Clustering in light nuclear systems

226 Pages·2017·18.78 MB·English

Clustering in light nuclear systems : a multi-methodic
approach
Daniele Dell’Aquila
To cite this version:
Daniele Dell’Aquila. Clustering in light nuclear systems : a multi-methodic approach. Nuclear Exper-
iment [nucl-ex]. Université Paris-Saclay; Università degli studi di Napoli Federico II, 2018. English.
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NNT : 2017SACLE035
Clustering dans les
noyaux légers: une approche
multi-méthodique
Thèse de doctorat de l'Università degli Studi di Napoli Federico II
et de l'Université Paris-Saclay
préparée à l'Université Paris-Sud
École doctorale n°576 Particules, Hadrons, Énergie, Noyau,
Instrumentation, Imagerie, Cosmos et Simulation (PHENIICS)
Spécialité de doctorat: Structure et réactions nucléaires
Thèse présentée et soutenue à Naples (Italie), le 15 janvier 2018, par
Daniele Dell'Aquila
Composition du Jury :
M. Gianluca Imbriani
Professeur, Università degli Studi di Napoli Federico II Président
M. Giuseppe Verde
Directeur de Recherche, Institut de Physique Nucléaire Orsay Directeur de thèse
M. Mariano Vigilante
Professeur, Università degli Studi di Napoli Federico II Directeur de thèse
M. Francesco Cappuzzello
Professeur, Università degli Studi di Catania Examinateur
M. David Verney
Directeur de Recherche, Institut de Physique Nucléaire Orsay Examinateur
M. Vincenzo Berardi
Professeur, Università degli Studi di Bari Examinateur
NNT : 2018SACLS093
Abstract
Clustering phenomena affect many aspects of nature and social sciences. They con-
sist in the creation of groups of correlated objects which modify the behaviour of a
given system introducing symmetries and order. As an example, in the largest scale
known to humans, cluster effects determine the formation of congregate of galaxies.
On human being scales, clustering is widely present in everyday aspects, leading to
collective social behaviours as consensus in social and technological networks and
synchronization in biological systems. In nuclear physics, clustering is one of the
most fascinating results of the Pauli exclusion principle and characterizes a large
variety of nuclear states, especially in light nuclear systems. Nuclear structures
resulting from these phenomena are quite unusual and peculiar, and their investiga-
tion is extremely important in the understanding of nuclear forces and their related
properties. As an example, cluster structures evolve from self-conjugated nuclei to
neutron-rich ones with the appearance of highly deformed structures. In the latter
case, the cluster centers are bounded together by means of extra-neutrons, which
act in a glue-like effect increasing the stability of the structure. Clustering plays
also a role in nuclear astrophysics, where it is involved in the creation of elements
in stars.
In this thesis, we experimentally investigate clustering aspects of light nuclear
systems with a multi-method approach and by using different and complementary
techniques. In Chapter one, we show how the appearance of clustering phenom-
ena is naturally encouraged by independent-particle approaches to nuclear structure
and how, for a detailed description of such aspects, further, collective models, are
required. After a comprehensive overview of theoretical models attempting to de-
scribe clustering phenomena in nuclei, such as the α-particle model, shell-like model
approaches, and microscopic models, and their predictions within physical cases
of recent interest, we make a systematic discussion of the experimental techniques
which are usually applied to point out such phenomena.
In Chapter 2 we describe the results of our experimental campaign, carried out
in different laboratories and facilities, aimed to improve the present knowledge of
clusters in light nuclei and their evolution with the neutron excess. These studies
have been performed by using nuclear reactions involving light nuclear systems. We
started from the 10Be nucleus. It is associated to a two α-like structure coupled
to two valence neutrons: it presents nice properties of symmetry. The structure
iii
Abstract
of this nucleus is explored by means of direct reactions which involve the popu-
10
lation of highly-excited states in Be and their subsequent in-flight decay. The
experiment was performed by using a fragmentation cocktail beam at the FRIBs
facility of INFN-LNS (Catania) and the CHIMERA 4π multi-detector. Invariant
10
mass techniques are used to reconstruct the spectroscopy of Be, giving the hint for
the existence of a new state, possibly associated to a new member of the molecular
rotational band.
