The present thesis deals with the study of nuclear reactions of weakly-bound few-body nuclei with stable targets at energies around the Coulomb barrier. A weakly-bound nucleus is characterized by having low binding energy and thus large probability to undergo a breakup during the interaction with another nucleus. The effect of breakup on other reactions such as fusion is still not well understood and represents an interesting issue to study in detail. Among weakly-bound nuclei, there are some which are particularly interesting to study because of their peculiar structure and the key role they play in astrophysics: the halo nuclei.

Using quantum Monte Carlo Methods, we compute the differential cross sections for elastic scattering of dark matter (DM) particles off light nuclei, up to $A=6$ (d, $^3$H, $^3$He, $^4$He, and $^6$Li). DM-nucleon one- and two-body currents are obtained to next-to-leading order in chiral effective theory, and they are derived from a DM-quark and DM-gluon effective interaction. The nuclear ground states wave functions are obtained from a phenomenological nuclear Hamiltonian, composed of the Argonne $v_{18}$ two-body interaction and the three-body Urbana IX. In this framework, we study the impact of one- and two-body currents and discuss the size of nuclear uncertainties. This work evaluates for the first time two-body effects in $A=4,6$ systems and provides the nuclear structure input that can be used to assess the sensitivity of future experimental searches of (light) dark matter, especially relevant for possible experimental targets such as $^3$He and $^4$He.

The thesis here presented is the result of a PhD research, with the aim to build a program able to solve the non-relativistic eigenvalue problem for the so-called cluster and nuclei (in particular the Beryllium-9 nucleus), in order to study them through the use of Effective Field Theory (EFT) potentials. After a brief introduction, that will show why this type of nuclei are important in the study of stellar nucleosynthesis, I introduce the Hyperspherical Harmonics basis with which the calculations were carried out. The following chapter has the momentum space as the main subject, ending with some results from the program. EFT and cluster nuclei are then introduced in the next chapter, together with the interaction I used for the cluster systems. The second to last chapter shows the results of the code, able to calculate the ground state of Carbon-12 and Beryllium-9 nuclei, two important nuclei in the process of stellar nucleosynthesis. The last chapter contains a brief summary and the future outlook on this research.

A study of methods in few-body nuclear physics is presented, in particular for the study of the photodisintegration cross section of 3He at low energies, and for the determination of phase shifts in low-energy three-body scattering. A possible extension of the methods considered to the study of a five-body problem is investigated.

The present work is conducted in the field of few-body methods and it concerns the extension of the Non-Symmetrized Hyperspherical Harmonics method in order to treat quantum systems with different species of particles and additional degrees of freedom, like particle mixing. The aim is to introduce it as a new tool in the ab-initio study of light hypernuclei, and, more in general, of few-body quantum systems composed by a variety of different objects. To this end precise benchmark results for light hypernuclei with A=3-5 are provided and the perspectives of applications to systems with A>5 and the employment of the most recent hypernuclear interactions are discussed.

This thesis is about three major aspects of the identification of top quarks. First comes the understanding of their production mechanism, their decay channels and how to translate theoretical formulae into programs that can simulate such physical processes using Monte Carlo techniques. In particular, the author has been involved in the introduction of the POWHEG generator in the framework of the ATLAS experiment. POWHEG is now fully used as the benchmark program for the simulation of ttbar pairs production and decay, along with MC@NLO and AcerMC: this will be shown in chapter one. The second chapter illustrates the ATLAS detectors and its sub-units, such as calorimeters and muon chambers. It is very important to evaluate their efficiency in order to fully understand what happens during the passage of radiation through the detector and to use this knowledge in the calculation of final quantities such as the ttbar production cross section. The last part of this thesis concerns the evaluation of this quantity deploying the so-called "golden channel" of ttbar decays, yielding one energetic charged lepton, four particle jets and a relevant quantity of missing transverse energy due to the neutrino. The most important systematic errors arising from the various part of the calculation are studied in detail. Jet energy scale, trigger efficiency, Monte Carlo models, reconstruction algorithms and luminosity measurement are examples of what can contribute to the uncertainty about the cross-section.

