of present-days clocks. This allows experiments which nuclear physicists can only dream of (pathway to huge systems, time resolved dynamics, tunable temperature). Thus cluster physics supplies worthwhile complementing information on finite fermion systems.

At the side of theoretical description, nuclei are much more demanding than clusters. Molecular physics is governed by the well understood electro-magnetic interaction. Modern methods of many-body theory allow a description at each level refinement and to derive systematically effective approaches for efficient lower-level treatment, e.g., density functional theory. The nuclear many-body problem, on the other hand, has not yet fully converged. The case is much more involved because nucleons are composite objects whose intrinsic energy scales are too close to nuclear scales. The solution lies in a cumbersome treatment at the elementary level of quantum-chromodynamics and we witness presently breath-taking progress in that direction, see e.g. Refs. 15 – 17. In spite of the huge differences at deeply microscopic level, the effective energy-density functionals for a mean-field treatment of structure and low-energy dynamics come out at the end very similar. Finally, there is a regime intermediate between fully microscopic treatment and mean-field approximation. This concerns the extension of effective mean-field theory by dynamical correlations which become important with increasing excitation energy. This can still be treated with effective interactions (in-medium scattering cross section) and it can be attacked much the same way for nuclei and electronic systems. The method of choice so far are kinetic equations at the semi-classical level of the Vlasov-Uehling-Uhlenbeck approach. ^{18 – 20} These powerful kinetic equations to not yet include quantum shell effects. This is still in a development stage. ²¹ Although much could be said about similarities between metal clusters and nuclei concerning kinetic equations, we will not address this topic here for reasons of space.

2.Basic properties: nuclei versus metal clusters

2.1.Orders of magnitudes and scales

At first glance, nuclei and metal clusters are extremely different objects. While nuclei are compact at fm scale and relate to energies at MeV scale, clusters are 5 orders of magnitude larger and 6 orders of magnitude less bound. However, looking at shear size can be deceiving. Rescaling observables in natural units reveals a great deal of similarities between these two systems. Both share a basic feature: they can be viewed as finite pieces of a Fermi fluid. Nuclei are composed as a two component system out of a proton and a neutron fluid. The valence electrons of simple metal clusters can be considered as an electron fluid immersed in a background of positively charges ions where the latter are treated as classical particles. Bo...

Table of contents

• Cover Page
• Title
• Copyright
• Preface
• Contents
• Part 1. General Cluster Properties
• Part 2. Particle Correlations in Dilute and Dense Matter
• Part 3. General Cluster Properties
• Part 4. Cluster Radioactivity/Fission and SHE
• Part 5. Cluster Effects in Nuclear Reactions
• Index