While the effects of clusterization are well visible and quite well understood in
beryllium isotopes, they are much less known in carbon isotopes. For this reason,
different neutron-poor and neutron-rich carbon isotopes are here investigated, pro-
11,12,13,16 11
viding interesting information on the carbon isotopic chain C. C, as well as
13
C, are studied by means of low energy compound nucleus reactions; respectively,
10 9
we measured the B(p,α) reaction (Ep = 0.6-1.0 MeV) and the Be(α,α) resonant
elastic scattering (Eα = 3.3-10 MeV) at the Tandem accelerator in Naples. We an-
alyzed the differential cross section with a comprehensive R-matrix approach, also
by including other data published in the literature. We succeeded in refining their
spectroscopy above the α-disintegration thresholds, with interesting speculation on
16
the existence of molecular rotational bands. The structure of the neutron-rich C
10
isotope is studied with the same experimental apparatus of the Be case by using
16
the most intense C beam produced up to date for nuclear physics experiments at
intermediate energies. We provide signatures of the possible existence of high-lying
excited states of this poorly known nucleus never observed before. To conclude our
12 +
studies of clustering in carbon isotopes, the Hoyle state in C (7.654 MeV, 0 )
was investigated via a high-precision dedicated experiment. The cluster properties
of this state are quite crucial; as an example, it has been predicted that its three
constituent α-particles may form a Bose-Einstein condensate. We proved, with an
unprecedented precision, the fully sequential decay width of this state by using the
14
N(d,α) reaction at 10.5 MeV at the Tandem accelerator of INFN-LNS. To achieve a
such high precision we developed a new hodoscope detector. Our result is important
since it provides stringent constraints on microscopic theoretical calculations which
describe clustering in nuclei, as well as to nuclear astrophysics for the production of
carbon and heavier elements in the universe.
19 20
Clustering phenomena in F and Ne have been studied by means of the
19
F(p,α) reaction at deeply sub-Coulomb energies (Ecm = 0.18-0.60 MeV) at the
AN-2000 Van der Graff accelerator of INFN-LNL. An analysis of angular distribu-
19
tions at various energies gives signatures of possible cluster structures in F. The
20
compound nucleus Ne spectroscopy is instead studied by means of a R-matrix
approach; the astrophysical relevance of our work is also discussed.
Chapter 3 is finally dedicated to a different, complementary, point of view in
the study of clustering phenomena: the analysis of Heavy Ion Collisions (HICs) at
intermediate energies. Cluster states, produced by overlapping zones formed in HICs
and characterized by high temperatures and low densities, can be used as a suitable
probe for nuclear structure and dynamics. We implemented a thermal model aimed
iv
Abstract
to reproduce in-flight resonance decay phenomena in HICs. This model has been
36 58
applied to the case of α-α correlations in Ar+ Ni central collisions data at various
bombarding energies (32-95 AMeV); they have been measured with the INDRA
4π multi-detector at the GANIL. The comparisons of data with thermal model
predictions allows us to make interesting speculations on the processes contributing
8
to the formation of Be states in such highly excited and diluted environments.
v
Contents
Abstract iii
Contents vi
List of Figures viii
List of Tables xii
1 Introduction: Clusters in Nuclear Physics 1
1.1 Clusters in nature and social sciences . . . . . . . . . . . . . . . . . . 1
1.2 Nuclear models and structure . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 A first approach to nuclear structure: the liquid drop model . 6
1.2.2 Towards a mean field approach: the Hartree-Fock method in
nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.3 The simplest independent particle model: the Fermi-gas model 10
1.2.4 The nuclear shell model . . . . . . . . . . . . . . . . . . . . . 12
1.3 Cluster models of nuclei . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.1 The α-particle model . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.2 Microscopic cluster models (RGM, GCM, OCM) . . . . . . . . 24
1.3.3 The quartet model . . . . . . . . . . . . . . . . . . . . . . . . 26
1.3.4 Molecular Dynamics (MD) models: clustering in unstable nuclei 28
1.3.5 The deformed harmonic oscillator (HO) . . . . . . . . . . . . . 29
1.4 Applications of cluster models . . . . . . . . . . . . . . . . . . . . . . 32
1.4.1 Light self-conjugated nuclei: 12C, 16O, 20Ne . . . . . . . . . . . 32
