One of the most significant advances in the historical development of our understanding of the microscopic structure of the atomic nucleus was made more than 50 years ago, when it was shown that nucleons (protons and neutrons) occupy orbitals in much the same way as electrons do around the nucleus. In this case, it is the other nucleons themselves which effectively generate a potential within which each nucleon moves. Over the years, experimental results have shown that the so-called 'nuclear shell model' is valid for a great number of nuclei, in particular those near closed shells, which correspond to gaps in the nuclear energy levels. However, recent experimental results have shown that, for neutron-rich nuclei, particularly those near neutron numbers 8, 20 and 28, the shell gaps become small (shell quenching) and the magic numbers, nucleon numbers corresponding to closed shells, are no longer valid. In addition, new magic numbers appear. The test of the limits of the shell model is one of the objectives of the present work. Questions nuclear physicists try to answer include: 'What is the origin of the elements?' and 'Why are the atomic elements that make up our world distributed in the quantities we observe?' The answers to these questions will help us to understand the processes involved in the creation of nuclei in the cosmic furnace. The nuclear shell model plays an important role in answering these question. According to some theories, the shell model has to be modified for nuclei with an excess of neutrons (neutron-rich nuclei) around the isotopes of tin with 50 protons and 82 neutrons. For example, for one of those isotopes, cadmium- 130, which has 48 protons and 82 neutrons, shell quenching had been predicted. Surprisingly, recent experimental studies have shown that the shell model is indeed still valid for this isotope of cadmium. Can this behaviour be an exceptional case for the cadmium Isotopes or is it a general behaviour for nuclei in the region? One way to answer this question is by establishing the excited states of neutron-rich neighbouring isotopes such as palladium (with 46 protons). The present proposal is concerned with the first experimental study of the excited states of the neutron-rich palladium isotopes near neutron number 82 to test the robustness of the shell closure. An additional phenomenon which we will study in the neutron-rich region below atomic number Z = 50 is 'magnetic rotation', a new mode of nuclear excitation which corresponds to the fastest magnetic rotor observed in nature. The present study will lead to an improved understanding of the underlying microscopic structure. The nuclei of interest will be populated using multinucleon transfer reactions which result from the interaction of a beam of energetic 96Zr ions with a thick target of 124Sn. The combination of the XTU tandem Van de Graaff and the ALPI linear accelerator at the Legnaro National Laboratory in Italy will be used to accelerate the 96Zr ions to an energy of 576MeV. The gamma-ray decay of the binary reaction fragments will be studied using the GASP array of 40 Compton-suppressed germanium detectors. Finally, the results of the experiment will allow a comprehensive analysis of a previous related experiment which used the CLARA/PRISMA detector systems at the Legnaro National Laboratory. The present experiment will allow essential gamma-ray coincidence relationships to be established for neutron-rich nuclei studied in the earlier experiment with mass numbers around 110. In this mass region we will continue to study the evolution of nuclear shape between the N = 50 and N = 82 magic neutron numbers.