Clusters in light nuclear systems: a multi-method approach

Clustering phenomena affect many aspects of nature and social sciences. They consist 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 \emph{consensus} in social and technological networks and \emph{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 investigation is extremely important in the understanding of nuclear forces and their related properties. As an example, cluster structures evolve from \emph{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 \emph{multi-method} approach and by using different and complementary techniques. In Chapter one, we show how the appearance of clustering phenomena 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 describe clustering phenomena in nuclei, such as the $\alpha$-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 $^{10}$Be nucleus. It is associated to a two $\alpha$-like structure coupled to two valence neutrons: it presents nice properties of symmetry. The structure of this nucleus is explored by means of direct reactions which involve the population of highly-excited states in $^{10}$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 $4\pi$ multi-detector. Invariant mass techniques are used to reconstruct the spectroscopy of $^{10}$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, providing interesting information on the carbon isotopic chain $^{11,12,13,16}$C. $^{11}$C, as well as $^{13}$C, are studied by means of low energy compound nucleus reactions; respectively, we measured the $^{10}$B(p,$\alpha)$ reaction ($\textrm{E}_p=0.6$-$1.0$ MeV) and the $^{9}$Be($\alpha$,$\alpha$) resonant elastic scattering (E$_\alpha=3.3$-$10$ MeV) at the Tandem accelerator in Naples. We analyzed 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 $\alpha$-disintegration thresholds, with interesting speculation on the existence of molecular rotational bands. The structure of the neutron-rich $^{16}$C isotope is studied with the same experimental apparatus of the $^{10}$Be case by using the most intense $^{16}$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 studies of clustering in carbon isotopes, the Hoyle state in $^{12}$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 $\alpha$-particles may form a \emph{Bose-Einstein} condensate. We proved, with an unprecedented precision, the fully sequential decay width of this state by using the $^{14}$N(d,$\alpha$) 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. Clustering phenomena in $^{19}$F and $^{20}$Ne have been studied by means of the $^{19}$F(p,$\alpha$) reaction at deeply sub-Coulomb energies ($\textrm{E}_{cm}=0.18$-$0.60$ MeV) at the AN-2000 Van der Graff accelerator of INFN-LNL. An analysis of angular distributions at various energies gives signatures of possible cluster structures in $^{19}$F. The compound nucleus $^{20}$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 to reproduce in-flight resonance decay phenomena in HICs. This model has been applied to the case of $\alpha$-$\alpha$ correlations in $^{36}\textrm{Ar}+ {^{58}\textrm{Ni}}$ central collisions data at various bombarding energies ($32$-$95$ AMeV); they have been measured with the INDRA $4\pi$ multi-detector at the GANIL. The comparisons of data with thermal model predictions allows us to make interesting speculations on the processes contributing to the formation of $^{8}$Be states in such highly excited and diluted environments.