1.4.2 Astrophysical relevance of clustering . . . . . . . . . . . . . . 42
1.4.3 Non-self-conjugated nuclei: nuclear molecules . . . . . . . . . 45
1.5 Techniques for the study of clusters in nuclei . . . . . . . . . . . . . . 53
1.5.1 Compound nucleus reactions . . . . . . . . . . . . . . . . . . . 54
1.5.2 R-matrix theory . . . . . . . . . . . . . . . . . . . . . . . . . . 60
1.5.3 Direct reactions and correlations . . . . . . . . . . . . . . . . . 62
1.5.4 The interplay between structure and dynamics: heavy-ion col-
lisions (HICs) and clusters . . . . . . . . . . . . . . . . . . . . 69
1.6 Summary and organization of the manuscript . . . . . . . . . . . . . 76
vi
Contents
2 Clustering in light systems: an experimental campaign 79
10
2.1 Be cluster states with breakup reactions . . . . . . . . . . . . . . . 79
2.1.1 Experimental apparatus and techniques . . . . . . . . . . . . . 80
6 4
2.1.2 Experimental results: He- He correlations . . . . . . . . . . . 82
2.1.3 Impact of our results on successive works . . . . . . . . . . . . 88
11 10 7
2.2 The structure of C with the B(p,α) Be reaction . . . . . . . . . . 88
2.2.1 Experimental apparatus and techniques . . . . . . . . . . . . . 90
2.2.2 Angular distributions, integrated cross-sections and S-factor
10
of the B(p,α0) reaction . . . . . . . . . . . . . . . . . . . . . 94
11
2.2.3 R-matrix fit of data and the spectroscopy of C . . . . . . . . 97
2.2.4 Impact of our results on successive works . . . . . . . . . . . . 101
12
2.3 Clustering in C: the decay path of the Hoyle state . . . . . . . . . . 103
14 12
2.3.1 Experimental technique: the N(d, α) C reaction . . . . . . . 104
2.3.2 Analysis of the direct α-decay width of the Hoyle state . . . . 106
2.3.3 Impact of our results on successive works . . . . . . . . . . . . 109
13 9
2.4 Clustering in C with α + Be reactions . . . . . . . . . . . . . . . . 110
2.4.1 Selection of reaction data-set . . . . . . . . . . . . . . . . . . . 110
2.4.2 Results of R-matrix fit of data . . . . . . . . . . . . . . . . . . 112
2.4.3 Impact of our data on molecular bands . . . . . . . . . . . . . 122
16
2.5 Clustering in C: towards the dripline . . . . . . . . . . . . . . . . . 124
2.5.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 124
2.5.2 Consequences of our investigation on successive works . . . . . 126
20 19 19 16
2.6 Cluster structures in Ne and F and their role in the F(p,α) O
reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
2.6.1 Experimental details . . . . . . . . . . . . . . . . . . . . . . . 129
2.6.2 Angular distribution analysis and R-matrix fit of data . . . . . 133
2.6.3 Impact of our results on successive works . . . . . . . . . . . . 137
3 Clustering in HICs as a link between structure and dynamics 139
3.1 Further details on correlations in HICs . . . . . . . . . . . . . . . . . 139
3.1.1 The thermal model for correlations in central HICs at low and
intermediate energies . . . . . . . . . . . . . . . . . . . . . . . 141
3.1.2 The In-Flight Decay Simulation Code . . . . . . . . . . . . . . 143
3.1.3 HBT interferometry in Nuclear Physics . . . . . . . . . . . . . 144
3.1.4 Characterization of the emitting source . . . . . . . . . . . . . 147
36 58
3.2 Application of the thermal model to α-α correlations in Ar + Ni
with the INDRA 4π multi-detector . . . . . . . . . . . . . . . . . . . 148
3.2.1 The INDRA experimental filter . . . . . . . . . . . . . . . . . 148
36 58
3.2.2 Analysis of α-α correlations in Ar + Ni systematics from
32 AMeV to 95 AMeV . . . . . . . . . . . . . . . . . . . . . . 155
3.2.3 Discussion on the reaction dynamics . . . . . . . . . . . . . . 162
Conclusions 169
vii
Bibliography 173
Ringraziamenti 189
A A new device for future clustering and correlation studies: OSCAR191
A.0.4 Detector’s layout . . . . . . . . . . . . . . . . . . . . . . . . . 191
A.0.5 Detector characterization . . . . . . . . . . . . . . . . . . . . . 194
A.0.6 Non-uniformity of the ∆E stage . . . . . . . . . . . . . . . . . 198
A.0.7 Channeling effects in ∆E detector . . . . . . . . . . . . . . . . 201
A.0.8 Correlations: the case of α-α correlation and the reconstruc-
tion of 8Be . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
B Résumé en langue française 207
List of Figures
1.1 Clustering in biological systems: fish schooling . . . . . . . . . . . . . . . 2
1.2 Clustering behaviour in social sustems: the bonobo . . . . . . . . . . . . 3
1.3 Binding energy per nucleon for self-conjugated nuclei . . . . . . . . . . . 7
1.4 Deviations between experimental nuclear masses and liquid drop model
masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Average energy of the first excited state for doubly-even nuclei as a func-
tion of the neutron number . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 16O excited states via multi-particles multi-holes shell model excitations . 16
1.7 Spatial correlations as a function of the relative distance between nucle-
ons in the case of non-congruent nucleons and congruent nucleons . . . . 17
1.8 Historical developments of cluster models of nuclei from 1930’s. . . . . . 19
1.9 Binding energy for the lightest self-conjugated nuclei as a function of the
number of bonds between between α-cluster centers . . . . . . . . . . . . 20
1.10 Geometrical arrangements of α-clusters in the α-particle model . . . . . 21
1.11 Terms contributing to the compute of the excitation energy of the (210)
quartet configuration of 16O . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.12 Energy levels of the deformed harmonic oscillator as a function of the
quadrupole deformation ϵ2 . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.13 Harmonic oscillator wave-functions and densities for 8Be . . . . . . . . . 32
1.14 The Ikeda diagram of self-conjugated nuclei . . . . . . . . . . . . . . . . 34
1.15 Decomposition of the THSR wave function describing the 12C g.s. . . . . 36
viii
List of Figures
12
1.16 Density distribution ρ(x, y) of the Hoyle state in from microscopic
calculations based on the Faddeev three-body formalism and Dalitz plot
of its decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
12
1.17 C energy spectrum from AMD calculations compared to to RGM and
GCM results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
12
1.18 C experimental bands compared with ACM calculations . . . . . . . . 39
16
1.19 Rotational bands of O calculated with the ACM from [98] . . . . . . . 41
1.20 Rotational spectra of the heteropolar diatomic molecule compared with
16 20
theoretical α + core calculations for O and Ne from [100] . . . . . . . 42
1.21 Levels involved in the 3α process . . . . . . . . . . . . . . . . . . . . . . 43
1.22 3α reaction rate calculated with different methods from [111] . . . . . . . 44
1.23 Modified Ikeda diagram to account cluster structures in the presence of
extra neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
10
1.24 Excitation energy spectrum of Be as a result of the variational calcu-
lations after spin-parity projection (VAP) in the AMD framework from
[120] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
1.25 Schematic representation of molecular orbit π and σ in the case of two
α-centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
11 11
1.26 Comparison between the mirror nuclei C and B low-lying states . . . 50
± 9 −
1.27 Parity-split rotational bands (K = 1/2 ) based on the Be(3/2 , g.s.)
+ α structure from [127] . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
13
1.28 Calculated C rotational bands in the GCM framework from [129] . . . 52
13
1.29 Spectroscopic factors of the C Hoyle analog state within the OCM
framework from [131] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
16
1.30 Density distrubutions of C valence neutrons and protons as computed
by AMD calculations from [132] . . . . . . . . . . . . . . . . . . . . . . . 54
16
1.31 Calculated positive parity energy levels of C, via the AMD, as a function
of their angular momentum J, from [132] . . . . . . . . . . . . . . . . . . 55
1.32 Energy scheme of a compound nucleus reaction . . . . . . . . . . . . . . 57
16 6 20
1.33 Angular distribution of O( Li,d) Ne α-transfer reaction from [150] . . 64
1.34 Kinematics of a breakup reaction . . . . . . . . . . . . . . . . . . . . . . 66
1.35 Angular correlation analysis of breakup fragments, from [153] . . . . . . 68
1.36 A schematic view of a symmetric Dalitz plot . . . . . . . . . . . . . . . . 69
1.37 Symmetry energy with and without cluster-production, from [157] . . . . 70
1.38 AMD calculations with and without clusters of HICs charge distributions,
from [160] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6
1.39 An example of d-α correlation function for the structure of Li, from [162] 72
8
1.40 Determination of the spin for the Erel = 0.774 MeV resonance in B from
7
p- Be correlations. From [164] . . . . . . . . . . . . . . . . . . . . . . . . 74
1.41 Caloric curve with isotopic thermometer and excited state thermometer
from [166] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
1.42 Excited state temperatures and isotopic temperatures as a function of
the incident energies in central HICs from [171] . . . . . . . . . . . . . . 76
ix