In this thesis we describe in detail the Monte Carlo simulation (LVDG4) built to interpret the experimental data collected by LVD and to measure the muon-induced neutron yield in iron and liquid scintillator. A full Monte Carlo simulation, based on the Geant4 (v 9.3) toolkit, has been developed and validation tests have been performed. We used the LVDG4 to determine the active vetoing and the shielding power of LVD. The idea was to evaluate the feasibility to host a dark matter detector in the most internal part, called Core Facility (LVD-CF). The first conclusion is that LVD is a good moderator, but the iron supporting structure produce a great number of neutrons near the core. The second conclusions is that if LVD is used as an active veto for muons, the neutron flux in the LVD-CF is reduced by a factor 50, of the same order of magnitude of the neutron flux in the deepest laboratory of the world, Sudbury. Finally, the muon-induced neutron yield has been measured. In liquid scintillator we found $(3.2 \pm 0.2) \times 10^{-4}$ n/g/cm$^2$, in agreement with previous measurements performed at different depths and with the general trend predicted by theoretical calculations and Monte Carlo simulations. Moreover we present the first measurement, in our knowledge, of the neutron yield in iron: $(1.9 \pm 0.1) \times 10^{-3}$ n/g/cm$^2$. That measurement provides an important check for the MC of neutron production in heavy materials that are often used as shield in low background experiments.

Lo scopo del Progetto Extreme Energy Events (EEE) e` di studiare raggi cosmici di energia estrema, eventi molto rari ma ricchi di informazioni. La grande difficolta` nell'affrontare la fisica dei raggi cosmici di altissima energia risiede nel flusso estremamente basso con cui tali particelle giungono sulla terra. Si utilizzano infatti reti molto estese di rivelatori: le informazioni che si possono ricavare derivano dalla rivelazione delle particelle secondarie prodotte nello sviluppo di sciami estesi di raggi cosmici primari che interagiscono con l'atmosfera terrestre. Il Progetto EEE prevede di dislocare su tutto il territorio italiano un array di telescopi (costituiti da Multi Gap Resistive Plate Chambers) per raggi cosmici secondari. Il lavoro presentato riguarda la simulazione Monte Carlo degli sciami e lo studio delle loro caratteristiche, la simulazione delle prestazioni di griglie di rivelazione differenti ed infine l'analisi dei primi dati raccolti nei telescopi di Bologna, con il conseguente confronto con la simulazione.

The atmospheric muon charge ratio, defined as the number of positive over negative charged muons, is an interesting quantity for the study of high energy hadronic interactions in atmosphere and the nature of the primary cosmic rays. The measurement of the charge ratio in the TeV muon energy range allows to study the hadronic interactions in kinematic regions not yet explored at accelerators. The OPERA experiment is a hybrid electronic detector/emulsion apparatus, located in the underground Gran Sasso Laboratory, at an average depth of 3800 meters water equivalent (m.w.e.). OPERA is the first large magnetized detector that can measure the muon charge ratio at the LNGS depth, with a wide acceptance for cosmic ray muons coming from above. In this thesis, the muon charge ratio is measured using the spectrometers of the OPERA detector in the highest energy region. The charge ratio was computed separately for single and for multiple muon events, in order to select different primary cosmic ray samples in energy and composition. The measurement as a function of the surface muon energy is used to infer parameters characterizing the particle production in atmosphere, that will be used to constrain Monte Carlo predictions. Finally, the experimental results are interpreted in terms of cosmic ray and particle physics models.

This thesis is concerned with effects of spin polarization in neutron stars. In particular, we focus on static and dynamic properties of dense neutron matter. We use two different kind of potential to perform our studies: the phenomenological two-body Argonne V$8$' potential plus the three-body Urbana IX force and a modern local version of chiral effective potential up to next-to-next-to-leading order (N$2$LO). Estimates are calculated for the neutrino mean free path in partially spin-polarized neutron matter starting from Quantum Monte Carlo (QMC) simulations and using mean-field approaches to compute the response function in the longitudinal and transverse channel. We also compute magnetic susceptibility of dense neutron matter from accurate QMC calculations of partially spin-polarized systems. Twist-averaged boundary conditions (TABC) have been implemented to reduce finite-size effects. In the results, we also account for the theoretical uncertainty coming from the chiral expansion scheme. These results may play a role in studying high-energy phenomena such as neutron star mergers and supernova explosions, although they have been computed only at T$=0$ K.