A derivation of the elastic scattering differential cross section, within a three-body eikonal model, that treats both central and spin-orbit interactions between the constituent projectile clusters and the target is presented. This formalism is then used in the theoretical study of the scattering of 8B from 12C at 40 MeV/nucleon. The proton halo candidate, 8B, is taken to consist of a single valence proton orbiting a 7Be core cluster. Calculation of the elastic scattering amplitude relies upon determining the phase shifts caused as the projectile passes through the region of interaction with the target. A form for the orbital angular momentum operator of each projectile cluster about the target is obtained that allows a relatively simple form for the spin-orbit phase shift functions, analogous to those for the central interactions, to be deduced. The study of the angular distribution of the elastic scattering differential cross section is carried out in two parts. Initially the effect of elastic break-up and recombination of the projectile during the scattering process, only taking into account central interactions, is studied. To gauge the magnitude of these effects, within the three-body model, the elastic scattering differential cross section, in the limit of no projectile break-up, is derived. Despite the very small binding energy of 8B it is shown that these effects are quite small. It is also shown, however, that these effects become more conspicuous as the valence proton becomes less localised about the core. Finally the effect of including spin-orbit interactions is studied. In the system under study these effects are shown to have an almost negligible effect on the angular distribution of the differential cross section. However, increasing the projectile kinetic energy to the region of hundreds of MeV/nucleon is seen to increase their significance. Future calculations hope to look at the angular distribution of the elastic scattering differential cross section and vector and tensor analysing powers of polarised beams of deuterons as these systems are expected to show more sensitivity to spin- orbit interactions. Furthermore, with the possibility of polarised beams of halo nuclei, the three-body Glauber model would be an ideal theoretical tool with which to study certain of their spin-related phenomena too.

Nesta dissertação discutimos a medida RAA desenvolvida para análise de observáveis de colisão núcleo-núcleo (AA), tendo em vista sua implementação em colisões próton-próton (pp). No contexto das colisões hadrônicas de altíssimas energias, o RAA compara quantidade de observáveis duros medidos em colisões AA com a quantidade do mesmo observável em colisões pp. As qualidades destas colisões são descritas pela teoria do modelo de Glauber, em que projeção analítica da produção esperada de quarks pesados (observável duro) é realizada para colisões nucleares por meio da sobreposição de colisões pp independentes. Esta projeção analítica é comparada no RAA à medida de quarks pesados em estado final de colisões AA, e desvios em relação à distribuição de momentos da seção de choque calculada teoricamente são interpretados como decorrentes da presença de plasma de quarks e glúons (PQG) na colisão medida. O plasma de quarks e glúons é o objeto de interesse do campo de estudos em que esta pesquisa se insere. Considerado presente em colisões AA centrais desde 2000, o plasma de quarks e glúons é o estado da matéria mais energético possível, em que os pártons produto da colisão se comportam livremente por breves instantes e sofrem expansão hidrodinâmica. Este processo acontece nos estágios inacessíveis da colisão. Algumas das medidas indiretas que indicam formação de plasma em colisões AA são detectadas em colisões de sistemas pequenos, pp e pA desde 2010. Ainda não foi medida supressão de provas duras no PQG. As tentativas de medir PQG em sistemas pequenos pelo método do RAA tem sido feitas por meio da comparação RpA, também definida pelo modelo de Glauber. Na presente pesquisa buscamos extrapolar o funcionamento do RAA para medidas em colisões pp. Como o núcleo em Glauber é formado por sobreposição de prótons, a resolução da descrição da colisão na teoria é discutida. Além disso verificamos que a concepção de que colisões pp não formam ambiente de PQG é importante para o estabelecimento da comparação RAA. Entendemos que as hipóteses sobre a física de estágios inacessíveis da colisão previstas pela teoria de Glauber são diferentes das hipóteses decorrentes de medidas de coletividade em sistemas pequenos. Propomos alternativamente comparações experimentais simples entre quantidades parecidas medidas em colisões pp que podem conter informações sobre supressão de observáveis duros em colisões pp de alta multiplicidade sem o uso de quantidades teóricas. / This master thesis adresses the measurement RAA, developed for the analysis of nucleus-nucleus (AA) collisions, aiming to implement the measure for proton-proton (pp) collisions. In the context of high energy hadronic collisions, RAA compares hard observables measured in AA collisions with the same observable measured in pp collisions. These collisions traits are described by the Glauber model, where an analitical projection of the expected heavy quark production (hard observable) is calculated through the superimposition of independent pp collisions. In RAA, that analitical projection is compared to the actual final state AA collisions measurements, and deviations with relation to the momentum distribution of the theoriticaly calculated cross section are regarded as arising from interaction of the heavy quark with a quark gluon plasma (QGP) formed in the measured collision. The quark gluon plasma is the fields object of interest in which this reasearch is undertaken. Since 2000, QGP is measured and presumed in central AA colissions.The quark gluon plasma is the most energetic state of nuclear matter, in which partons behave as deconfined matter and undergo hydrodynamic expansion. That happends in the first inaccessible stages of the collisions. Some of the indirect measurements that point to the formation of QGP in AA collisions have been detected small systems, pp and pA, since 2010. Is yet to be measured hard probes PQG supression in these systems. Current attempts to evaluate this supression have been made with the RpA comparison, also defined with the Glauber model. In this study, we attempt to extrapolate the RAA operation to pp collision measurements. As the nucleus in Glauber is modeled as a superimposition of pp collisions, the theory\'s resolutuon in describing AA collisions is discussed. We also notice that the concept of pp collisions not formimg QGP is relevant for RAA comparisons. We appreciate that the theoretical hipothesis on the physics of the inaccessible first stages of collisions as foreseen with the Glauber model are different than the hipothesis that stem from collectivity in small systems. We propose alternatively simple experimental comparisons between similar quantities measured in pp collisions without the use of theoretical quantities.

With the use of an incoherent binary nucleon-nucleon collision model of heavy ion collisions for simulating particle production, it is demonstrated that the nuclear modification factors, R_{AA} and R_{CP}, are less than unity for hard scattering in the absence of any nuclear modification effects. The nuclear modification factor R_{dAu} is also shown to approach or exceed unity only if p_T broadening is taken into account. With a simple phenomenological parameter, the mean nucleon energy loss fraction, this model yields particle distributions that are comparable to those of experiment. The nuclear geometry is described by the Glauber model, and particle production is simulated by the PYTHIA event generator.